text:
Changes to PPP Loans Under the Paycheck Protection Program Flexibility Act
On June 3, 2020, Congress passed and on June 5, 2020, the President signed the Paycheck Protection Program Flexibility Act of 2020 (the "PPP Flexibility Act") to modify certain provisions of the CARES Act related to forgiveness of Paycheck Protection Program ("PPP") loans, to allow recipients of loan forgiveness to defer payroll taxes, and for other purposes. The PPP Flexibility Act attempts to address the difficulties experienced by many PPP loan recipient businesses in meeting the requirements for loan forgiveness while their business is still subject to COVID-19 restrictions.
The PPP Flexibility Act makes the following modifications to the PPP:
Extended Maturity of Loans: For loans made after the date of enactment of the PPP Flexibility Act that have a remaining balance after reduction based on loan forgiveness, creates a minimum maturity date of five years from when the borrower applies for loan forgiveness and permits lenders and borrowers of previously originated PPP loans to mutually agree to modify the maturity terms of the loan to conform with the five-year minimum.
The CARES Act set the maximum PPP loan term at 10 years, and the SBA in its rules set the term for two years. This change extends the two-year repayment term to five years for new loans, acknowledging the reality that many businesses potentially will be suffering the impacts of COVID-19 restrictions for several years to come. It will be important for borrowers that already have PPP loans to discuss modifying their repayment dates with their lenders if the borrowers expect a portion of their loan to not be forgiven.
June 30 Deadline to December 31, 2020 Change For Use of Proceeds: Expands the period for use of the PPP loan proceeds from expiring June 30, 2020 to expiring December 31, 2020.
For borrowers who have more recently received a PPP loan or may still obtain a PPP loan, the previous June 30 deadline for using the PPP loan proceeds was unworkable as it could fall before the end of the eight-week period. This extension provides all borrowers the flexibility to apply the loan proceeds for allowable uses through the end of the year; however, for forgiveness, funds will need to be used within the specified "covered period."
Time Period Extended For Forgiveness: Changes the "covered period" in which PPP loan proceeds must be used for certain purposes to be eligible for forgiveness from eight weeks from origination of the loan to the earlier of: (i) 24 weeks from origination or (ii) December 31, 2020 (although permits borrower of previously originated loan to elect eight-week covered period).
This change provides a larger spending window for borrowers to deploy the PPP funds as needed for their business operations, instead of forcing them to use funds when their business may not yet have reopened or is still operating at reduced capacity.
Added Employee Availability or Inability to Return to Same Level of Business to Forgiveness Considerations: Provides that loan forgiveness is determined without regard to the reduction in full-time equivalent employees if:
The borrower in good faith is able to document an inability to rehire individuals who were employees on February 15, 2020 and an inability to hire similarly qualified employees for unfilled positions on or before December 31, 2020;
The borrower in good faith is able to document an inability to return to the same level of business activity as the borrower's business was operating at before February 15, 2020, due to compliance with requirements or guidance issued by Health and Human Services, CDC, or OSHA during the period beginning March 1, 2020 and ending December 31, 2020 related to the maintenance of standards for sanitation, social distancing or any other worker or customer safety requirement related to COVID-19.
In the SBA's Interim Final Rule on Loan Forgiveness, a borrower's loan forgiveness would not be reduced due to reduction in FTE with respect to those employees that were offered in writing to be rehired on the same terms and rejected the offer and the borrower informed the applicable state unemployment insurance office of the rejected offer. This change adds to that concept. Perhaps more importantly, the change alternatively provides a broad exception from the proportionate reduction in loan forgiveness due to reductions in FTE if as of December 31, 2020 the borrower still has been unable to return to full business activity due to compliance with federal (but not state) regulatory guidance or restrictions. If the COVID-19 pandemic continues for many months, as some predict, this flexibility may eliminate the FTE-based loan forgiveness reduction test for many borrowers.
Modified Payroll Cost Forgiveness Limit to 60%: Requires for forgiveness that at least 60% of the loan proceeds (rather than at least 75% of the potential forgiveness amount) be used for payroll costs, and permits up to 40% to be used for the other uses that are subject to forgiveness (i.e., payment of interest of any covered mortgage obligation, any covered rent obligation, or any covered utility payment).
In its Interim Final Rules and the Loan Forgiveness Application, the SBA added a requirement that at least 75% of the loan forgiveness amount must be used for payroll costs within the covered period for forgiveness. With this change, Congress provided that at least 60% of the proceeds must be used for payroll cost for forgiveness purposes; meaning that borrowers must spend at least 60% on payroll or none of the loan will be forgiven. There is an expectation that this may be changed to restore the sliding scale. In any event, the change may provide slightly more flexibility for use of proceeds for the other critical overhead expenses of mortgage interest, rent, and utility payments under contracts in place as of February 15, 2020.
Replaced Six-Month Deferral with Deferral Until the Date the Loan Forgiveness Amount Is Remitted to Lender: Extends the deferral period for the initial payment on the PPP loan until the forgiveness amount has been remitted by the SBA to the lender.
Originally under the CARES Act, no payment was required under a PPP loan until six months after the loan was funded. With the extension of the covered period for forgiveness, it was necessary to extend the initial payment date. To understand the implications of this change, a borrower now has until 24 weeks after funding of the PPP loan or December 31, 2020 (whichever is earlier) to apply the loan proceeds toward certain permitted uses that would then serve as the basis for calculating the amount of loan forgiveness. At that point, the borrower would apply for loan forgiveness with its lender, who has 60 days to act on the application, and forward its recommendation on to the SBA. The SBA then has 90 days to act on that recommendation and to remit the forgiveness proceeds and interest to the lender, at which point the payments on the unforgiven balance of the PPP loan would begin.
Required Payments if No Forgiveness Application Within 10 Months: Provides that if a borrower does not apply for forgiveness, the earliest date for commencement of payments of principal, interest and fees is 10 months after the last day of the covered period.
If the timing schedule described above is not applicable because a borrower does not apply for forgiveness, at a minimum the loan would be deferred 10 months after the 24-week covered period.
Payroll Tax Deferral Benefit: Allows borrowers to benefit from the payroll tax deferral notwithstanding the forgiveness of PPP loan indebtedness.
The CARES Act provides employers the ability to defer certain payroll taxes that otherwise would be payable before January 1, 2021, to be paid 50% by December 31, 2021, and the remainder by December 31, 2022, but had excluded from this payroll tax deferral certain businesses that benefit from forgiveness of PPP loan indebtedness. This change removes that exclusion so that PPP loan borrowers who obtain PPP loan forgiveness can also benefit from the payroll tax deferral without limitation.
These changes are intended to address concerns expressed by borrowers since enactment of the CARES Act by providing borrowers more time to use loan proceeds, thereby enabling them to wait to rehire employees or restore employee hours until such time that their business is again operating and such employees are needed. Although Congress finally heard the borrowers' frustration, these changes may be coming too late for many loan recipients who already rehired employees to meet the previous requirement to spend 75% of forgiveness proceeds on payroll costs within eight weeks notwithstanding that their businesses were still closed or operating at significant reduced capacity. For more recent PPP loan recipients, these changes under the PPP Flexibility Act should provide businesses the ability to more strategically plan use of the PPP loan proceeds to sustain their business through this COVID-19 pandemic which is stretching out longer than initially expected.
Schwabe's attorneys have been closely following the updates to the PPP loan rules so that we can assist our clients in navigating the changes. For more information on how we may be able to assist you, please contact us today.
Carmen CalzacortaShareholder
Manufacturing, Distribution and Retail
ccalzacorta@schwabe.com
Mark LongRetired Shareholder
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Retired Shareholder
Charmin Shiely


She walked alone and somehow wasn't alone. She didn't feel scared, she didn't feel left out for the memories of "Their days" held her hand and helped her move forward. She walked until she was tired and when she stopped to rest, the memories gave her courage to walk again.
He on the other hand, didn't walk ahead. He decided to take a halt. He stayed where she had left hoping that some day the Memories of "Their days" would bring her back. He was sure that some day she would find a way back home. Only he didn't know it himself.
And Memories... They just did what they had to do!
I am Meenal Shirodkar. A Chef by education, An English Language Trainer by Profession and A writer by heart.
I usually am not a very disciplined writer and would admit that a constant seeker of approval. I indulge in writing random stories and poems... although there isn't any set theme or genre to my work, a lot of it revolves around Feelings, Emotions and Relationships. I am in love with the idea of being in love, and that may reflect in my work.
I have been born and brought up in the most beautiful city of Mumbai and that contributes to many free thinking thoughts that float in and out of my work. Some of the Orthodox minds might cringe their noses at my work, but as long as my characters are convinced of and believe in their actions I am a happy writer! I know it may sound arrogant, but unless I stand by my creation, I cannot expect any one to take it seriously. So i believe in every emotion that flows through the words you are about to read.
Although this is the first time I am opening my Pandora Box to you all, I have been secretly writing for more than a decade. What started as an extra curricular activity, is now a stress reliever and soon to be a choice of career for me. So now I seek the approval of all the readers around the world to encourage me on this Path that I wish to take!


text:
Title: Ideological manipulation in the translation of political discourse : a study of presidential speeches after the Arab Spring based on corpora and critical discourse analysis
Author: Farhan, Athil Khaleel
Awarding Body: University of Surrey
Current Institution: University of Surrey
https://surrey.eprints-hosting.org/841207/
The present study explains that ideology can affect translators' linguistic selections which can consequently shape the receivers' worldviews. Owing to the fact that after the Arab Spring, new leaders with different ideologies and belonging to different political movements sprung forth, their political discourse has become a subject of increasing interest. The language these leaders use to promote their own political and ideological visions and the way to interpret them requires analysis to detect the possibility of translators' intervention in the translation of these speeches. Adopting a mixed approach of corpus linguistics and critical discourse analysis, the present study focuses on investigating the manipulation of the source text ideology in the translation of presidential speeches after the Arab Spring. The source texts analysed in this study are 20 speeches by the former Egyptian president Morsi translated into English by five translators of various ideological backgrounds. The analysis of these source texts is based on the extraction of keywords and a selection of keywords with ideological content. The analysis of the target texts, on the other hand, focuses on the use of ideological keywords in lexical patterns and grammatical structures to detect ideological manipulation in translation. The thesis aims to describe systematically the means through which translations transfer, strengthen, or mitigate the ideology underlying the source texts. Using five parallel corpora of the source texts and their translations, the thesis also aims to ascertain whether the lexical choices and the syntactic structures employed in the target texts engender changes in the ideological content of the source texts and their underlying ideology. The results reveal that two out of the five translations project a manipulated ideology that is at variance with the ideology underlining the original texts. One translation strengthens the ideology of the source texts, whereas the other two translations aim to maintain the original ideology unchanged. This indicates that instances of ideological manipulation are probable even in the translation of presidential speeches due to the nature of the source texts, the ideology underlying them as well as the possibility of an ideological clash.
Supervisor: Frankenberg-Garcia, Ana ; Asimakoulas, Dimitris Sponsor: Iraqi Government

redpajama_set_name: RedPajamaCommonCrawl


Can acupuncture help persistent viral infections?
Q: I catch too many viral illnesses/flu like illnesses, about 6 or 7 a year. I am fit and well in between and not chronically ill, I am a 60 year old lady and my only other problem is asthma which is well controlled with inhalers. Could acupuncture help?
A: You have probably heard people talk about a weakened immune system; in fact, it is a rather over-used term in modern times. However, it does sound as though this really is the case for you, especially if you are relatively fit and healthy the rest of the time.
From a Chinese medicine perspective the point of greatest interest is that you have asthma. Although it may be well-controlled it does show that there is probably some weakness in the Lung energy. We cannot be absolutely certain from the name alone; there is no direct correspondence between symptoms and disturbance in the function of an Organ (capitalised to denote the Chinese understanding of an Organ), and quite often a named condition can have its root elsewhere. However, in the majority of cases the Lung energy is involved, and this is of particular interest because the Lung is closely associated with what is called in Chinese the Wei Qi, the defensive energy of the body. If the Lung is weakened or weaker, then it is less able to circulate the defensive energy, and in theory the body is then less well protected from what the Chinese call external invasion.
Of course, being a 2500 year old tradition there is always room for plenty of disagreement about where Wei Qi develops or is generated, but most writers seem to agree that the Lung is primarily involved in its effective circulation. Boosting this energy may have an impact on improving your defences. We would be more cautious about making any claims about your asthma. The evidence is not as strong as for some named conditions which we treat, and we find that many doctors strongly advise patients against interfering with patterns of treatment which maintain good control over the condition.
How does one's defensive energy become weakened? Well, there are many ways in which one can interpret the balances of energies in the body, and in many diagnostic systems there is not necessarily a correspondence between where a symptom turns up and its originating cause. A skilled practitioner should be able to make sense of the overall pattern, but may well find out that there is a hereditary element to the problems. Our health is determined to a very large extent by the energy of our parents who create us and also by their health at the time of our conception. If this has been at all compromised on either front, then it may leave a legacy of under-performance which might make someone more vulnerable as time goes by to opportunistic viral infections. This is something which we believe can be helped by treatment.
All of this, of course, is speculation based on very little information! The best advice we can offer, given that we think there may be some benefit from treatment, is to visit a BAcC member local to you for an informal chat about whether acupuncture is likely to help. Most members are happy to give up a little time without charge, and face to face it will be far easier to offer an individualised opinion about the possible benefits.
Can acupuncture help Mal de Debarquement disorder?
Q: I have been diagnosed with Mal de Debarquement disorder with going on 2 1/2 months of balance issues. Have tried physical therapy, chiropractic, and now acupuncture. My acupuncturist has dealt with dizziness, but no one with this disorder. Any advice to share? We have worked on the sinus, ears, etc.
A: MdDS is quite a rare condition, although the overlap with a number of better documented problems such as Meniere's Disease or vertigo could mean that it is under-reported. As is always the case with relatively rare conditions there is hardly any research, even in conventional medical literature.
We searched for whatever we could find, and there are certainly a number of anecdotal accounts from people with this condition who have found acupuncture in combination with some fairly low level medications has done the trick. This sample is self-selecting, though; there is less chance that someone who hasn't found it useful will post the bad news.
For problems like this we have to say that the way that Chinese medicine works, interpreting the symptoms against a completely different theoretical framework and supplementing what is reported with findings from, for example, looking at the tongue, taking the pulse at the wrist and other clinical observations, can sometimes generate solutions where conventional medicine cannot. Chinese medicine is based on an understanding of energy, called 'qi', and its flow, rhythm and balance in the body. The flow is affected both functionally by weaknesses in the Organs of the body which sustain it, and also positionally because of local blockage and disturbance. It is probable that a practitioner may find evidence of changes or blockages in the flow, and by re-aligning these start to reduce the symptoms. This is certainly the case with other balance problems, where the evidence for the effectiveness of acupuncture treatment, while not conclusive, is certainly encouraging enough to suggest that treatment is worth a try.
The best advice we can give is that you visit a BAcC member local to you and seek a brief face to face assessment. We are confident that in person they will be able to offer a much better view of what may be possible. The only caution we have is that conditions can become more difficult to treat the longer they have been entrenched, and a fifteen year history suggests that improvements may take a while. However, life is full of surprises, and we have seen longstanding problems vanish almost overnight, so the best idea is probably to have no expectations either way.
we have not found anything else which would affect what we have said either way.
The only addition we would make to this answer is to mention that there are one or two other forms of treatment, notably cranial osteopathy, which might also offer some relief and improvement. Although the evidence for acupuncture and MdDS is a bit thin, there is a considerable amount of good quality research on vertigo and other balance problems like Menieres and labyrinthitis. From a Chinese medicine perspective, the disease labels of western medicine are less interesting to us than the functional disturbances which a patient reports. We have ways of interpreting these within the conceptual grid of Chinese medicine which makes direct equivalences hard to establish - some presentations with different western names are the same as far as we are concerned, and twenty people with the same named presentation may be treated twenty different ways.
Hopefully a practitioner will find something which makes sense of your problem and can give you a much clearer idea than we can here of the potential for treatment with acupuncture.
Could acupuncture be beneficial for peri menopause ?
which is refreshingly candid about the chances of treating menopausal symptoms, and refers to a number of papers which seem to provide encouraging results. One of the main reasons which bedevils the results of research is that the treatment is often compared to a 'sham' treatment, and both generate better results than the control group. As a consequence the treatment is said to be 'no better than sham' and all down to a placebo effect. We, however, would say that there is no such thing as 'sham' acupuncture; sticking needles anywhere will generate a result, and it's the difference between good and better treatment. As one of our medical colleagues said, if sham treatment is better than conventional treatment, who cares how it works, just use it!
In essence, though, we have to say that traditional Chinese medicine has been addressing the problems of the menopause for over 2000 years, and over that time has looked in enormous detail at the kind of energetic changes which occur at this time of life. Interpreting these against the backdrop of the patient's constitutional energy is where the skill of the practitioner lies. This is more than just deciding out of the five causes for a symptom which specific treatment will work best. Chinese medicine treats the person, not the condition, and simply picking off the symptom while leaving the overall balance untreated will in many cases mean that the symptom returns. This is why we are quite concerned about people learning formula treatment for named conditions; sometimes they work, sometimes they don't, and when they don't people wrongly conclude that acupuncture treatment does not work.
The best advice we can offer is that you visit a BAcC member local to you for a brief face to face assessment of what may be possible. Most members do not charge for a short interview, and face to face they can give you a much better idea than we can at a distance of what may be possible. A postcode search facility on our home page will identify the practitioners nearest to where you live and work.
Can facial acupuncture slow down ageing process?
Q: I understand you can have acupuncture on the face, to slow down/ help with the ageing process!! Is this correct please?
A: There has been something of a boom in recent years in the use of acupuncture treatment to reduce the appearance of ageing. There is little or no research to validate claims for success, but this is really no surprise. It is difficult to imagine how one could design a meaningful trial with objective outcome measures. However, when something is popular and enduring, which this appears to be, then there is usually something in it. You can fool some of the people some of the time.......!
There are literally thousands of practitioners operating in this field, not all of them professional acupuncturists with a full degree level training. We have said for many years that local interventions like this will only have enduring effect if they are underpinned by constitutional treatment. The face does reflect very well the overall balance of the person, and it would be unrealistic to expect to improve one part of the system when the rest of it is showing signs of overall imbalance and disruption. The best that one might hope for is a short term fix requiring further treatment a few weeks down the line. While this falls within the normal pattern of beauty treatment, we rather hope that our members that use facial/cosmetic acupuncture are aiming for something a little better.
reasonably reputable courses around, and these are a minimum requirement, in our view. Some of the needle techniques are not within mainstream treatment, and the face is not a place for amateurish treatment. Second, is the person properly insured and registered for what they do? Many beauty practitioners take short courses without any information about safety, waste disposal, registration for skin piercing and proper insurance. This could have serious implications if something goes wrong.
Because we have yet to agree standards for this specific practice we have no way of telling which BAcC members offer this type of treatment. However, if you use our home page postcode search facility and retrieve a list of names, it should be fairly easy to search on google to see who offers this. Those who do tend to use it in their PR. If not, most practitioners know which of their colleagues to refer people to for speciality treatment, and it should take you very little time to find someone who can offer facial treatment alongside traditional treatment aimed at restoring balance overall.
Can acupuncture assist with persistent hiccups?
IAs this expert knows only too well from personal experience, persistent hiccups/hiccoughs can be a very distressing experience, not the increasingly funny experience which many observers seem to find it.
Most practitioners during their training learn a number of what we call 'first aid points' which are known to have an effect on specific conditions. There are certainly two or three which are commonly used to stop hiccups, and one additional one which appears to be effective for treating children with persistent hiccups. Overall, though, there isn't a great weight of evidence, and we would be a little remiss to suggest that acupuncture definitely provided a solution.
However, that said, we are practising a system of medicine where hiccups, a symptom like any other, is not always seen as the problem itself but is usually a manifestation of other imbalances and blockages in the system. As you may have read, Chinese medicine is premised on the understanding of the body as a system of energy in flow, and the skill of the practitioner lies in making sense of symptoms within the general background context against which they appear. This is why the same symptom can often be treated in a dozen different ways in a dozen different patients depending on what internal causes are allowing it to develop.
The short answer to your question is that you may have to visit a BAcC member local to you for them to be able to see what is going on and try to make sense in Chinese medicine terms of what is happening. This is the only way that you will get a clear idea of how treatable the problem is. What we can say, though, is that with conditions like this we tend to take the view that if they are going to respond they will do so quite quickly, and as such we would caution a prospective patient about getting engaged in a long run of treatment with no obvious improvement. We would suggest three or perhaps four treatments would be the maximum we ourselves would offer before reviewing the case in depth and deciding whether there is any point in carrying on.
This all sounds rather negative, especially when many of us have stuck a needle in with almost immediate effect like a party trick. However, everything works for someone, but something doesn't necessarily work for everyone, so we would advise caution.


text:
\section{Introduction}

The Cosmological Constant (CC) problem has been a major challenge in field theory and cosmology for several decades. On the one hand, the CC is interpreted as the vacuum energy density and the prediction of the standard quantum field theory calculation gives the theoretical result up to the Planck scale bigger than the observational value about 120 order of magnitudes \cite{Weinberg:1988cp}. This contradiction poses a serious problem and remains as the unsolved problem in high energy physics. On the other hand, the CC can be used to describe the accelerating expansion of the universe at the present time or the dark energy problem \cite{Peebles:2002gy,Padmanabhan:2002ji,Carroll:2000fy}. Nowadays, the interpretation of the CC as dark energy becomes the standard model of cosmology known as the Lambda Cold Dark Matter (LCDM) and the LCDM model can describe most of the cosmological data. However, according to the CC problem, we need the correct theory or better solution for explaining the fundamental mechanism of the CC problem. This leads to a number of the theoretical models proposed to solve the smallness of observed values of the CC. In particular, an approach from the Beyond Standard Model (BSM) of particle physics is received a lot of attention, for instances, supersymmetric model, large extra dimension approach of CC, string landscape and etc. See Refs.\cite{Burgess:2004kd,Banks:2014pqa,Mavromatos:2015jzo,Burgess:2007ui,Lue:2005ya,Bull:2015stt,Polchinski:2006gy,Denef:2007pq,Douglas:2019kus} for reviews on this subject.
One of interesting approach for describing the smallness of the CC value is the gravitational phase transition. The phase transition arises from the bubble nucleation of the true vacuum in the false vacuum spacetime when the bubble pops up and expands until filling up the whole spacetime. This means that the CC of the false vacuum is changed to the new value of the CC according to new vacuum energy of the true vacuum. The mechanism of this gravitational phase transition is originally proposed by Refs.\cite{Coleman:1977py,Coleman:1980aw}. The phase transition for Einstein gravity coupled to the 3-form fields is studied and the results revealed that the CC can be dynamically changed into several values from the infinite decay of the false vacuum and this leads to an alternative approach to describe the CC problem \cite{Brown:1987dd,Brown:1988kg}. More interestingly, Ref.\cite{Gomberoff:2003zh} has used the same gravitational setting but hosting the black hole inside the bubble. Then a thermalon, the instanton solution of the thermal trigger for the bubble nucleation, plays the role as a mediator of the phase transition. Under this consideration, the bubble with the three-form charge induces the decay of the dS false vacuum into another smaller dS true vacuum. In order to thermally trigger the phase transition, one needs the source of the exotic matter fields with negative pressure. Alternatively, Refs.\cite{Camanho:2012da,Camanho:2013uda} have proposed new mechanism analogous to the thermalon mediated the phase transition by introducing the higher order gravity into the system. There are two solution branches of the higher order gravity corresponding to negatively and positively effective cosmological constants (AdS and dS spacetime, respectively).
Initially, the false vacuum is displayed by the AdS spacetime. The true vaccum is represented by the dS geometry emerged from the creation of bubble with black hole inside. The bubble then expands very rapidly until it reaches the cosmological horizon. This changes the values of the effective CC from negative to positive values due to the thermalon mediated AdS to dS phase transition without inclusion of any matter fields coupled to the gravity. This is the salient feature of this type of gravitational phase transition.

On the other hand, the existence of the graviton mass provides an interesting results in either quantum theory of gravity and cosmology (see \cite{Hinterbichler:2011tt,deRham:2014zqa} for reviews). A consideration of the graviton mass has been received attentions for several decades \cite{deRham:2016nuf}. In particular, a so-called dRGT massive gravity \cite{deRham:2010kj} becomes a well defined theory of massive gravity. Several problems of the graviton mass is solved by using the dRGT massive gravity approach, for instances, redundancy of the spin d.o.f. \cite{Fierz:1939ix}, vDVZ discontinuous \cite{vanDam:1970vg,Zakharov:1970cc}, Vainshtein screening \cite{Vainshtein:1972sx} and the unstable ghost modes of the massive gravity \cite{Boulware:1972yco}. In addition, massive gravity and its extentions can be used to describe dark energy \cite{DAmico:2011eto,Akrami:2012vf,Akrami:2015qga}. Moreover, the dRGT massive gravity is also extensively studied in various aspects, for examples, black hole solution and its thermodynamics properties \cite{Ghosh:2015cva}, quasinormal modes \cite{Burikham:2017gdm}, dark matter \cite{Panpanich:2018cxo}, gravitational lensing \cite{Panpanich:2019mll} and wormholes \cite{Tangphati:2020mir}.

In this work, we will utilize the thermalon formalism with the higher order gravity to study the AdS to dS phase transition by including the effect of the massive gravity in five dimensional spacetime. The main motivation of this work is that the Gauss-Bonnet term is non-trivial in the spacetime dimension higher than four \cite{Lovelock:1971yv} and it has been widely used in brane cosmology \cite{Charmousis:2002rc, Sheykhi:2007gi, Deruelle:2000ge, Cai:2005ie, Lidsey:2003sj, Lidsey:2002zw}. Interestingly, one can consider the effects of the graviton mass since the massive graviton is well defined in the large extra dimension of the brane cosmology paradigm \cite{Gabadadze:2003jq,Cho:2001su}. Therefore, it is worth exploring the gravitational phase transition with the massive gravity in five dimensional spacetime. Charged black holes in Gauss-Bonnet-massive gravity and their thermodynamic properties is explored in \cite{Hendi:2015pda}. Phase transition of charged black hole in Gauss-Bonnet-massive gravity coupled with Yang-Mills field is investigated in \cite{Meng:2016its}. Moreover, the Gauss-Bonnet gravity in five dimension is employed to study the thermalon mediated AdS to dS phase transition in various aspects, e.g., study the critical point of the phase transition in the vacuum solution \cite{Camanho:2015zqa}, phase transition in black hole chemistry picture \cite{Hennigar:2015mco} and inclusions of Maxwell \cite{Samart:2020qya} and Kalb-Ramond \cite{Samart:2020mnn} fields.

We will organize the paper as follows. The gravitational action of the higher order gravity with the massive gravity is set up and the corresponding branch solutions are given in section \ref{sec2}. The junction condition between two regions of AdS and dS vacua is derived and the dynamics of bubble nucleation is analyzed in section \ref{sec3}. In section \ref{sec4}, the gravitational phase transition in the thermodynamics phase space is studied in details. Finally, we close the paper with the conclusion in the section \ref{sec5}.

\section{The Einstein-Gauss-Bonnet with the presence of the Massive gravity}\label{sec2}
In this section, we will set up the system of the AdS to dS gravitational phase transition via the thermalon mediation. The five dimensional action of Einstein-Gauss-Bonnet-massive gravity (EGBMG) with a presence of the bare CC ($\Lambda$) is given by
\begin{align}
    S &= \int d^5x \sqrt{-g}\left[R-2\Lambda+\alpha \mathcal{L}_{GB} + m^2 \mathcal{U}(g,\phi^a)\right], \label{action}
\end{align}
where $R$ is Ricci scalar, $\alpha$ is the Gauss-Bonnet coupling constant carrying the mass dimension $-2$ and $m$ can be interpreted as graviton mass. We have set $16\pi G_5 = 1$ with $G_5$ is Newton constant in five dimensions through out this work. The Gauss-Bonnet term takes a form
\begin{align}
    \mathcal{L}_{GB} &= R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma} - 4 R_{\mu\nu}R^{\mu\nu} + R^2.
\end{align}
The graviton potential $\mathcal{U}$ is a function of metric tensor $(g)$ and St\"{u}ckelberg field $(\phi^a)$. It is defined by
\begin{align}
    \mathcal{U} &= \sum_{i=1}^{4}c_i \mathcal{U}_i,
\end{align}
where $c_i$ are constants and
\begin{align}
    \mathcal{U}_1 &= \left[ \mathcal{K} \right], \nonumber \\
    \mathcal{U}_2 &= \left[ \mathcal{K} \right]^2 - \left[ \mathcal{K}^2 \right] , \nonumber \\
    \mathcal{U}_3 &= \left[ \mathcal{K} \right]^3 -3 \left[ \mathcal{K} \right]\left[ \mathcal{K}^2 \right] + 2 \left[ \mathcal{K}^3 \right], \nonumber \\
    \mathcal{U}_4 &= \left[ \mathcal{K} \right]^4 -6\left[ \mathcal{K}^2 \right]\left[ \mathcal{K} \right]^2 + 8\left[ \mathcal{K}^3 \right]\left[ \mathcal{K} \right] + 3\left[ \mathcal{K}^2 \right]^2 - 6 \left[ \mathcal{K}^4 \right].
\end{align}
The matrix $K^{\mu}_{\nu} = \delta^{\mu}_{\nu} - \sqrt{g^{\mu\sigma}f_{ab}\partial_{\sigma}\phi^a\partial_{\nu}\phi^b}$, $[\mathcal{K}]=\mathcal{K}^{\mu}_{\mu}$ and $[\mathcal{K}^n]=(\mathcal{K}^n)^{\mu}_{\mu}$, where $f_{ab}=diag(0,0,\frac{c^2}{1-k\rho^2},c^2\rho^2,c^2\rho^2\sin^2\theta)$ is called fiducial metric with constants $c$ and $k$.
Varying the action (\ref{action}) with respect to $g^{\mu\nu}$ yields Einstein field equations,
\begin{align}
    G_{\mu\nu} + \Lambda g_{\mu\nu} + \alpha T_{\mu\nu}^{GB} + m^2 T_{\mu\nu}^{MG} &= 0\,. \label{EFE}

\end{align}
The effective energy-momentum tensors, $T_{\mu\nu}^{GB}$ and $T_{\mu\nu}^{MG}$ are defined by
\begin{align}
        T_{\mu\nu}^{GB} &= 2\left[R_{\mu\nu}R-\nabla_\nu\nabla_\mu R\right] + 4 \left[\nabla^{\rho}\nabla^{\sigma} R_{\mu\rho\nu\sigma} + \nabla^{\sigma}\nabla^{\rho} R_{\mu\rho\nu\sigma} + R_{\mu\rho\sigma\delta}R_{\nu}^{\rho\sigma\delta}\right] \nonumber \\
    &~~~-\frac{1}{2}g_{\mu\nu}\left[R^2 + 2 R_{\rho\sigma\delta\lambda}R^{\rho\sigma\delta\lambda} -4\Box R \right], \nonumber \\
    T_{\mu\nu}^{MG} &= -\frac{c_1}{2}g_{\mu\nu}\left(\mathcal{U}_1-\mathcal{K}_{\mu\nu}\right)-\frac{c_2}{2}\left(g_{\mu\nu}\mathcal{U}_2 - 2\mathcal{U}_1\mathcal{K}_{\mu\nu}+2g_{\rho\nu}\mathcal{K}_{\sigma}^{\rho}\mathcal{K}_{\mu}^{\sigma}\right) \nonumber \\
    &-\frac{c_3}{2}\left(g_{\mu\nu}\mathcal{U}_3+3\mathcal{U}_2g_{\mu\nu} + 6g_{\rho\nu}\mathcal{U}_1 \mathcal{K}_{\sigma}^{\rho}\mathcal{K}_{\mu}^{\sigma} -6g_{\rho\nu}\mathcal{K}_{\sigma}^{\rho}\mathcal{K}_{\lambda}^{\sigma}\mathcal{K}_{\mu}^{\lambda}\right) \nonumber \\
    &-\frac{c_4}{2}\left(g_{\mu\nu}\mathcal{U}_4 - 4 \mathcal{U}_3\mathcal{K}_{\mu\nu} + 12g_{\rho\nu}\mathcal{U}_2\mathcal{K}_{\sigma}^{\rho}\mathcal{K}_{\mu}^{\sigma}  - 24g_{\rho\nu}\mathcal{U}_1 \mathcal{K}_{\sigma}^{\rho}\mathcal{K}_{\mu}^{\sigma}
    + 24 g_{\rho\nu}\mathcal{K}_{\sigma}^{\rho}\mathcal{K}_{\lambda}^{\sigma}\mathcal{K}_{\alpha}^{\lambda}\mathcal{K}_{\mu}^{\alpha}\right).
\end{align}
The static spherically symmetric with constant of spatial curvature $k$ is given by
\begin{align}
ds^2 &= -f(r)dt^2 + f^{-1}dr^2 + r^2 \left(\frac{d\rho^2}{1-k\rho^2} + \rho^2d\theta^2 + \rho^2\sin^2\theta d\phi^2\right).
\label{line-element}
\end{align}
The solutions of the metric tensor, $f(r)$ in Eq.(\ref{line-element}) is obtained by solving Einstein field equations (\ref{EFE}). It reads
\begin{align}
f_{\pm} &= k + \frac{r^2}{4\alpha}\left(1 \pm \sqrt{1 + \frac{16k^2\alpha^2}{r^4} + \alpha\left(\frac{4\Lambda}{3} + \frac{16m_0}{r^4} \right) - m^2\alpha\left( \frac{8cc_1}{3r} + \frac{8c^2c_2}{r^2} + \frac{16c^3c_3}{r^3}\right)  } \right).   \label{metricfn}
\end{align}
Here $m_0$ is integration constant which can be interpreted as black hole's mass. If we set graviton mass to zero, $m=0$, this solution can be compared with those found in \cite{Camanho:2015zqa,Hennigar:2015mco,Samart:2020qya,Samart:2020mnn}. Thus, it is more convenient to define the following quantities
\begin{align}
    \alpha \to \frac{\lambda L^2}{2},~~~\Lambda \to \frac{6}{L^2},~~~m_0 \to \frac{\mathcal{M} -\lambda k^2 L^2}{2},
\end{align}
where $L$ is the AdS or dS length scale and $\lambda$ is the dimensionless Gauss-Bonnet coupling. We also define shorted-hand notation for the massive graviton term as
\begin{align}
    c c_1 m^2 \to \gamma_a,~~~ c^2 c_2 m^2 \to \gamma_b,~~~ c^3 c_3 m^2 \to \gamma_c.
\end{align}
Therefore, the metric describing AdS outer ($+$) and dS inner ($-$) spacetime are written by
\begin{align}
f_{\pm} &= k + \frac{r^2}{2\lambda L^2} \left( 1 \pm \sqrt{1 + 4\lambda \left(1 + L^2 \left[ \frac{\mathcal{M}}{r^4} - \frac{\gamma_a}{3r} - \frac{\gamma_b}{r^2} - \frac{2\gamma_c}{r^3}     \right]\right)} \right).
\label{metric-fpm}
\end{align}
Alternatively, the solution of EGBMG can be obtained by introducing the following polynomials function
\begin{align}
    \Upsilon[g] &= -\frac{1}{L^2} + g + \lambda L^2 g^2 = \frac{\mathcal{M}}{r^4} - \frac{\gamma_a}{3r} - \frac{\gamma_b}{r^2} - \frac{2\gamma_c}{r^3}. \label{Upsilonfunc}
\end{align}
Thus the function $g$ can be explicitly written as
\begin{align}
g_{\pm} &= - \frac{1}{2L^2\lambda}
\left[1 \pm \sqrt{1 + 4\lambda
\left( 1+L^2
\left( \frac{\mathcal{M}}{r^4} - \frac{\gamma_a}{3r} - \frac{\gamma_b}{r^2} - \frac{2\gamma_c}{r^3}
\right)  \right)} \right],
\end{align}
or equivalently,
\begin{align}
    g_{\pm} &= \frac{k-f_{\pm}}{r^2}.
\end{align}
We will use two branches of solution Eq.(\ref{metric-fpm}) of the EGBMG theory for studying the gravitational phase transition in the next section.

\section{Junction condition and bubble dynamics}\label{sec3}
In this section, we will define the junction condition connecting two region (AdS and dS as outside and inside, respectively) of the spacetimes to study the bubble dynamics. To ensure the continuity between the two spacetimes, the so-called junction conditions must be satisfied. The junction condition of EGBMG is defined in terms of co-moving time component of the canonical momenta ($\Pi$) (see detail derivation in Refs.\cite{Samart:2020qya,Camanho:2015zqa,Camanho:2013uda})
\begin{align}
\Pi_{\pm} &= \frac{2}{3}\lambda L^2 g_{\pm}\sqrt{H-g_{\pm}}+\frac{4}{3}H\lambda L^2 \sqrt{H-g_{\pm}} + \sqrt{H-g_{\pm}}, \label{eqg}
\end{align}
where $H=\frac{k+\Dot{a}^2}{a^2}$. Here $a\equiv a(\tau)$ is a scaled factor defined on the induced line elements of the timelike hypersurface ($\Sigma$). We remark that, at the boundaries outer AdS and inner dS spacetimes, the metric of hypersurface $\Sigma$ takes the similar form (see more details in \cite{Samart:2020qya}). The derivative with respect to co-moving time coordinate $\tau$ will be denoted by $\dot{a}=\frac{da}{d\tau}$.

The junction condition can be obtained from
\begin{align}
\Pi_{+}^2 - \Pi_{-}^2 \rvert_{r_{\pm}=a} &= 0,
\label{junction-con}
\end{align}
where this condition is evaluated at the boundaries between two manifolds (outer and inner spacetimes). By substituting Eq.(\ref{eqg}) into the above condition, we obtain
\begin{align}
-\Dot{a}^2 &= k + \frac{a^6}{4L^2\lambda \mathcal{A}}\left(g_+\left(3+2g_+ L^2\lambda\right)^2 - g_-\left(3+2g_- L^2\lambda\right)^2\right),
\end{align}
where
\begin{align}
\mathcal{A} &\equiv 3\left(\mathcal{M}_+-\mathcal{M}_-\right)  - a^3 \left(\gamma_{a+}-\gamma_{a-}\right)  -3a^2 \left(\gamma_{b+}-\gamma_{b-}\right) - 6a \left(\gamma_{c+}-\gamma_{c-}\right).
\end{align}
The junction condition can be expressed in term of kinetic and effective potential as
\begin{align}
\frac{1}{2}\Dot{a}^2 + V(a) =0.
\end{align}
In order to obtain above equation, we have used the imaginary time, i.e., $\tau \to i\tau_E$ in the derivative leading to $(da/d\tau)^2 \to -(da/d\tau_E)^{2}$.
The effective potential can be shown explicitly
\begin{align}
V &= \frac{a^6}{8L^2\lambda \mathcal{A} }\left[4\left(2+g L^2\lambda\right)\left(\frac{\mathcal{M}}{a^4} - \frac{\gamma_a}{3a} - \frac{\gamma_b}{a^2} - \frac{2\gamma_c}{a^3}\right) + g(1+4\lambda)\right]_{-}^{+} + \frac{k}{2},
\label{effpot}
\end{align}
where we have used the following notation
\begin{align}
\left[\mathcal{O}\right]_{-}^{+} &\equiv \mathcal{O}_+ - \mathcal{O}_-.
\end{align}
The derivative of effective potential with respect to $a$ is determined by
\begin{align}
V'(a) &=
\frac{a}{8L^2\lambda\mathcal{A}^2}\Big(3a^5\Big[ a^2 \gamma_{a} + 2 a  \gamma_{b} + 2 \gamma_{c+}\Big]_-^+ \Big[g(1+4\lambda) + 4(2+gL^2\lambda)\Upsilon[g(a)]\Big]_{-}^{+}
\nonumber\\
&\qquad\qquad\quad + \Big[ 12\mathcal{M} + 6a^4 (1+4\lambda)g - \gamma_{a} a^3 (13+6gL^2\lambda) \nonumber\\
&\qquad\qquad\qquad\quad - 6\gamma_b a^2 (5+2gL^2\lambda) - 6\gamma_c a (7+2gL^2\lambda) \Big]_{-}^{+}
\Big),
\label{diff-effpot}
\end{align}
The effective potential in Eq.(\ref{effpot}) and its derivative in Eq.(\ref{diff-effpot}) are useful to explain the dynamics of the bubble nucleation and the discussion will be given later. More importantly, we shall assume the continuity of gravity mass by setting
\begin{align}
    \gamma_a = \gamma_{a_+} = \gamma_{a_-}, \quad
    \gamma_b = \gamma_{b_+} = \gamma_{b_-}, \quad
    \gamma_c = \gamma_{c_+} = \gamma_{c_-}.
\end{align}
These continuities greatly simplify the expression of effective potential. Imposing $V(a_{\ast})=V'(a_{\ast})=0$, one can explicitly determined $\mathcal{M}_{\pm}$ at the thermalon location, $a_{\ast}$ as
\begin{eqnarray}
\mathcal{M}^{\ast}_\pm &=& \frac{1}{12\lambda L^2 a_{\ast}^4}
\Big[ 3 a_{\ast}^6(1+4\lambda)\big(6k\lambda L^2 +  a_{\ast}^2(3+2g^{\ast}_\mp\lambda L^2)\big)
\nonumber \\
&&  - 2\lambda L^2 a_{\ast}^5\big(9k\lambda L^2 + a_{\ast}^2(4 + 3g^{\ast}_\mp\lambda L^2)\big)\gamma_a
\nonumber \\
&&  - 12\lambda L^2 a_{\ast}^4\big(3k\lambda L^2 + a_{\ast}^2(1 + g^{\ast}_\mp\lambda L^2)\big)\gamma_b
-12 \lambda^2 L^4 a_{\ast}^3 (3k+a_{\ast}^2 g^{\ast}_\mp)\gamma_c \Big],
\label{thermalon-mass}
\end{eqnarray}
where $g^{\ast}_{\pm}=g_{\pm}(a_{\ast})$. From definition of the $\Upsilon$ in Eq.(\ref{Upsilonfunc}), we obtain
\begin{align}
    \Upsilon[g^{\ast}_\pm]
    &= C_1 g^{\ast}_\pm + C_2,

\end{align}
where the coefficients $C_{1,2}$ are then determined as
\begin{align}
    C_1 &= \frac{1}{2} + \left[2 - \frac{L^2}{a_{\ast}}\left(  \frac{\gamma_a}{2} + \frac{\gamma_b}{a_{\ast}} + \frac{\gamma_c}{a_{\ast}^2}\right)\right]\lambda, \label{coeff1}\\
    C_2 &= \frac{3\left(1+4\lambda\right)}{4\lambda L^2} -  \frac{3k\left(1+4\lambda\right)}{2a_{\ast}^2}  + \frac{\gamma_a}{a_{\ast}} + \frac{2\gamma_b}{a_{\ast}^2} + \frac{2\gamma_c}{a_{\ast}^3}. \label{coeff2}
\end{align}
Thus we can solve these equations simultaneously which yield
\begin{align}
    g^{\ast}_\pm &= -\frac{\left(1+C_1\right) \mp \sqrt{1-2C_1-3C_1^2+4\lambda\left(1+C_2 L^2\right)}}{2\lambda L^2}.

\end{align}
We note that the $g_\pm^\ast$ correspond to AdS and dS geometries and the condition $g_+^\ast \neq g_-^\ast$ is required since we study the phase transition between those spacetimes. Therefore by using Eq.(\ref{coeff1}--\ref{coeff2}), the $g^{\ast}_{\pm}$ can be expressed in terms of $k,\lambda,L^2,\gamma_a,\gamma_b$ and $\gamma_c$. After deriving all relevant equations, we are ready to analyze the bubble dynamics.
\begin{figure}[h]
    \centering
    \includegraphics[width=0.45\textwidth]{fig1}
    \includegraphics[width=0.45\textwidth]{fig2}
\caption{Effective potential plotted as function of $a$ for $a_{\ast}=1$, $L=1$, $k=1$: Left fixed $\lambda=0.015$ and $\gamma_i=$ 0, 2.5, 5, 7.5, 10 (red, green, blue, black, magenta), Right fixed $\gamma_i=5$ and $\lambda=$ 0.001, 0.003, 0.005, 0.007, 0.01 (red, green, blue, black, magenta), where $i=$ \{$a$, $b$, $c$\}
} \label{fig:figVeff}
\end{figure}
From now on, the spherical bubble, $k=1$ will be studied throughout this work. In Fig.~\ref{fig:figVeff}, we display an example of behaviour of effective potential against $a$. In this figure, we fix $\gamma_a=\gamma_b=\gamma_c$. We vary $\gamma_i$ while keep other parameters fixed in the left figure. The right figure shows the effective potential with $\lambda$ is varied. Despite having various parameters, throughout this work, we shall particularly focus on the set of parameter which yield $\mathcal{M}^*_{\pm}$ are real positive value. As the results, the Fig.~\ref{fig:figVeff} clearly shows that the effective potential has the maximum value at the given thermalon position, $a_\ast = 1$. This means that the thermalon is in the unstable mode and ready to roll down from the top of the effective potential. Consequently, the bubble, representing dS space with true vacuum can expand and leading to the AdS to dS phase transition eventually. In Fig.~\ref{fig:figMpara}, parameter spaces where $\mathcal{M}^*_{\pm}>0$ are illustrated. In each plots, we fix bubble location and AdS (dS) length scale to be unity. The GB coupling constant is chosen to be 0.1. With given $\gamma_c$, allowed value of $\gamma_a,\gamma_b$ can be obtained. The shaded regions increase as $\gamma_c$. We should emphasize that the plots in Fig.~\ref{fig:figMpara} are only partially displayed for demonstration purpose. From our numerical investigation, the shaded regions can be extended rightward and upward.

\begin{figure}[h]
    \centering
    \includegraphics[width=0.32\textwidth]{fig3a}
    \includegraphics[width=0.32\textwidth]{fig3b}
    \includegraphics[width=0.32\textwidth]{fig3c}
\caption{Possible parameter space between $\gamma_a-\gamma_b$ for fixed $a_{\ast}=1$, $L=1$, $k=1$, $\lambda=0.1$: Left $\gamma_c=-1$, Middle $\gamma_c=0$, Right $\gamma_c=1$.}
\label{fig:figMpara}
\end{figure}
In general, the bubble can be either expanded or collapsed after rolling down from the effective potential. However, we are interested only the expanding bubble case which can change the values of the effective CC from the false vacuum AdS space to the true vacuum dS space asymptotically. Therefore, a consideration of the collapsing bubble case is neglected in this study. One can see Ref.\cite{Camanho:2013uda} for more detail discussions of the collapsing bubble that leads to violation of the cosmic censorship hypothesis.

We close this section by providing a brief discussion on how we ensure that the bubble will expand to infinity reaching the cosmic horizon and changing the effective CC to the new value a whole spacetime. By considering the definitions of the canonical momenta of the AdS (outside) and dS (inside) spaces and the junction condition in (\ref{eqg}) and (\ref{junction-con}), respectively, we find,
\begin{eqnarray}
H \approx \frac{1}{2\left( \mathcal{M}_+ - \mathcal{M}_-\right)}\left[ a^4\int_{g_-}^{g_+}dg\,\Upsilon\big[g\big] - \Big[g\left(\mathcal{M} -a^3\gamma_a -a^2\gamma_b -a\gamma_c \right)\Big]_-^+\right].
\end{eqnarray}
Here the above expression is obtained up to the first order expansion of the  $1/H$. We can see explicitly that $H\equiv \dot{a}/a$ (speed of the bubble expansion) approaches to $\infty$ when $a \to \infty$. This corresponds to the the bubble expansion to infinity at the finite time.

\section{Gravitational phase transition}\label{sec4}
This section presents a central result of this work on the AdS to dS phase transition mediated by thermalon in EGBMG theory. This section is divided into two parts. First, we discuss how we obtain physically corrected thermalon configuration. Second, from a set of parameter in EGBMG which allowed thermalon configuration, we analyse thermodynamic phase space of the gravitational phase transition.

\subsection{Thermalon configurations, horizons and Nariai bound}
Since we need to ensure that the thermalon's location $a_{\ast}$ lies in the casual connected region outside the black hole. Thus, it is convenient to firstly determine the casual structure of the metric Eq.(\ref{metricfn}). The horizon's location can be obtained by imposing $f_-(r_{H})=0$. This yields quartic equation
\begin{align}
    r_{H}^4 - \frac{\gamma_a L^2}{3} r_{H}^3 - \left(1+\gamma_b\right)L^2 r_{H}^2 -2\gamma_c L^2 r_{H} + L^2 \left(M^{\ast}_- - \lambda L^2\right) &= 0. \label{quartic}
\end{align}
The roots of this equation can be interpreted as the dS branch (inner spacetime) horizon. In general, there will be four possible roots. However, only real positive roots are physically relevant. An example plot of metric function $f$ is illustrated in fig.~\ref{fig:metricfn}. In these plots, the bubble position is always fixed to unity i.e., $a_{\ast}=1$. Two roots of $f_-$ correspond to event horizon ($r_H$) and cosmological horizon ($r_C$). We observe that as $\gamma_a,\gamma_b$ increases the metric function also increases. In addition, increasing in $\gamma_a,\gamma_b$ does not significantly alter the location of the event horizon while the cosmological horizon is shifted to a larger value. Moreover as we expect, the radius of cosmological horizon becomes larger as $L$ is increased.

\begin{figure}[h]
    \centering
    \includegraphics[width=0.8\textwidth]{fig4}
\caption{Plot of $f_-$ when $a_{\ast}=1,k=1$ Red: $L=1,\lambda=0.2,\gamma_c=1$ (dashed) $\gamma_a=0,\gamma_b=0$ (solid) $\gamma_a=0.6,\gamma_b=0.5$ and Blue: $L=3,\lambda=0.015,\gamma_c=0.5$ (dashed) $\gamma_a=0,\gamma_b=0$ (solid) $\gamma_a=1.6,\gamma_b=0.8$. The subplot displays a close up behaviour of metric function $f$.} \label{fig:metricfn}
\end{figure}

Equation (\ref{quartic}) is in a standard form of quartic equation $a r^4 + b r^3 + c r^2 + d r + e =0.$ The roots of this equation are given by

\begin{align}
    r_{1,2} &= -\frac{b}{4a} - S \pm \frac{1}{2}\sqrt{-4S^2-2p+\frac{q}{S}}, \\
    r_{3,4} &= -\frac{b}{4a} + S \pm \frac{1}{2}\sqrt{-4S^2-2p-\frac{q}{S}},
\end{align}
where we have defined the following parameters
\begin{align}
    p &\equiv \frac{8ac-3b^2}{8a^2} = -\frac{L^2}{24}\left(L^2\gamma_a^2+24\left(1+\gamma_b\right)\right), \nonumber \\
    q &\equiv \frac{b^3-4abc+8a^2d}{8a^3} = -\frac{L^2}{216}\left(L^4\gamma_a^3 + 36L^2\gamma_a\left(1+\gamma_b\right) + 432\gamma_c\right), \nonumber \\
    S &\equiv \frac{1}{2}\sqrt{\frac{1}{3a}\left(P+\frac{\delta_0}{P}\right)-\frac{2p}{3}}, \nonumber \\
    P &\equiv \left(\frac{\delta_1 + \sqrt{\delta_1^2 - 4 \delta_0^3}}{2}\right)^{1/3}, \nonumber \\
    \delta_0 &\equiv c^2 - 3 b d + 12 a e = 12\mathcal{M}^*_-L^2 + \left(\left(1+\gamma_b\right)^2 - 2\gamma_a\gamma_c - 12 \lambda\right)L^4, \nonumber \\
    \delta_1 &\equiv 2c^3 - 9 b c d + 27 b^2 e + 27 a d^2 - 72 a c e = \left(72 \mathcal{M}^*_-\left(1+\gamma_b\right) + 108\gamma_c^2\right)L^4  \nonumber \\
    &+ \left( 3\mathcal{M}^*_- \gamma_a^2 - 2 \left(1+\gamma_b\right)\left( 1 + \gamma_b\left(2+\gamma_b\right) -3 \gamma_a\gamma_c + 36\lambda  \right)   \right)L^6 -3\lambda \gamma_a^2 L^8.
\end{align}

Thus we can now plot the horizon radius as a function of thermalon's location $a_\ast$ and this is demonstrated in fig.~\ref{fig:fig5}. To be physically relevant, we pay our attention only to the case where the thermalon is located within the casual region of inner spacetime i.e. $r_H \leq a_\ast \leq r_C$. In practice, we fix the maximum value of bubble location at $a_\ast = 1$ where the spacetime approaches the Narai limit $r_H \sim r_C$. We remark that, throughout this work, we shall especially focus on the case where 1) both $\mathcal{M}^*_{\pm}$ are real positive. 2) the metric function Eq.(\ref{metricfn}) has at least two positive real roots. 3) The thermalon always stay between black hole's event horizon and cosmological horizon. We need to ensure that these three conditions are met throughout our investigation.

\begin{figure}[h]

    \includegraphics[width=0.32\textwidth]{fig5a}
    \includegraphics[width=0.32\textwidth]{fig5b}
    \includegraphics[width=0.32\textwidth]{fig5c}
\caption{Location of horizons as a function of $a_{\ast}$ when $k=1$, $L=1$,  $\lambda=0.2$, Left: $\gamma_a=-2.393,\gamma_b=2.197,\gamma_c=0$, Middle:
$\gamma_a=-0.931$, $\gamma_b=-0.035$, $\gamma_c=1.5$, Right: $\gamma_a=0.532$, $\gamma_b=-2.266$, $\gamma_c=3$. The red, black and blue curved are event horizon, thermalon (bubble) location and cosmological horizon respectively. } \label{fig:fig5}
\end{figure}

\subsection{Thermodynamics of the AdS to dS phase transition mediated by thermalon}
This subsection aims to investigate the gravitational AdS to dS phase transition in the thermodynamics phase space. We follow Refs.\cite{Camanho:2015zqa,Camanho:2013uda,Camanho:2012da,Hennigar:2015mco,Samart:2020mnn,Samart:2020qya} for all formalisms in this study. The gravitational phase transition in this work is a generalization of the well known Hawking-Page (HP) phase transition \cite{Hawking:1982dh} where at the critical temperature the thermal AdS space becomes unstable and then decays to the the AdS black hole with the lower free energy. We employ the generalized HP phase transition in this work. The decay mechanism proceeds via nucleation of the bubbles or the thermalon mediation where the initial false vacuum state is the thermal AdS. When it is unstable and decay into black hole inside the bubble of true vacuum dS space at the critical temperature. This phase transition is produced by the quantum tunneling or jumping over the wall of the quasi particle state in the Euclidean sector of the bubbles called the thermalon \cite{Gomberoff:2003zh,Camanho:2012da,Camanho:2013uda}. In other words, the thermalon effectively changes the branch of the false vacuum AdS solution to another true vacuum dS solution.

Taking this phase transition mechanism into account, one can calculate the thermodynamics properties of the thermalon in the same fashion as black hole thermodynamics are calculated. The Euclidean action of the thermalon, $\mathcal{I}_E$ has been derived in \cite{Camanho:2012da,Camanho:2013uda} and it is given by
\begin{eqnarray}
\mathcal{I}_E = \beta_+\,\mathcal{M}_+ + S\,,
\end{eqnarray}
where $\beta_+$, $\mathcal{M}_+$ and $S$ are the inverse Hawking temperature, mass of the external observer in the asymptotic thermal AdS and the entropy of the dS black hole, respectively. The Gibbs free energy of the thermalon in the canonical ensemble is written by  \cite{Camanho:2015zqa,Camanho:2013uda,Frassino:2014pha},
\begin{align}
    F &= \mathcal{M}_+ - T_+ S.
    \label{free-energy}
\end{align}
To obtain the Gibbs free energy of the thermalon, one can use the on-shell regularization method by subtracting the thermal AdS space background \cite{Camanho:2015zqa,Camanho:2013uda,Hennigar:2015mco}. More importantly, there are two competing phases in this system i.e., the thermal AdS (outside) and the thermalon hosting the black hole in the dS space (inside). Then, we will study the phase transition by comparing the Gibbs free energy of the thermalon to the thermal AdS one. In practice, we can set the Gibbs free energy of the thermal AdS space as zero ($F_{\rm AdS} = 0$) since $F_{\rm AdS}$ has already considered as the background subtraction.
The Hawking temperature of inner five dimensional dS black hole in EGBMG can be defined by \cite{Cai:2003kt}
\begin{align}
    T_- &= \frac{1}{4\pi r_H}\left[ \sum_{n=0}^{2} \frac{ k c_n \left(4-2n\right)}{\left(k r_H^{-2}\right)^{1-n}}  + \gamma_a r_H + 2 \gamma_b + \frac{2\gamma_c}{r_H}  \right]\left[\sum_{n=0}^2 \frac{nc_n}{\left(kr_H^{-2}\right)^{1-n}}\right]^{-1},
    \label{T-}
\end{align}
where
\begin{align}
    c_0 &= -L^{-2},~~~~~c_1 = 1,~~~~~c_2 =\lambda L^2. \nonumber
\end{align}
Moreover, the Bekenstein-Hawking entropy is given by  \cite{Cai:2003kt}
\begin{align}
        S &= 4\pi r_H^5 \sum_{n=0}^2 \frac{nc_n\left(kr_H^{-2}\right)^n}{k\left(5-2n\right)}.
        \label{entropy}
\end{align}
The Hawking temperature of outer AdS spacetime is computed by
\begin{align}
    T_+ &= \frac{\sqrt{f_+(a_\ast)}}{\sqrt{f_-(a_\ast)}}T_-.
    \label{T+}
\end{align}
\begin{figure}[h]

    \includegraphics[width=0.45\textwidth]{fig6a}
    \includegraphics[width=0.47\textwidth]{fig6b}
\caption{The Hawking temperature (left) and free energy (right) of thermalon configuration as function of $a$ for various value of $\lambda$ with $k=1$, $L=1$, $\gamma_a=-2.296$, $\gamma_b=2.048$ and $\gamma_c=0.1$.} \label{fig:fig6}
\end{figure}
\begin{figure}[h]

    \includegraphics[width=0.8\textwidth]{fig7}
\caption{Free energy $F$ of the thermalon configuration as a function of the themperature $T_+$ for various value of $\lambda$ with $k=1$, $L=1$, $\gamma_a=-2.296$, $\gamma_b=2.048$ and $\gamma_c=0.1$. The subplot displays the behaviour of free energy at larger value of $\lambda$. The colored code can be found in Fig.~\ref{fig:fig6} } \label{fig:fig7}
\end{figure}
We plot $T_+$ and $F$ as a function of the thermalon radius, $a$ and the results are shown in Fig.~\ref{fig:fig6}. In Fig.~\ref{fig:fig6}, the temperature and free energy are plotted as a function of the thermalon's location. It is clear that the temperature increases with bubble position. As $\lambda$ increases, the slope of $T_+$ becomes more flatten. Moreover, we observe phase transition in free energy plots. As $a$ increases, the thermalon configuration becomes more thermodynamically preferred. The phase transition is apparently more obvious as $\lambda$ is larger. The phase transition occurs at larger bubble's location as $\lambda$ increases. Additionally, we observe that the physically relevant thermalon configuration exists at a smaller thermalon's location $a$ at lower $\lambda$.

By substituting results in Eqs.(\ref{thermalon-mass},\ref{T-},\ref{T+},\ref{entropy}) in the thermalon free energy Eq.(\ref{free-energy}), we are ready to study the thermodynamics phase space between $F$ as function of $T_+$.
The relation between the Gibbs free energy and Hawking temperature $T_+$ is illustrated in Fig.~\ref{fig:fig7}. In this figure, the parameter $\lambda$ is varied while the others are kept fixed. As $\lambda$ increases, the free energy become less dependent on temperature (the slope becomes more inclined). According to our numerical investigation, we particularly choose the value of $\gamma_a=-2.296, \gamma_b=2.048$ and $\gamma_c=0.1$ such that the thermalon's location lies between the cosmological and event horizons. At small $\lambda$, the minimum value of $F$ is increasing as $\lambda$ becomes larger. However, the minimum starts to decrease from $\lambda=0.25$ until it reaches the lowest value at $\lambda=1.2$. After that, the minimum of free energy rapidly increases as $\lambda$ increases.

As a result, we find that thermalon always produces the AdS to dS phase transition since all Gibbs free energies of the thermalon are negative at their maximum temperature for all possible values of the given Gauss-Bonnet coupling, $\lambda$. This is an interesting result in this work because usually, the Gauss-Bonnet coupling, $\lambda$ plays the role as the order parameter of the AdS to dS phase transition in both without \cite{Camanho:2015zqa,Hennigar:2015mco} and with the presences of the gauge fields \cite{Samart:2020qya,Samart:2020mnn}. Our results suggest that with a proper value of $\gamma_{a,b,c}$, the gravitational phase transition from AdS to dS is inevitable. This means that in this scenario, the couplings of the massive gravity, ($\gamma_{a,b,c}$) play the role as the order parameter rather than the Gauss-Bonnet coupling, ($\lambda$) in this type of phase transition.

\section{Conclusion}\label{sec5}

In recent years, the most widely studied theory in the higher curvature gravities is known as Einstein-Gauss-Bonnet (EGB) theory of gravity. The EGB theory of gravity is a special case of the Lovelocks gravity. The GB term is only nontrivial in spacetime dimensions $(4+1)D$ or greater. In this work, we have studied gravitational phase transition from AdS to dS geometries by engaging the well-defined massive theory of gravity to the EGB one. This inclusion basically features a matter field sector in the theory.

The thermalon induces the decay of the negative effective cosmological constant to the positive one due to the higher-order gravity effects and the decay mechanism proceeds through nucleation of the bubbles or the thermalon of true vacuum (dS) inside the false vacuum (thermal AdS) Refs.\cite{Camanho:2012da,Samart:2020qya}. It was demonstrated that the probability of the decay, $P$, of
the thermalon effectively jumping from AdS to dS branch
solutions is governed by $P\propto e^{I_{E}}$ with $I_E$ being the Euclidean action difference between initial thermal AdS and the thermalon (bubble state). As a result, the system will end up in the stable dS black hole after the thermalon
expansion reaching the asymptotically dS region in a
finite time.

We have also determined the thermodynamics phase space of the Hawking temperature and free energy and found that the free energy of the thermalon is always negative at the maximum of Hawking temperature for all specific values of the parameters of the massive gravity sector. Additionally, we have also discovered that a generic behavior of the phase transition in the EGBMG theory is affected by the specific values of the parameters in the massive gravity instead of the GB coupling in contrary to those cases found in the previous publications in which the authors have studied the vacuum and the charged cases.

With presence of the massive gravity sector, we have demonstrated that the phase transition mediated by thermalon from AdS to dS asymptotics is inevitable in the present work. and specific valued of the parameters in the massive gravity behave as the order parameters in the phase transition instead of the Gauss-Bonnet coupling. Interestingly, our results are in line with the claim that the generalized gravitational phase transition is a generic behavior of the higher-order gravity theories when the matter field is included.

\begin{acknowledgments}
This work (Grant No. RGNS 64-217) was financially supported by Office of the Permanent Secretary, Ministry of Higher Education, Science, Research and Innovation. We are graceful to Chakrit Pongkitivanichkul for useful discussion. P. Channuie acknowledged the Mid-Career Research Grant 2020 from National Research Council of Thailand (NRCT5-RSA63019-03). D. Samart is financially supported by the Mid-Career Research Grant 2021 from National Research Council of Thailand under a contract No. N41A640145. S.P. would like to acknowledge Piyabut Burikham for his advice and support.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


A Neo-nazi takes over a remote school, makes it into a training camp, and attempts to convert its students into personal army. A young yoyo-wielding "delinquent" student named Saki seeks to stop this with the help of her friends. However they must first lead all the students to safety. ~~ The movie closely follows a TV and manga series Sukeban Deka written and illustrated by Shinji Wada.


MICHAEL ROWLAND: The Federal Opposition has committed to closing what it calls a tax loophole that gives shareholders cash refunds for dividend imputation credits even if they pay no tax at all. Labor says the policy will inject $5 billion a year into Government coffers.
VIRGINIA TRIOLI: So let us hear from the other side, Mathias Cormann is the Federal Finance Minister and we are pleased to say he joins us from Parliament House. Good morning Minister.
VIRGINIA TRIOLI: The Labor Opposition says it is aiming to make the taxation system fairer. That is hard to argue with, isn't it?
MATHIAS CORMANN: This is just the latest example of Bill Shorten's high taxing agenda. What every Australian can see again today is that should Bill Shorten become Prime Minister, no one in Australia will be safe from his high taxing agenda. He has already announced higher taxes for workers, for homeowners, for professionals, for small business and now self-funded retirees. Wherever you look, he wants to hit people with higher taxes to fund his reckless spending sprees and that is not the right way forward for Australia. A higher taxing agenda will lead to less investment, less effort and indeed lower growth, fewer jobs and lower wages.
VIRGINIA TRIOLI: I am going to jump in there because I think it is really important to clarify this at this point, that is a very big hyperbolic rant there. To quote the Opposition Leader, the change only affects a very small number of shareholders who currently have no tax liability and use their imputation credits to receive a cash refund and this is the key point, they will no longer receive a cash refund but they will not be paying any additional tax. This morning, for accuracy, you cannot go on in relation to this about paying more tax.
MATHIAS CORMANN: You are allowing yourself to be misled by Bill Shorten's shifty rhetoric. Bill Shorten always…interrupted.
VIRGINIA TRIOLI: But as I can see it, the cash refund goes away but there isn't an additional tax.
MATHIAS CORMANN: Bill Shorten always dresses up any higher taxes in his rhetoric around the politics of envy instead of pursuing the politics of opportunity. What is happening here is, tax that has already been paid and which should not have been paid because various Australians do not have a marginal tax rate at the same level as the company tax rate, is provided by way of income tax refund, which incidentally was introduced in the late 90s with bipartisan support. When the Howard Government introduced this, senior Labor Members of Parliament at the time pointed out that that was a policy that they had taken to the previous election, that it was a logical extension of the Paul Keating reforms introducing dividend imputation…interrupted.
VIRGINIA TRIOLI: Sure, but times change and Budget bottom line changes as well. This is at least one concrete plan Minister, to save the Budget almost $6 billion in the first year. You are offering tax cuts while leading economists such as Chris Richardson and others strongly argue you should still be focusing on Budget repair. That is what this policy seems to be doing.
MATHIAS CORMANN: We are focused on Budget repair. Under the Coalition the Budget is getting back into surplus by 2020-21 and remaining in surplus all the way through. At the last election… interrupted.
VIRGINIA TRIOLI: Chris Richardson's point is that you need to get there sooner rather than 2020-21.
MATHIAS CORMANN: Well 2020-21 is actually not that far away. What I would put to you is that, whatever way Bill Shorten tries to dress this up, this is going to be a tax hit, a $59 billion tax hit by his own numbers, which will hit low and middle-income earners the hardest. If you are a self-funded retiree on a low income, you will pay more tax. If you are a pensioner who has invested in some shares, you will pay more tax. More than a million retirees, many of them pensioners or part pensioners will pay more tax under this proposal. This is just the latest. We have had $165 billion worth of Labor tax grabs announced before. There is no question that under Labor the overall tax burden in the economy would increase beyond the 23.9 per cent cap that we have imposed on ourselves. Higher tax burden in the economy will lead to less investment, will lead to lower growth, which would lead to fewer jobs and lower wages. That is precisely the opposite to what we are trying to achieve. We are working to make our economy stronger, more prosperous, to ensure that people across Australia have the best possible opportunity to get ahead. Bill Shorten wants to hit people working to get ahead for six.
VIRGINIA TRIOLI: I feel like we are in the middle of an election campaign already Minister. You mentioned wage growth and where people's wages are. Wage growth in Australia we all know is at historically low levels and basic household struggles are now a broad reality. In that context, isn't the ACTU's minimum wage claim of $50 a week reasonable?
MATHIAS CORMANN: Firstly, wages growth has been picking up and the key is to ensure that wages growth continues to pick up on the back of stronger growth and…interrupted.
VIRGINIA TRIOLI: It is still historically low.
MATHIAS CORMANN: If I may, wages growth has been picking up and it is important for wages growth to pick up on the back of stronger economic growth and stronger profitability of businesses employing people across Australia. We do have one of the highest minimum wages in the world. These are decisions that are made independently by the Fair Work Commission. The Fair Work Commission appropriately will consider the economic impact, the impact on work force participation…interrupted.
VIRGINIA TRIOLI: Of course they will, but I am asking if you think it is reasonable?
MATHIAS CORMANN: What I am saying is that the Fair Work Commission needs to consider this very carefully. If you increase the minimum wage further when we already have one of the highest minimum wages in the world, without taking steps to improve the profitability of business, you will drive more people into the unemployment queues and that is not what we need and that is not what we want.
VIRGINIA TRIOLI: Do you really not have a sense of just how tough it is for so many households across Australia just to meet their weekly bills? That is not surprising to you, is it Minister?
MATHIAS CORMANN: We absolutely have a sense of this and that is why we are working very hard on our plan to strengthen growth and create better opportunities for all Australians to get ahead. We also understand that the only way that all Australians can have the best possible opportunity to get ahead is to ensure that those businesses employing nine out of 10 working Australians have the best possible opportunity to be successful and profitable into the future. In the end, it is those businesses that have to create the new jobs and have to pay the higher wages that we want Australians to be able to benefit from.
VIRGINIA TRIOLI: Mathias Cormann, just finally this morning, I wanted your reflections on the big Australia discussion. If we need a national population strategy and most experts seem to agree that we do. Does the focus need to be more on immigration levels or infrastructure?
MATHIAS CORMANN: When it comes to immigration levels, the focus ought to be on attracting the right set of skills and the right people into Australia to help us build a stronger, more prosperous, more successful Australia into the future…interrupted.
VIRGINIA TRIOLI: So we still need that skilled migration scheme, you think?
MATHIAS CORMANN: Of course we need to continue to attract skilled migrants and at the right level, consistent with the needs of our economy and the infrastructure development needs to run in parallel. We have to ensure that we plan and that we continue to invest and develop the infrastructure that we need in order to accommodate those people that are joining us here in Australia.


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Mississippi to step up reading instruction for third-graders
April 22, 2014 in Education, News
Senate Education Committee Chairman Gray Tollison, R-Oxford, (AP Photo/Rogelio V. Solis)
JACKSON, Mississippi (AP) — State officials say they plan to use bolstered state funding to hire more literacy coaches and better train teachers as schools seek to meet legislative requirements that all third graders read at a basic level by next year or be flunked.
Lawmakers gave the Mississippi Department of Education $15 million to spend on the program, up from $9.5 million this year. Officials with the department say they intend to use the money to hire 45 literacy coaches and supervisors, up from 31 this year. Those coaches will cover 74 target schools in 50 districts, up from 50 schools in 30 districts. The state has tried to focus on schools with the lowest reading scores.
Trecina Green, who leads teacher training efforts for the department, said the state will expand a training program run by Dallas-based Cambium Learning to 6,500 K-3 teachers from 3,500 this year.
If the requirement for a minimum score, which advocates call the third-grade gate, had been in effect last year, about 5,000 of Mississippi's 37,000 third graders would have failed. The mandate was signed into law last year.
Students who fail can still go on to fourth grade if they have a disability, if they show acceptable reading levels on some other assessment, or if they've had two or more years of intensive support. Any student who fails and is promoted is supposed to get more help in fourth grade.
The $15 million meets the amount Gov. Phil Bryant had proposed for the program last year. Alabama and Florida, with similar programs, each hired hundreds of literacy coaches. Many Mississippi districts have hired their own literacy coaches in addition to the state effort.
Cambium's Sopris Learning unit will get $3.7 million in the 2015 budget year, a $500,000 increase over the $3.2 million the state is spending this year. The training comes in two phases, each consisting of 15 to 20 hours of online work and three days of face-to-face training for teachers at target schools. Participating non-target schools get two days of face-to-face training.
Officials told the state Board of Education on Thursday that they hope to enroll teachers in training in the courses starting next year. In Senate Bill 2572, which Gov. Phil Bryant has yet to sign into law, legislators called for elementary teachers to pass a test showing they know up-to-date reading instruction methods. If Bryant signs the bill, the requirement would take effect July 1, 2016.
The same bill calls for the state Department of Education to provide literacy coaches in 10 C-rated school districts "in a geographically concise region," using an additional $700,000. Senate Education Committee Chairman Gray Tollison, R-Oxford, who pushed the measure, said he wants the University of Mississippi to coordinate the effort and for the state to choose districts near Oxford.
Tollison said he supports the department's aim to hire "quality over quantity" when it comes to coaches. But he said it's important to expand support to mid-rated districts.
"The tests are going to take effect next year and the intent was to get them as much support as possible," he said.
Tags: literacy coaches, Mississippi Department of Education, teachers, third graders
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text:
Q: Stop page from reloading after alert in if statement I am facing this issue here.After i click alert in if statement the page should not reload.I have tried everything here

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So as you can see in if statement when sel.options[sel.selectedIndex].text!="Meeting Room Name the alert is showed after i click ok the page should not reload.I have tried each and every solution and referred many posts.
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            {
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                    else    //if no meeeting room or more then one meeting room is selected.
                    {
                        //alert("Please refresh page and click on new booking your booking is conflict with other user.");
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                    //sel.options[sel.selectedIndex].text= selectedValueres ;
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                else    //if no meeeting room or more then one meeting room is selected.
                {
                    alert("Please select One Meeting Room");
                    return;

                }
             }

            }

        return false;

});

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