Scuba diving can be a great pastime for you if you love the water. In the summer it's a great water sport where you can cool off while keeping physically fit! However there are aspects that you will want to consider first. These will indeed help you better decide if it's for you, and make it very enjoyable as well.
Beyond these, you also need a wetsuit, fins, and other items that will help protect you from the underwater environment where you might need to keep warmer, as well as protected from sharp objects and certain water life.
If you're a Scuba Diving enthusiast or simply want to learn more facts about Scuba Diving, then be sure to visit the Scuba Diving Certification Site. Clive thoroughly recommends this site so check it out today here: - http://www.bestscubadivingcertification.com. For excellent and helpful Scuba Diving advice.


Every country can be defined by the food they eat, and how they prepare and cook this food. The same is true for different states within many countries, or even down to particular regions. The extraordinary range of differing food preferences of the population of each country, state or region has an uncanny knack of capturing the essence of each area's personality, whether stodgy, optimistic, mean, generous, pleased with themselves, bold, passionate, laconic, pride in what they do, risk-takers, disciplined, over-bearing, particular, unimaginative, creative, challenging; and the list goes on.
This book richly captures the unique and powerful personality of those wonderful people who make up Australia's cattle station region; that vast, rugged and unforgiving yet mystical wilderness that is our cattle station country.
These cattle station recipes and stories bring alive the optimistic, resilient, sharing, enterprising, self-confident, risk-taking, creative, laconic and proud free spirits that characterise our cattle station communities.


Scottish Pagan Federation Conference and other gatherings. She is senior priestess and co-founder of Mother Grove Goddess Temple and the Coalition of Earth Religions/CERES, both in Asheville, NC.
For over 20 years DJ Steve Sidewalk has spun in the NYC club scene from TUNNEL and LIMELIGHT to SPLASH and XL to present day RITZ. SIDEWALK is also known for his Tea dances in Fire Island, Provincetown, Ogunquit and Asbury Park. He has been involved with big circuit party weekends such as Ascension, Pines Party Weekend, Cherry Weekend and is headlining the Winter Rendezvous Gay Ski Weekend in Stowe VT this year. SIDEWALK also travels the country with guest dj residencies in cities like PALM SPRINGS, WILTON MANORS, MIAMI, LAS VEGAS, DC, BALTIMORE, LA, NEW ORLEANS, and BOSTON. Steve Sidewalk has won many awards such as Get Out Magazine's 'Best Club DJ of the year' for six consecutive years 2011 – 2016. He has also won 2015 Odyssey Magazine 'Best Club DJ of 2015' and has been nominated for several Glammy Best DJ Awards. He has worked with celebrities and artists including Lady Gaga, Nick Jonas, Theresa Guidice, Marc Jacobs, Estelle, The Wanted and Wynter Gordin, He also has worked with big name djs like Shep Pettibone, Peter Rauhofer, Hex Hector, Tony Moran, Tracy Young, Danny Tenaglia, Victor Calderone, Boris and many more. Sidewalk's broad based northeast following and guest residencies across the US is a testament to his unique dj style and his brilliant acumen to stay in tune with the pulse of dance music.
Lady D is professional Psychic Medium and Paranormal Investigator who has been helping both the living and the dead for over 25 years. As a historian for Evergreen Cemetery in Morristown, NJ, Lady D is exceptionally knowledgeable about headstone symbolism, funerary and burial rites. She serves the Iron Garden as Host & Resident Psychic.
Robert L. Schreiwer is a founder of Urglaawe, a Ziewer in Distelfink Sippschaft, and a practicing Braucher and Hex. Through the Pennsylvania German Heathen Alliance for the Urglaawe, he has been conducting a project to gather oral lore from all regions of Deitsch settlement and is currently working on other language and cultural advancement projects. He is the current Steer for the Troth, the Founder and Elder of the Troth's In-Reach Heathen Prison Services program, Manager of Heathens Against Hate, and the Troth Steward for Pennsylvania. He presented at the Parliament of the World's Religions in 2015 and 2018.
Witchcraft, a magical tradition that blends Celtic Paganism, Druidry and Old World Witchcraft.
Joe Monteleone has 17 years of experience with the esoteric Tarot and has practiced a unique mix of Eastern and Western spirituality his whole life. He fuses his intellectual understanding of occultism with his intuition. Channeling to give clients deep and practical insight, remove blocks, and reveal their beautifully true nature. He uses the Tarot as a map of the highest cosmic landscapes to the lowest mundane corridors of everyday life to help seekers find their way. He regularly reads at parties, clubs, special events, new age stores, and his personal clientele. He has notably read for Facebook, the New York Renaissance Faire, and radio with a guest appearance on All Business Media FM. He is a member of the Holistic Business Association. He also performs Tarot! Joe is also professional dancer where he incorporates the Tarot into multimedia dance ritual works. Noted for "spiritual and artistic achievements" by The Dance Enthusiast and "Magical-thinking-made-reality" by the Huffington Post. He has performed nationally and internationally to great acclaim.
Staten Island's own Mark Eadicicco – Psychic, Witch & Medium continues to perform his amazing Psychic and Medium readings for close to 30 years. Having the talented gift to speak to those who have passed, combined with his amazing psychic ability seasoned with his New York; no nonsense approach has brought Eadicicco much attention and a loyal clientele as well.
Growing up in New York City Mark Eadicicco is a hereditary Witch – with knowledge of the Craft bestowed upon him by his Mother, the Eadicicco family took many trips up to Salem Massachusetts each year for Mark to take classes with his longtime friend and teacher Lois Devine (Mark's first teacher and was first initiated by Lois). Mark is also a Third-Degree High Priest in the Cabot Tradition of Witchcraft, personally taught and initiated by Laurie Cabot "The Official Witch of Salem".
Combining his talents with the knowledge of his elders, Mark teaches "The Eadicicco Tradition of Witchcraft" in New York City while owning and operating Staten Island's oldest and original Witch Shoppe. Where he performs his readings and has a 3-4 month waiting list for his life changing sessions. Along with his partner Richie, Mark creates and Magickally charges his own line of products including candles, potions and other handmade items. Mark performs public rituals throughout the year with his coven and teaches his workshops and classes all over the country to sold out crowds.
Babalosha Obba Kilona is an Oriate, a priest within the De la Casa de Nicocco Sevilla tradition of the Lukumi/Santeria religion. He was crowned in Cuba fourteen years ago with the Orisha Eleggua and has received over 150 Orishas. Unlike many of his counter parts, he attempts to open the doors to welcome "outsiders" in understanding Santeria with honest discussions and dispel its misconceptions. His knowledge and experience are apparent in his teachings of this highly misunderstood religion. Reverend Bea is a Santera, Palera, High Priestess in Witchcraft, Master Teacher in a number of healing practices as well as an ordained minister and certified Life Coach. She is also a member of the paranormal investigation team, Paranormal Spirit Finders, providing spiritual support and guidance to both the living and the dead.
James Jacob Pierri Of AusetGypsy carries over 20 + years experience in the art of Fortune Telling and Divination! He is a published Astrologer and author, Tarot Card/Deck Artist, seen on TV ( MTV, HGTV,WPIX, FOX), heard on Radio and Podcast.
James has toured nationally and internationally and has also worked with Museums providing presentations and classes on varied Metaphysical Subjects such as Tarot, Astrology, Palmistry, Mysteries Of Isis, Wicca and more. James is an legally Ordained Priest in the Temple Of Isis and also carries Wiccan Clergy status. Studied Neo-Pagan Research at CherryHill Seminary and member of The Fellowship Of Goddess Isis and Covenant Of The Goddess. Heading The Iseum Of The Sacred Lotus, a living Temple to Isis.
Creator of AusetGypsy, a 20+ year successful fortune telling business of many forms in which he provides spiritual consultations for the pubic, private appointments, large scale events, festivals, celebrities and 2 brick and mortar locations under his hat!


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   * @member {string} [cert] The SSL cert data in PEM format encoded as base64
   * string
   * @member {string} [key] The SSL key data in PEM format encoded as base64
   * string. This is not returned in response of GET/PUT on the resource. To
   * see this please call listKeys API.
   * @member {string} [cname] The CName of the certificate.
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The cash bail system is being ended in Berkshire County.
District Attorney Andrea Harrington says the system creates unequal tiers based on whether a defendant is rich or poor.
Harrington said she would end cash bail during her 2018 campaign.
She has instructed prosecutors in her office to only seek bail in rare instances where the person charged is a flight risk.


text:
Local Restaurant Takes on ALS Ice Bucket Challenge
A local restaurant joined in on the ALS Ice Bucket Challenge that has been sweeping across the country, and the restaurant staff have a ten year-old boy to thank for their chilly experience.
On Monday, August 25, the staff of Suzie's Place gathered in front of their Sykes Street restaurant to pour buckets of ice water over their heads in support of the ALS initiative.
"I nominated the Suzie's Place staff, and my grandparents," ten year-old Quinton Armitage told The Independent. "They seem like people that would do it. I'm hoping they're going to freak out."
Though he attempted, Quinton could not conceal the huge smile on his face, due to the fact that his mother, Amanda, is part of the family business that is Suzie's Place, and he was looking forward to watching his mother douse herself with ice water.
"I want to wish them good luck, and I hope I'm not grounded," laughed Quinton, who added that the high profile of the ALS campaign has taught him about a disease he had previously had never heard of. "I've learned that it's a very serious disease that shuts down your whole body, and it's horrible."
ALS (Amyotrophic Lateral Sclerosis),also commonly known as Lou Gehrig's disease in North America, is a neuro-degenerative disease that is characterized by muscle spasticity, rapidly progressive weakness due to muscle atrophy, and difficulty in speaking, swallowing, and breathing. ALS is the most common of the five motor neuron diseases.
Most who suffer from the disease have an average survival time of three to five years, and only an estimated four percent survive longer than ten years.
Another participant in the event was Quinton's sister Mya, who wanted to address one of the recent criticisms of the ALS Ice Bucket Challenge – the wasting of water. Mya told The Independent that Suzie's Place restaurant recycles the run-off water from their air conditioning unit to water their gardens, and they used that same recycled water for the challenge.
Before pouring the icewater-filled buckets over their heads, each participant nominated others to take up the challenge including some local businesses. The Meaford Independent, Ted's Range Road Diner, the Knights' of Meaford hockey team, Muxlow Pharmacy, and the entire staff of Miller Waste was challenged by the Suzie's Place staff to take on the challenge.
Nearly $1.5 million has been raised across Canada for the ALS initiative. In the United States the initiative has raised more than $50 million.
Donations can be made at Suzie's Place restaurant, where more than $100 had already been collected in the two hours prior to the challenge.

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text:
Station Urle is een spoorwegstation in de Poolse plaats Urle.

Urle

redpajama_set_name: RedPajamaWikipedia


text:
Abstract Comics and Visual Language
Abstract Comics is a new collection of non-representational comics by a variety of authors, including my esteemed blogging colleague Derik Badman. Besides being a beautifully done work of artistry and imagination, among particular crowds it spurs the question "If these are comics, then what 'are comics'?"
To this end, the book (and the nature of the contents in general) makes a good conversation piece. They also make a great example of how to distinguish the difference between "Comics" and my notion of "Visual Language", which is made clearest by teasing out just what parts of cognition these comics engage.
First, we should ask the question "Are abstract comics of this sort 'comics' at all?" I would have to say "YES" — simply because they call them so. However, they are not instances of visual language.
To repeat my theory… Visual language is a system of patterns (from people's heads) in that expresses concepts through the graphic modality using sequential images. So, visual language uses three interlocking cognitive systems:
1. Graphic modality
2. Meaning
3. Sequential structure (i.e. grammar)
Like spoken or signed languages, this system is culturally relative, meaning that different cultures use different visual languages (for example, "standard" manga style versus "standard" superhero style dialects), and this system is used socioculturally in comics paired along with written languages.
Comics are written in visual language (± text) the same way that novels are written in English. Novels aren't English, and Comics aren't visual language. (This equation would essentially be McCloud's position, that comics "are" sequential images).
Given this, abstract comics most definitely are comics — because they call themselves comics, they are formatted like comics, they are made by people affiliated with comics, sold in comic stores, etc. They satisfy most all the sociocultural aspects that one would expect comics to fulfill.
However, they do not use visual language. They don't use representational depictions that reflect patterns in people's heads. They don't seem to have any sort of grammar of narrative structure. They don't depict any meanings at all. In other words, they use just one of visual language's structures from our cognitive system*:
3. Sequential structure (i.e. grammar)**
They are merely playing with the graphic modality in a sequential way that entirely lacks meaning (in the conceptual sense, not necessarily the "artsy" sense).
As a result, abstract comics make a great example of comics (and art) that lack visual language. This is the inverse of something like an airplane safety card, which is representational, but lies outside the sociocultural category of calling it "comics." I should say also, that this isn't a bad thing — it's quite fun, clever, and creative, and further goes to my point that these notions of "comics" and "visual language" are separate.
* Interestingly, the one cognitive structure they do use though, is visual language's navigational system for how to move through a page layout. In many ways this is an ancillary system to the primary VL system for expressing meanings in sequence, but it is curious that this seems to be one of the formal ways in which abstract comics get to call themselves "comics".
** I haven't analyzed the pieces in the book enough, but it is not inconceivable that graphic sequences with no meaning could still retain a narrative grammar. For example, Action Star substitution incorporated into a sequence with purely visual surrounding panels could lend to this result.
After reading this post, and your "Un-Defining Comics" article, I'm wondering why you stop at define Visual Language with the three criteria listed here and what exactly you mean when say that Abstract Comics don't fulfill the criteria of meaning.
For example, how do you define the word "the"? It is a definitive article, but what does it mean? If you look at the problem this way, doesn't the "meaning" aspect of visual language become more complicated?
However, this is not my main concern with your definition. My main concern is with how you are defining meaning. While looking at an abstract painting or drawing, I find a lot of meaning, but not something that I can explain in text. How can someone look at something and not gain some meaning, even if it is subconscious?
Finally, I'm not sure that 'grammar' is a necessary part of any language. Within linguistics, there is a set definition of language that is usually defined by the International Phonetic Alphabet, but I'm not sure what grammar can mean for visuals/images. It seems like an attempt commodifying art – which wants to pervert and disrupt traditional (Western) logic (see JF Lyotard, among others). Since you also mention sequential structure, what is unstructured about abstract comics/art? Isn't a single-panel work structured in some way?
Check out Aaron Meskin's article "Defining Comics?" from the Journal of Aesthetics and Art Criticism (2007). The basic argument is that we need to stop trying to define comics and play with the form.
In a way, this is a very modernist approach to visuality, trying to define and control art that makes meaning.
Thank you for the reply. I don't mean to say this negatively, but it doesn't sound like you understand the linguistic understanding of language.
First, IPA is not a way of "defining language" — it is a way of describing sound systems. All natural languages use a grammar (syntax), which is the thing that sets apart gestures (not language) from sign language (language). I know several words in Korean, but without knowing the grammar no one in their right mind would say I "speak Korean."
"Meaning" as I discuss it here refers to "semantics" or "conceptual structure" that is the propositional information of a reference. Abstract art of all kinds might express emotive or visual information, but it is not conceptual. That is, there is no "reference."
Your example of the "the" is not technically a "word" (it's a clitic) and in its function as a definite article it modifies the meaning of other words. Not all aspects of meaning are concrete.
Abstract art has no conceptual meaning at all (though, as I said, it does have "artistic/interpretive" meaning).
Finally, I've read Meskin's article. I thought it was decent, though partially a cop out.
I should also state that in no way have I tried to "define and control art that makes meaning." I've merely teased out the issues involved and am fully supportive of art that uses all types of expression.
Oh, I should also note that on your first comment, Visual Language certainly has other traits than those three, but those are the primary fields for any type of language:
1. Modality (verbal, graphic, manual)
2. Meaning (semantics – i.e. "Reference")
3. Grammar
See my above post for why abstract comics don't fulfill the criteria of meaning.
Walaka of Earth 2 says:
Neil, I think there's an internal contradiction in this piece. First you say:
"Comics are written in visual language (± text) the same way that novels are written in English" and then you show that abstract comics do not, in fact, use visual language. Normally this would work out to Abstract Comics ≠ Comics.
But you also say "[…]abstract comics most definitely are comics — because they call themselves comics."
By this logic, if I write a novel in a coding system that is clearly not English or any other written language, one which has no meaning or sequential structure, it's still a novel (an abstract novel?) if I say it is, if I am a writer, if it's formatted like a novel, and it's sold in bookstores.
Isn't that patently absurd, or at least stretching the definition of "novel" beyond any usefulness?
And isn't that what you are doing to the term "comics" as well?
I appreciate your constant and relentless distinction between "visual language" and "comics" and what each should or can describe, but as a critic of an art form, you're a very good linguist. There are questions about what "comics" is that are worth asking, questions that either don't concern themselves with the detailed structure of visual language or which can dovetail nicely with it, similar to questions about poetry and prose that aren't in the province of linguistics.
Like the man with a hammer who sees every problem as a nail, you seem to want to answer every query about comics with a definition of visual language. The question "Are abstract comics of this sort 'comics' at all?" calls for discussion that would be be useful and illuminating to students of the form, not merely a peremptory "yes" from the college of linguistics.
I so highly value your work and eagerly anticipate your dissertation; I think you add a valuable voice to the ongoing conversation. I just wish that, more often than you seem to do, you would remember that just as not every question about prose can be answered in terms of generative grammar, not every question about comics can be answered in terms of visual language.
Sorry for the long reply. Thanks for all your work.
Thanks for the comments Walaka.
Perhaps I should have clarified my statement that "comics use visual language" with a "mostly" thrown in before the "use" (I had deleted it in editing). The point of that statement is to depart from McCloud's notion that the two are not the same thing.
This is not a definition of "comics", which is why I don't define "comics" as "being visual language" which is not at all what I believe. The only logical problem comes when you define "comics" as "something written in visual language" (or imply the reverse) — which I don't.
In fact, by my standards, nowhere in this piece do I attempt to "define comics" at all except to say that it is socioculturally defined (i.e. not by any distribution of sequential/individual images and/or text).
Some comics don't use visual language — that's the reason for saying that the two things are different, and that abstract comics exist without needing to use visual language.
And, that's the whole point of this post: the two notions are different, and defining each does not rely on the other. Indeed, I would even go so far as to say that one of the main reasons abstract comics are great is because they don't use visual language. And, the grand discussion emerges from how they challenge people to recognize that separation.
Damian Duffy says:
Since my linguistics knowledge is admittedly sketchy at best, please excuse any misunderstanding of your post, but I don't think it's accurate to say that abstract comics entirely lack meaning in the conceptual sense. Rather, it seems to me that conceptual meaning is there, just less fixed. For example, I recall Andrei Molotiu stating that someone viewing one of his pieces had interpreted it as a narrative about invading aliens. The same piece might also be construed as a depiction of the lives of microscopic organisms. It seems as though the sociocultural links to to comics and the use of comics layouts in abstract comics implies a narrative grammar even if one is not made explicit through identifiably representational imagery. There is, in my experience, still an illusory sense of some sort of "movement" or passage of "time" in many abstract comics. In my opinion, abstract comics don't delineate a split between comics and visual language so much as reify the conflation of comics and visual language (i.e. McCloud's use of comics as a singular term).
In fact, the term "abstract comics" implies a play on this conflation of the narrative (comics, in their traditional socio-cultural construction as popular culture) and the non-narrative (abstract art, as a sociocultural signifier of artistic form devoid of narrative content.)
Damian, nice comments. I would agree. Abstract comics use graphics in a way that is not "purposefully" meaningful, but meaning can be interpreted the same way that you can see things in clouds or abstract paintings.
This is finding concepts where they weren't put — like hearing "John is dead" when playing the Beatles record backward. It's not actually said, but can be "heard" if the listener puts their intention to hear it.
Leon1234 says:
Great and wonderful, informative blog!:)
Qim Karna says:
beside using iconics or figurative drawings or representational graphic, comics also using abstract graphic representation (non-representational).
The strokes, lines (speed, radial, etc), or any arbiter graphic expression.
Take a closer look to japanese comics 'manga', they used many abstract graphics to convey 'feeling'
So, imho comics is not just construct by 'language' but also non-language.
The technique (art) to tell something through comics' pictures/drawings/graphics need to be 'socialized', so the new reader get used to its symbolicism and get trained his/her ability of visual literacy.
Thanks for the comment. The non-figurative aspects of meaning like speed lines and things are still part of the visual language's vocabulary. Those are just things with symbolic reference instead of iconic reference.
See my paper "A Visual Lexicon" for a larger explanation of all the parts of this visual language vocabulary.
Blaise Larmee says:
it it possible that abstract comics use a language that is not shared by the reader? a language that has no references outside itself? just curious. cometscomets
Ernesto Priego says:
Hello Neil,
First of all let me say I have followed your work for some time. I have also quoted you in my PhD dissertation. We are both interested in similar things, obviously…
This post made me cringe a couple of times, though. Let me focus on the one that I find the most unsettling:
"[Abstract comics] do not use visual language. They don't use representational depictions that reflect patterns in people's heads."
In this same sense, would you say that abstract painting or experimental writing does not *use* visual language? In other words, would you say that a painting like this one does not *use* visual language merely because it is not figurative?
This is a complex issue, but I think it can be discussed in simple terms. Alphanumeric symbols, for example, do not necessarily represent anything concrete. They are not referents. Even a single word, out of a syntactic structure, can have equivocal referents ("chip," for example, can many different referents, depending on many conditions). It is syntax, and not vocabulary or individual symbols, what provides referential meaning.
I fail to grasp why your understanding of meaning is limited to figurative (should I understand "anthropomorphic?) referentiality.
What provides meaning to many of the comics included in Abstract Comics is not anything strictly extratextual (the fact they have been called "comics," or sold in comics shops, or done by people who do other types of comics as well), but the fact that they use the general syntax of comics (in a nutshell, still panels meant to be read in a particular/suggested sequence). The content of individual panels (what Barbieri would call "micronarrative units") is visual (it's certainly not musical), and their disposition in grids/layouts suggest both an existence in space and time. The visual signs contained in the individual panels and composing the pages do transmit messages, and an interpretive process is carried out by the reader. How can this not be meaning, and how can it not be an expression of visual language?
Ernesto, thanks for the comment.
I use the term "visual language" to mean something very specific — not in a general "visual communication" way that is vogue (and makes me cringe at the lack of knowing what language is).
Abstract comics and art, like the one you linked to, are definitely NOT visual language. The only patterns they might represent are, as I said in the post, ones related to "graphic structure."
Fore example, think of Charles Schulz's Peanuts. He draws consistent patterned lines and curves for particular ways of representing particular things. These are patterns in his head of how to draw faces, hands, etc.
Now, if you subtract away the meaning — anything concrete (characters) or symbolic (i.e. non-figurative: speed lines, action stars, etc.) that actually has meaning to it — then all you're left with is the graphic patterns. This would be the same as using sounds from language with no reference in them (i.e. "nonsense" words like "flark, smiggit, or plonaz" which use English phonology, but no meaning). Letters are the same — on their own they are visual patterns connecting only to sound, but no meaning.
This is what abstract comics do. They use visual shapes and sometimes patterns, but those patterns have no reference (be it concrete or symbolic).
I do agree with you that some aspects of reference do come out of sequence. However, just because there are panels does NOT mean that there is meaning, nor that sequential panels mean there is sequential meaning. There are two parts to this:
1) Arrangements of panels in a layout are read through a system of navigational rules that tells you which panel should be read next. This is connected to, but does not rely on, meaning. (See my paper "Navigating Comics").
2) In the actual creation of meaning, it is a fallacy that panels on their own insinuate the passage of time and space. Panels serve only as attentional units, not time/space units. (See my papers "TimeFrames…Or Not" and "A Visual Lexicon" along with the podcast "The Function of Panels"
Thanks again for your comments.
Thanks for your reply, Neil. I can see how your understanding of the term "visual language" is very specific, and in that sense I understand your argument.
Would you be willing to consider a different meaning of "meaning," though?
In other words, why limit "meaning" to what is referential? I may be wrong, but it's as if you were applying the verifiability principle of logical positivism to the study of comics…
Your use of meaning seems to refer to "cognitive meaning." Even cognitive meaning admits denotation and connotation. Perhaps in abstract art, or in "mere" graphic patterns, meaning is constructed through denotation, in the absence of literal referentiality?
In certain poetry, for example, "nonsense" words *and* their graphic disposition on the page collaborate in the transmission –if not construction– of meaning. I would suggest it is similar in comics.
I appreciate the conversation and the thought-provoking posts. Thank you.
Ernesto — glad you're enjoying the discussion. That's why I maintain the blog!
To me, there is no meaning without some form of reference. Unless there is some concept in the brain that is engaged, it does not have meaning.
Of this, there is two types though, what I call in the post "conceptual" vs. "artsy" meaning. Here's how I described these in another discussion:
The difference that I make between "conceptual meaning" and "artsy meaning" is in some sense a degree of immediacy. Conceptual meaning is just plain straightforward meaning — how words and images express reference. "Artsy meaning" is interpretive, and often overlain onto conceptual meaning (when present), often a "post hoc inference".
For example, an image springs to mind from Thompson's Blankets where the main character is standing with arms outstretched and casting a shadow. The conceptual meaning is just that: "guy with arms outstretched casting shadow." But, the pose as a cross gives us "symbolic" meaning associating to Christ and the character's religious conflicts — this is the "artsy" meaning.
Artsy meaning is less straightforward without this sort of direct imagery, like when people make up a story or interpretation of what some painting/story/etc is "about" above and beyond what is directly given (i.e. "it's a painting about the complexities of living in a harsh ghetto" as opposed to "it's a man holding a basketball in the projects" or something like that).
As I say in the post, abstract comics and art don't have this conceptual meaning.
But, as Damian notes above, we might try to fill in conceptual meaning where there isn't any already. In this case, I'd say the "artsy" meaning is an act of coming up with conceptual meaning, the same way as you can imagine faces or objects in clouds.
It might be appropriate to say this is denotative vs. connotative, though to me this latter "artsy meaning" is a very different process than in referential conceptual meaning. It is often conscious, and often post-hoc.
I hope that long answer makes sense…
Thanks for your reply!
Considering you are already reading Blankets (which implies a series of given circumstances, including understanding English, knowing of indie comics, etc.) wouldn't it be some kind of aphasia not to be able to get the Christ connotation?
What you refer to as "artsy" seems to be the metaphoric/paradigmatic axis, the "conceputal" the syntagmatic axis.
I find it hard to reconcile a separation of both.
Obviously, this is what I mean by "aphasia".
If you want to think about these as being paradigmatic/syntagmatic, that's fine I suppose. I personally don't subscribe to this sort of semiology/structuralism (the cognitive revolution pretty much ushered it out).
Artsy meaning doesn't have to be metaphorical. If you go to "metaphor" in Lakoff's sense, there are metaphors at work in the very basic conceptual meanings.
Neil, it just hit me that what you are saying is that comics *are* not a language *in themselves*. (I'm slow…)
Since you don't personally subscribe to structural semiology, I assume you don't agree with people like Umberto Eco, Luis Gasca, Daniele Barbieri or Roman Gubern when they wrote about "the language(s) of comics."
I am not discussing the difference between "comics" and "visual language" as you define it. I am talking about "comics" being a language in themselves.
I would suggest all comics share a particular modality, meaning (if understood more broadly than in the cognitive sense you subscribe to) and grammar.
For me, what's been called "abstract comics" is the equivalent to, say, Luciano Berio's or John Cage's music. What they did *is* music, but not in the same way than, say, Mozart or the Beatles…
It is *music* not because it was (not without scandal) socioculturally agreed as music –you can find Berio's CDs in the music section of shops and libraries– but because they "speak" the language of music, and therefore *are* music…
Of course that the discussion now would be if there's "conceptual meaning" in music… if there's not, then it's not a language… and I guess it is here where we have our main disagreement.
I wonder how you feel about object-oriented philosophy. My preference to speak of a poetics of comics scares me away from any attempt at fixing referential meanings.
Thank you again for the conversation.
afdumin says:


text:
Q: Hover Effect Looks Buggy ( Microsoft Edge ) I have a Problem, in Edge this Hover Effect Looks realy bad :(

Microsoft Edge:
Link Hover GIF (imgur)

Google Chrome:

Link Hover GIF ( imgur )
In Google Chrome it looks fine, but as soon as I try Microsoft Edge it looks very shitty. Is there a way to fix it?
Code:
HTML

Problem Title

Date

105,00&€
</div

CSS

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}
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  box-sizing: border-box;
  margin-bottom: 35px;
}
@media screen and (min-width:640px){
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@media screen and (min-width:1000px){
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.uk-panel-space .mod-ohanah--events .event--event__mod {
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  height: 260px;
}
.mod-ohanah--events .event--event__mod__item:focus {
  outline: none;
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}
.mod-ohanah--events .event--event__mod__item:hover {
  background: #f14a70;
  color: #FFF;
  text-decoration: none;
}

.mod-ohanah--events .event--event__mod__item .event--mod__title {
  font-size: 20px;
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  transition: all 0.667s cubic-bezier(0.16, 1, 0.29, 0.99);
}
@media screen and (min-width: 768px){
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    font-size: 16px;
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}
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}
@media screen and (min-width:1220px){
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}

.uk-panel-space .mod-ohanah--events .event--event__mod__item .event--mod__title {
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}
.mod-ohanah--events .event--event__mod__item:hover .event--mod__title {
  color: #FFF;
}

.mod-ohanah--events .event--event__mod__item .event--mod__date {
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}

.mod-ohanah--events .event--mod__price {
  line-height: 38px;
  padding: 0 18px;
  background: #f4f4f4;
  box-sizing: border-box;
  border: 1px solid transparent;
  font-size: 14px;
  font-weight: bold;
  color: #797979;
  position: absolute;
  bottom: 30px;
  left: 35px;
  transition: all 0.667s cubic-bezier(0.16, 1, 0.29, 0.99) !important;
}
.mod-ohanah--events .event--event__mod__item:hover .event--mod__price {
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A: Maybe you should try adding
transition: background 0.667s cubic-bezier(0.16, 1, 0.29, 0.99), color 0.667s cubic-bezier(0.16, 1, 0.29, 0.99);

Refer to each property that needs to be transitioned
In stead of
transition: all 0.667s cubic-bezier(0.16, 1, 0.29, 0.99);

A: This Problem got fixed with the new Fall Creators Update.

redpajama_set_name: RedPajamaStackExchange


text:
\section{Introduction}

During the last decades our knowledge of gravity has extremely been improved with general relativity (GR) remaining our best classical theory to describe it. Some inconsistencies or debates in the cosmology community rise from time to time, such as the Hubble constant tension nowadays, but they are in no way a direct test of GR. All direct tests are consistent with the theory, see e.g. \cite{Will:2014kxa}.
On the other hand, GR is a classical theory and therefore partial. It is for example geodesically incomplete for most of its solutions \cite{Hawking:1973uf} like black holes which contain spacetime singularity. Also, some theoretical arguments challenge our knowledge in cosmology and the existence of the cosmological constant. Recently, a lot of attention has focused on the String Swampland \cite{Vafa:2005ui,Palti:2019pca} which rejects any de Sitter solution \cite{Agrawal:2018own} and therefore the existence of the cosmological constant. The origin of the recent acceleration of the universe could be due to a scalar field. This would be a very interesting promotion of the relevance of scalar fields in the dynamics of the universe. At the same time, many studies try to see if scalar fields could be locally observed, and what are their effects around black holes. For example, we can ask if we could observe any deviation from Kerr black hole by measurement of quasi-normal modes \cite{Giesler:2019uxc}. Even if the answer is, at present time, negative, quintessence and their extensions with non-standard kinetic terms, attracted considerable interest. It is rather common for effective field theories to have scalar fields and non-linear terms, such as e.g. the ones originated from D-branes models \cite{Garousi:2000tr,Bergshoeff:2000dq,Sen:2002in}.

The first non-linear model of this type has been proposed in 1934 by Born and Infeld \cite{Born:1934gh} with a non-linear electromagnetic field to avoid the infinite self-energy of the electron in classical electrodynamics. For our concern in this paper, the models originated in cosmology in the context of inflation \cite{ArmendarizPicon:1999rj} and later adapted to dark energy \cite{ArmendarizPicon:2000ah}. These models can also be used to describe dark matter \cite{Sen:2002in,ArmendarizPicon:2005nz}. This last approach permits us to approximate dark matter by a non-linear quintessence field and therefore identify the possible effects of dark matter on gravitational collapse.

The numerical study of spherical gravitational collapse has a long history which began with the work of the collapse of ideal fluid spheres with an equation of state $P=2\rho/3$ \cite{May:1966zz}. They found that collapse could lead to the formation of a black hole or a bounce according to initial conditions. Many new codes have been later developed with a focus on applications to realistic stellar collapse. But there has also been considerable interest into more theoretical problems such as critical phenomena. Choptuik \cite{Choptuik:1992jv} has shown that if $p$ is a parameter describing some aspect of the initial distribution of scalar field energy, there exists a critical value $p^\star$ which denotes the threshold of black hole formation. For $p<p^\star$, the scalar field disperses to infinity while for $p>p^\star$ black hole forms. In the supercritical regime, meaning for $p>p^\star$ but very close to the threshold, a universal behavior appears (i.e. independent of the initial data) relating the mass $M$ of black holes to a universal scaling behavior
\begin{align}
M\propto (p-p^\star)^{\gamma}~,~~~\gamma\simeq 0.37
\end{align}
This solution has been repeatedly verified, also by using a fully 3D code \cite{Healy:2013xia}. But as in critical phenomena, there exist classes of universality. Adding a mass term to the theory \cite{Brady:1997fj}, which introduces a length scale, produces also a universal behavior but with a different scaling parameter $\gamma$. See also studies with a massive complex scalar field \cite{Hawley:2000dt}, with radiation fluid \cite{Evans:1994pj} or with extra dimensions \cite{Sorkin:2005vz}.

In this paper, we study a natural extension of the work performed by Choptuik, by studying models known as K-essence. We will consider the generic theory and summarize the various conditions for the viability of these models at classical as well as quantum level. We will derive the characteristics for these models and therefore their hyperbolicity. In section 3, using a spherically symmetric spacetime we will obtain the constraints and evolution equations. For numerical purposes, we will assume a particular K-essence model which will be studied in the weak as well as the strong gravitational regime before conclusions.

\section{K-essence}

Let us consider the following action
\begin{align}
\mathcal{S}=\int {\rm d}^4x \sqrt{-g}\Bigl[\frac{R}{2}+K(\phi,X)\Bigr]
\end{align}
where $\phi$ is a scalar field representing the matter sector, $X=-\frac{1}{2}\partial_\mu\phi\partial^\mu\phi$ is the canonical kinetic term and $K$ is a generic function of the scalar field and the kinetic term\footnote{Note that our metric signature is $(-,+,+,+)$}. Considering only the sub-class of scalar-tensor models of gravity, more generalized extensions have been constructed, from Galileons \cite{Nicolis:2008in}, to Horndeski \cite{Deffayet:2009wt,Kobayashi:2011nu,Horndeski:1974wa} to beyond Horndeski \cite{Zumalacarregui:2013pma,Gleyzes:2014dya,Gleyzes:2014qga}. Even if these models seem to have been finely constructed, they appear to have a well-posed Cauchy problem only in high symmetrical backgrounds such as Friedmann or spherically symmetric spacetimes. But generically, they suffer from a major problem \cite{Papallo:2017qvl}. The equations of motion are not strongly hyperbolic for most Horndeski models except K-essence which arise as the most legitimate sub-class of scalar-tensor theories.

In this paper, we will consider models where the action is a function of $X$ only, it inherits an additional shift symmetry i.e. an  invariance under constant translation in field space, $\phi \rightarrow \phi +c$, for any constant $c$. It is important to notice that demanding the existence of  stationary configurations requires shift symmetry \cite{Akhoury:2008nn}, sometimes after a field redefinition. This restriction makes the model equivalent to a perfect fluid with no vorticity. In fact, the variation of the action in shift symmetry models gives\footnote{We consider $G=c=1$} $G_{\mu\nu}=8 \pi T_{\mu\nu}$, where the energy-momentum tensor is defined as
\begin{align}
T_{\mu\nu}=K_{,X}\partial_\mu\phi \partial_\nu\phi+g_{\mu\nu}K
\end{align}
It is well known that this stress-energy tensor can be put in a hydrodynamical language,
\begin{align}
T_{\mu\nu}=(\rho+P)u_\mu u_\nu +P g_{\mu\nu}
\label{eq:Tmunu}
\end{align}
where we define an effective four-velocity $u_\mu=\partial_\mu\phi/\sqrt{2X}$, density $\rho=2XK_{,X}-K$ and pressure $P=K$. We see also that the pressure is a function of the energy density only, $P=P(\rho)$. Therefore, choosing an action is equivalent to specifying an equation of state (EoS) for the equivalent hydrodynamical model. For example, considering $K=(\alpha X^{1/2\beta}-A)^\beta$, the EoS is $P=A\rho^{(\beta-1)/\beta}$, a polytropic law similar to various models describing neutron stars (without the anisotropic stress tensor).
Notice also that $K(X)$ models can be related to canonical complex scalar field theories \cite{Babichev:2018twg} where the potential of the complex scalar field is defined by $K(X)$. More than an equivalence between these theories, it is an extension or UV completion. In fact, the complex scalar field can be seen as a theory with 2 real scalar fields with an $O(2)$ symmetry. It's only when one of these fields is frozen, that the model reduces to K-essence.

For shift-symmetric K-essence models, the speed of sound for small perturbations around a given background coincide with the usual definition of the sound speed for the perfect fluid \cite{Garriga:1999vw},
\begin{align}
c_s^2=\frac{K_{,X}}{K_{,X}+2XK_{,XX}}\equiv \frac{\partial P}{\partial \rho}
\end{align}
The variation of the action wrt the scalar field gives
\begin{align}
\label{eq:KG}
\nabla_\mu(K_{,X}\nabla^\mu\phi)=\tilde{g}^{\mu \nu}\nabla_{\mu\nu}\phi = 0
\end{align}
where the effective metric is defined as
\begin{align}
\label{eq:gtilde}
\tilde{g}^{\mu\nu}=g^{\mu\nu} K_{,X}-K_{,XX}\partial^\mu\phi\partial^\nu\phi
\end{align}
or the inverse metric
\begin{align}
\tilde{g}_{\mu\nu}=\frac{1}{K_{,X}} g_{\mu\nu}+c_s^2\frac{K_{,XX}}{K_{,X}^2} \partial_\mu\phi\partial_\nu\phi
\end{align}
A theorem due to Leray \cite{Wald:1984rg} proves that the generalized Klein-Gordon equation has a well posed Cauchy problem if the metric is Lorentzian which has been proved to be equivalent to $c_s^2>0$ \cite{ArmendarizPicon:2005nz}. This condition is often referred to as the classical condition. On the other hand, a stronger condition related to the Hamiltonian of field perturbations to be positive definite (in cosmological context) implies $K_{,X}>0$ and $K_{,X}+2XK_{,XX}>0$ \cite{ArkaniHamed:2003uy}, this condition is often dubbed in the literature as the quantum stability condition, because if other sectors such as gravity or standard model particles couple to scalar field described by an unbounded Hamiltonian from below, it would create states of atoms which never decay if excited, a situation never observed in nature (a more careful discussion is proposed in \cite{Babichev:2018uiw}).

K-essence models are considered as an effective low energy description of some more fundamental theory. Therefore, we should impose it to be consistent with basic requirements of quantum field theory, such as Lorentz
invariance, unitarity, analyticity... \cite{Adams:2006sv,Nicolis:2009qm}. Considering the tree-level scattering amplitude, between two massive particles on a flat background, these restrictions impose $K_{,XX}>0$ \cite{Melville:2019wyy}. All these conditions imply non-superluminal propagation $(c_s^2<1)$.

In summary, we consider models of gravity defined by a shift-symmetric K-essence action with conditions $K_{,X}>0$ and $K_{,XX}>0$. Notice that gravitational collapse for such models have been previously considered \cite{Leonard:2011ce} but with models violating one of these conditions. For there models, a sonic horizon ($\tilde{g}^{rr}=0$) could be defined inside the luminal apparent horizon ($g^{rr}=0$) during gravitational collapse because the model allow superluminal propagation. As it has been shown for the first time in \cite{Babichev:2006vx}, perturbations of the scalar field could escape from the inside of the black hole defined by the luminal apparent horizon without violating causality, because they emerge outside of the sonic horizon. By imposing our conditions, we exclude these situations. The sonic horizon will be always larger than the luminal apparent horizon and might merge together in the future.

Notice that these conditions imply that null energy conditions will not be violated, which turned out to be central in singularity theorems. The weak energy condition plays an important role, it implies that matter has always a non diverging effect on congruences of null geodesics. It has been very influential, e.g. the area theorem proved by Hawking \cite{Hawking:1973qla,Hawking:1973uf} states that if matter satisfies the null convergence condition
or equivalently in general relativity the null energy condition\footnotetext{For every null vector $n^\mu$, the null convergence condition is defined as $R_{\mu\nu}n^\mu n^\nu\geq 0$ while $T_{\mu\nu}n^\mu n^\nu\geq 0$ defines the null energy condition}, the area of the black hole event horizon can never decrease, statement very similar to the second law of thermodynamics \cite{Ashtekar:2004cn}.

\section{Model and equations}

In polar-areal coordinates \cite{Choptuik:1992jv}, the metric takes the form
\begin{align}
{\rm d}s^2 = -\alpha(t,r)^2 {\rm d}t^2+a(t,r)^2 {\rm d}r^2+r^2({\rm d}\theta^2+\sin^2\theta {\rm d}\phi^2).
\end{align}
If simpler, this choice is not the most appropriate because it is valid until it forms a trapped surface. Unfortunately, as we will see a trapped surface associated with the effective metric might form before the normal trapped surface, which will break the numerical evolution before the formation of the black hole. The sonic horizon forms when $\tilde{g}^{rr}=0$ which always forms before the apparent horizon defined by $g^{rr}=0$, which can be seen easily from eq.(\ref{eq:gtilde}) if we assume the conditions $K_{,X}>0$ and $K_{,XX}>0$. Also, in general, to solve the gravitational collapse we foliate the spacetime with spacelike hypersurfaces, a  breakdown of the evolution occurs when the hypersurface of constant time becomes null, i.e.
\begin{align}
g^{\mu\nu}\nabla_\mu t \nabla_\nu t = 0 ~~~|| ~~~\tilde{g}^{\mu\nu}\nabla_\mu t \nabla_\nu t = 0
\end{align}
which implies $g^{00}=0$ or $\tilde{g}^{00}=0$. Using eq.(\ref{eq:gtilde}), it is also trivial to see that following our conditions, if $g^{00}=0$ occurs, it will always happen before $\tilde{g}^{00}$ vanishes. Therefore, we conclude that our numerical evolution will fail if $g^{00}=0$ or $\tilde{g}^{rr}=0$. Even if this coordinate system is not the most appropriate, we will be able to deduce some interesting results.

In order to reduce the K-essence field equation of motion to a system of first-order PDEs, we define two auxiliary fields \cite{Choptuik:1992jv}
\begin{align}
\Phi(t,r) &\equiv \partial_r \phi(t,r)\\
\Pi(t,r) &\equiv \frac{a(t,r)}{\alpha(t,r)}\partial_t\phi(t,r)
\end{align}
The $tt$- and $rr$-components of Einstein equation gives
\begin{align}
\label{eq:constraint1}
\frac{a'}{a}+\frac{a^2-1}{2 r} &=4\pi r \Bigl(K_{,X}\Pi^2-a^2 K\Bigr)\\
\label{eq:constraint2}
\frac{\alpha'}{\alpha}-\frac{a^2-1}{2 r} &=4\pi r \Bigl(K_{,X}\Phi^2+a^2 K\Bigr)\\
\text{with}~~X &=\frac{1}{2a^2}\Bigl(\Pi^2-\Phi^2\Bigr)
\label{eq:X}
\end{align}
These equations contain no time derivatives, so they are constraints, they must be satisfied at each time. These are the same equations than the Hamiltonian and Momentum constraints obtained after a $3+1$ decomposition of Einstein equations. The dynamics of the system is given by the definition of the auxiliary fields which imply
\begin{align}
\label{eq:Phi}
\dot\Phi = \partial_r\Bigl(\frac{\alpha}{a}\Pi\Bigr)
\end{align}
The second evolution equation is given by the generalized Klein-Gordon equation (\ref{eq:KG}) and the $tr$-component of the Einstein equation
\begin{align}
\label{eq:Pi}
\Bigl(K_{,X}+K_{,XX}\frac{\Pi^2}{a^2}\Bigr)\dot\Pi = \frac{1}{r^2}\partial_r\Bigl(r^2\frac{\alpha}{a}\Phi K_{,X}\Bigr)+8\pi r \frac{\alpha}{a}\Phi \Pi^2 X K_{,X} K_{,XX}+K_{,XX}\frac{\Phi \Pi}{a^2}\partial_r\Bigl(\frac{\alpha}{a}\Pi\Bigr)
\end{align}
For numerical purposes, we need to define a particular model. We choose the simplest extension of quintessence, which fulfill the previous conditions
\begin{align}
K(X)=X+\beta X^2
\end{align}
The constant $\beta$ could take any value but as mentioned previously, we need to impose the condition $K_{,XX}>0$ which suggests $\beta>0$. This condition which implies a standard UV completion of the theory, turns out to be also related to hyperbolicity of the equations and therefore causality. Maybe a deep relation could be obtained between hyperbolicity of classical equations and standard Wilsonian field theory description of the quantum version.

To integrate our system of equations, we define an initial profile of the field $\phi(t=0,r)$ implying $\Phi(0,r)$ to which we add a second initial condition $\Pi(0,r)=0$. These two functions are sufficient to integrate the constraint equations (\ref{eq:constraint1},\ref{eq:constraint2}) by assuming boundary conditions. Regularity of the system imposes $a(t,r=0)=1$, and without loss of generality we choose $\alpha(t,r=0)=1$ which corresponds to choosing the time coordinate at $r=0$ to be the proper time. A change in this value corresponds to a trivial rescaling of the time coordinate and would have no physical consequences. Fourth order Runge-Kutta (RK4) method is used to integrate these constraint equations. These values of $(\alpha,a)$ are then entered into the evolution equations (\ref{eq:Phi},\ref{eq:Pi}) to find $(\Phi,\Pi)$ at the next time step with RK4. This process is repeated until the scalar field disperses to infinity and forms flat spacetime or until forms an apparent horizon. The two families of initial data that we adopt are
\begin{align}
&\text{Family A:}~~~\phi(0,r)=\phi_0 r^3 e^{-(\frac{r-r_0}{d})^q}\\
&\text{Family B:}~~~\phi(0,r)=\phi_0 \tanh\frac{r-r_0}{d}
\end{align}
where ($\phi_0,r_0,d,q$) are constants. For each family of initial conditions, we keep only $\phi_0$ as a free parameter, the others are fixed to $(r_0=20,q=2,d=3)$. The system is evolved between $r=10^{-50}$ and $r=50$ from $t=0$ until it forms an apparent horizon ($r_H$) featuring fixed mesh refinement. The r-spacing $\Delta r$ varies from the finest value near the origin to larger values of $r$ in 5 different sectors. Near the origin and until $r_H$ (which is approximately determined in a first run) the resolution is $\Delta r=10^{-4}$, this r-spacing is progressively increased 4 times until it reaches $10^{-2}$ at larger $r$. The time resolution is also fixed but satisfies the Courant-Friedrichs-Lewy condition $\Delta t=\Delta r/5$ where $\Delta r$ takes 5 different values as defined by each sector (from $\Delta r=10^{-4}$ to $\Delta r=10^{-2}$). All results are verified by modifying the resolution in space and time and for most of them we checked with a fixed mesh of $\Delta r=10^{-4}$ in all space. All results presented in the paper are stable under these tests.

We should emphasize that the energy-momentum tensor defined in eq.(\ref{eq:Tmunu}) describe an observer with four-velocity $u_\mu=\partial_\mu\phi/\sqrt{2X}$ and therefore in general case with a radial velocity. For that observer, the energy density could be negative. In fact, even for the simplest case where $K=X$, we would have $\rho=X$, which from eq.(\ref{eq:X}) and the initial condition $\Pi=0$ gives $\rho=-\Phi^2/2a^2$ which is at initial time, negative. In order to define the energy density measured by a static observer at position $r$, we would need a new four-velocity $n^\mu=(1/\alpha,0,0,0)$ and therefore for this observer an energy density
\begin{align}
\bar\rho=T_{\mu\nu}n^\mu n^\nu=2XK_{,X}+\frac{\Phi^2}{\Pi^2-\Phi^2}(K+2XK_{,X})
\end{align}
which at $t=0$ gives $\bar\rho=-K=-X>0$ for $K=X$.

\section{Characteristics}
Following standard textbooks \cite{Courant:1962}, we compute the characteristic structure of our system (see also \cite{Ripley:2019hxt}). It is sufficient to analyze the evolution equations of $(\Phi,\Pi)$ defined in eqs.(\ref{eq:Phi},\ref{eq:Pi}) in which we need to replace $(\alpha',a')$ from the constraint equations to reach a system of 2 equations of the following form $E^{(i)}[\alpha,a,w^{(j)},\partial_r w^{(j)}, \partial_t w^{(j)}]=0$ where $w^{(1)}=\Phi$ and $w^{(2)}=\Pi$. We introduce the principal symbol
\begin{align}
P^i_j(\xi_a)\equiv \frac{\delta E^{(i)}}{\delta (\partial_a w^{(j)})}\xi_a
\end{align}
where $(\xi_t,\xi_r)$ define the characteristic covector. By solving the characteristic equation defined by det$[P^i_j(\xi_a)]=0$, we deduce the characteristic speed as $c=-\xi_t/\xi_r$.
\begin{align}
\label{char}
c_\pm = \frac{-K_{,XX}a\alpha \Pi \Phi\pm a^3\alpha \sqrt{K_{,X}(K_{,X}+2XK_{,XX})}}{K_{,X}a^4+K_{,XX}a^2\Pi^2}
\end{align}
In the case of a canonical scalar field, $K=X$, we obtain $c_\pm = \pm \alpha/a$ which reduce to the characteristic speeds of GR and the equation is always hyperbolic. In the generic case, the sign of $K_{,X}(K_{,X}+2XK_{,XX})$ defines the character of the system. If positive, it is hyperbolic, when negative it is elliptic and if $K_{,X}(K_{,X}+2XK_{,XX})=0$ it is parabolic.
Notice that, this condition is similar to $\det \tilde g =0$ or equivalently to the sign of the eigenvalues of the effective metric $\tilde g$. Even if we impose the condition  $\beta>0$, the hyperbolicity of the equations can be lost after some time of evolution. In fact, the condition $K_{,X}(K_{,X}+2XK_{,XX})\equiv (1+2\beta X)(1+6\beta X)>0$ can be violated if $-1<2\beta X<-1/3$ (for any sign of $\beta$). Because we imposed $\beta>0$, this condition is violated if $X$ is sufficiently negative which translates into a model developing large enough space-like gradients ($\Phi>\Pi$ from eq.(\ref{eq:X}))\footnote{We thank the anonymous referee for suggesting this possibility}. This behavior was already predicted in \cite{ArmendarizPicon:2005nz, Rendall:2005fv}. But remained to know if for generic initial conditions, large space-like gradients of the solution could form. This was recently proved numerically to happen in \cite{Bernard:2019fjb}. But $\beta >0$ remains a better option which allows some initial conditions to develop without any loss of hyperbolicity, contrary to $\beta<0$ case.

\section{Numerical results}
\subsection{Weak field regime}
In the weak field regime, when $\phi_0\ll 1$, the scalar field bounces at the origin $(r=0)$ and then disperses to infinity. We see in Fig.(\ref{Fig:weak}) this behavior for 3 different time\footnote{Time is the iteration step and not proper time at $r=0$} and for 3 different values of $\beta=\{0,5,10\}$ for the 2 families of initial conditions. For $t=4000$ for family A and $t=1000$ for family B, the field is yet collapsing. Around $t=9500$ for Gaussian initial conditions and $t=10000$ for the second family of initial conditions the field bounces at $r=0$ and finally at a later time, the field disperses to infinity. We see that the parameter gives a small variation to the dynamics of the scalar field because of the weak regime studied in this section. Even if we can notice that for larger values of $\beta$, the field takes more time to bounce and therefore reaches infinity a bit later compared to $\beta=0$. Notice that taking larger values of the constant $\beta$ increases the mass of the spacetime and therefore we get closer to the threshold of black hole formation.

\begin{figure}
\includegraphics[scale=0.3]{Figures/fA_po_4000.pdf}
\includegraphics[scale=0.3]{Figures/fA_po_9500.pdf}
\includegraphics[scale=0.3]{Figures/fA_po_16000.pdf}
\includegraphics[scale=0.3]{Figures/fB_po_1000.pdf}
\includegraphics[scale=0.3]{Figures/fB_po_10000.pdf}
\includegraphics[scale=0.3]{Figures/fB_po_16000.pdf}
\caption{Scalar field profile $\phi$ in the weak field  regime, for $\beta = 0.0$ (solid line),  $\beta = 5.0$ (dashed line) and $\beta = 10.0$ (dash-dotted line). Upper panel is for Gaussian family type of initial conditions (Family A) while the bottom panel represents family B. \label{Fig:weak}}
\end{figure}

\subsection{Strong field regime}
We know that when the initial mass of the scalar field added in the spacetime is large, the collapse of that field produces a black hole. In this paper, we run simulations varying the amplitude of the K-essence scalar field $\phi_0$ from a value in the weak limit regime to a value where the final result of the evolution is the creation of an event horizon (collapse of the metric) or a sonic horizon (collapse of the effective metric). As we described previously, since our metric is not horizon penetrating, we cannot evolve the spacetime beyond the formation of any horizon. We found 4 different regimes. For $\beta=5$, we found situations described in Fig.(\ref{Fig:4regimes}) but which are generic for any value of $\beta \neq 0$. We found

\begin{itemize}
\item For an amplitude of the scalar field small, $\phi_0=3.7~ 10^{-6}$ for $\beta=5$, we observe the formation of a sonic horizon without being able to continue the simulation to know if a black hole forms. But it is interesting to notice that during a very short period of time, the simulation continues and this regime shows a loss of hyperbolicity related to the condition $K_{,X}+2X K_{,XX}=0$. This result is similar to \cite{Bernard:2019fjb}.
\item Increasing the amplitude of the initial field, the sonic horizon is present, but now the metric tends to collapse forming an event horizon with the same radius than the sonic horizon (within the accuracy of our simulation). This behavior is observed when $\beta$ parameter is not too strong. We do not observe any loss of hyperbolicity.
\item Increasing the amplitude of the scalar field, the evolution ends because of the formation of a sonic horizon, as in the first situation, but this time the dynamics of the metric seems clearly to indicate that black hole would form in the future and it seems that hyperbolicity will not be lost, the function $K_{,X}+2X K_{,XX}$ is far from vanishing.
\item For strong values of $\phi_0$ both metrics collapse at the same radius (within the accuracy of the numerical evolution). This behavior was observed for all values of $\beta$. The larger the value of $\beta$, the larger the value of $\phi_0$ producing this behavior. In this case, a BH forms and hyperbolicity is maintained until the end of the simulation.
\end{itemize}

In general, the formation of a sonic horizon indicates the formation of an event horizon in the future except in the first regime described earlier where the hyperbolicity is lost and therefore the BH never forms.

\begin{figure}
\includegraphics[scale=0.34]{Figures/po_37e-06.pdf}
\includegraphics[scale=0.34]{Figures/po_5e-06.pdf}
\includegraphics[scale=0.34]{Figures/po_6e-06.pdf}
\includegraphics[scale=0.34]{Figures/po_8e-06.pdf}
\caption{Last time evolution before formation of a horizon. The event horizon forms when $g^{rr}=0$ and the sonic horizon when $\tilde{g}^{rr}=0$. For $\phi_0=3.7~ 10^{-6}$ and $\phi_0=6 ~10^{-6}$ forms a sonic horizon while the event horizon is not yet formed, while for $\phi_0=5~10^{-6}$ and $\phi_0=8~10^{-6}$ both horizons form at the same time within our numerical precision.
\label{Fig:4regimes}}
\end{figure}

As shown in Fig.(\ref{Fig:4regimes}) depending on the initial value of the amplitude of the scalar field, we have either the formation of sonic horizon without the existence yet of an event horizon or both horizons (sonic and luminal) form and are indistinguishable. To illustrate these behaviors in a better way, in Fig.(\ref{FamilyAB}) we show the variation of the apparent radius defined either by the sonic horizon or by both horizons when formed simultaneously. We see e.g. for $\beta=5$ and for the Family A of initial conditions that we have 4 different regimes corresponding to the cases described in Fig.(\ref{Fig:4regimes}). The first and the third regime (in orange) corresponds to the formation of the sonic horizon while the second and the last (in blue) corresponds to the simultaneous formation of both horizons. Notice that for larger values of $\beta$ some regimes disappear.
In case of the Family A and $\beta=5$, the blue lines seem to form only 1 line if extended. In fact, we expect, in this case, the third regime where only a sonic horizon forms to evolve in time with an increasing sonic horizon until it forms the link between the second regime and the last. This behavior can be observed in all cases like e.g. $\beta=1$ for Family B, where the 2 blue lines seem clearly to be extended to each other.

Therefore, we expect the sonic horizon to be dynamical and evolve in time until the formation of the event horizon if hyperbolicity is not lost. Because in all our simulations, the spacetime seems to converge to the Schwarzschild solution, we expect both horizons to join in the future (see Appendix \ref{Appendix}). Therefore we presume that for larger time evolution, the radius of the black hole formed should describe a continuous function of the initial condition $\phi_0$ except if hyperbolicity is lost as shown in the first branch. Surprisingly, the first branch which does not represent a BH because hyperbolicity is lost, and therefore an event horizon will never form, shows a universal behavior as if it represents the threshold of black hole formation.

\begin{figure}
\begin{tabular}{ccccc}
\multicolumn{2}{c}{Family A} & & \multicolumn{2}{c}{Family B} \\
\includegraphics[scale=0.21]{Figures/BH-for_1,0.pdf}	&
\includegraphics[scale=0.21]{Figures/BH-for_5,0.pdf}	& &
\includegraphics[scale=0.21]{Figures/BH-for_0,5-B.pdf}	&
\includegraphics[scale=0.21]{Figures/BH-for_1,0-B.pdf}	\\
\includegraphics[scale=0.21]{Figures/BH-for_9,0.pdf}	&
\includegraphics[scale=0.21]{Figures/BH-for_20,0.pdf}	& &
\includegraphics[scale=0.21]{Figures/BH-for_3,0-B.pdf}	&
\includegraphics[scale=0.21]{Figures/BH-for_15,0-B.pdf}
\end{tabular}
\caption{Radius of the first horizon formed as a function of the amplitude of the initial scalar field, $\phi_0$,  for various values of $\beta$. Blue-branch represents formation of both horizons at the same time while orange-branch describes formation of sonic horizon only. Results are shown for Gaussian family (first two columns) and the Family B initial conditions (last two columns).
\label{FamilyAB}}
\end{figure}

\begin{figure}
\includegraphics[scale=0.45]{Figures/clines-B5-po-3,5.pdf}
\includegraphics[scale=0.45]{Figures/clines-B5-po-8.pdf}
\caption{Integral curves of the ingoing (orange) and outgoing (blue) characteristic speed $c_\pm$ defined by eq.(\ref{char}) for $\beta=5$ and gaussian initial conditions. In the left panel, $\phi_0=3.5~10^{-6}$ and therefore the solution belongs to the first branch, where we have formation of only the sonic horizon. In the right panel, $\phi_0=8~10^{-6}$ and therefore it belongs to the last branch where a black hole forms.
\label{Fig:caustic}}
\end{figure}
We can see from Fig.(\ref{Fig:caustic}) the evolution of the characteristic line defined from eq.(\ref{char}) in $(t,r)$ coordinates. In the first case, a sonic horizon is formed but we do not expect a black hole to form as explained previously, while in the second case, an event horizon forms at normalized radius $r=1$. Recently, it was shown that in flat spacetime, these models could produce caustics \cite{Babichev:2016hys}. But as it can be seen from Fig.(\ref{Fig:caustic}), the characteristic lines do not intersect. We haven't found any formation of caustics in our simulations. In the second case, where the event horizon forms, indicated by the lines converging to $r=r_s$ of the characteristic lines, the BH is Schwarzschild.

In fact, every time a black hole forms, the exterior solution is Schwarzschild as we can see in Fig.(\ref{FIG:R}). Considering e.g. the Family A of initial conditions
and for various values of $\phi_0$ which all correspond to the fourth branch where the event horizon forms at the same time than the sonic horizon (blue-branch in Fig.(\ref{FamilyAB})), we have represented the curvature scalar $R$ and the Ricci tensor squared $R_{\mu\nu}R^{\mu\nu}$ during the last moment of evolution before black hole formation. We see that for all values of $\phi_0$ the curvature scalar and the Ricci tensor squared vanish for $r$ larger than the event horizon indicating the formation of the Schwarzschild solution which has also been checked directly from the metric. This behavior has been observed for both families of initial conditions and for all values of $\beta$. The end state of the evolution when the event horizon is formed is the Schwarzschild spacetime. Notice also that the event horizon increases with increasing $\phi_0$ as expected.
\begin{figure}
\begin{tabular}{cc}
\includegraphics[scale=0.47]{Figures/R-b10-Ult-Rama.pdf} 	&
\includegraphics[scale=0.47]{Figures/R2-b10-Ult-Rama.pdf}
\end{tabular}
\caption{Curvature scalar $R$ and Ricci tensor squared $R_{\mu\nu}R^{\mu\nu}$ as a function of the radial radius $r$ at last time $t$ before formation of the event horizon for $\beta=10$ and $\phi_0$ corresponding to the last branch. The vertical line represents the position of the event horizon for each initial condition $\phi_0$.}
\label{FIG:R}
\end{figure}

On the other hand, when the sonic horizon forms first, the metric is not Schwarzschild as seen in Fig.(\ref{FIG:R2}). In this case, we expect the system to continue to evolve until the formation of the Schwarzschild spacetime or a loss of hyperbolicity. This behavior should be checked with coordinates such as Gullstrand-Painlev\'e.
\begin{figure}
\begin{tabular}{cc}
\includegraphics[scale=0.47]{Figures/R-PrimeraRama.pdf} 	&
\includegraphics[scale=0.47]{Figures/R2-PrimeraRama.pdf}
\end{tabular}
\caption{Curvature scalar $R$ and Ricci tensor squared $R_{\mu\nu}R^{\mu\nu}$ as a function of the radial radius $r$ at last moment $t$ before formation of the sonic horizon for various values of $\beta$ and $\phi_0$ corresponding to the first branch. The vertical line represents the position of the sonic horizon.}
\label{FIG:R2}
\end{figure}
For a given family of initial conditions and for a given $\beta$, values of $\phi_0$ lower than the first branch produce dispersion and therefore flat spacetime while values taken within this branch produce a sonic horizon and later a loss of hyperbolicity. It is interesting to see from the curvature in Fig.(\ref{FIG:R2}) that we are still far from the Schwarzschild solution and therefore the formation of the event horizon, but very surprisingly, considering the sonic horizon we found a universal behavior. For any family of initial conditions and for any $\beta$, there exist a critical value of $\phi_0$ named $\phi_i$ in Fig.(\ref{TendencyLine}) around which the radius of the sonic horizon follows a universal behavior given by
\begin{align}
r=r_0+(\phi_0-\phi_i)^{\gamma}~,~~~\gamma\simeq 0.51
\end{align}
Because of the existence of an additional scale in our system ($\beta$), we have a non vanishing minimum radius of the black hole corresponding therefore to Type I critical phenomena \cite{Gundlach:2007gc}.

\begin{figure}
\begin{center}
\includegraphics[scale=0.8]{Figures/TendencyLine.pdf}
\caption{Radius scaling relation of the sonic horizon for the two families of initial conditions and for various values of $\beta$. Data with filled markers correspond to Family A. Data with empty markers correspond to Family B.}
\label{TendencyLine}
\end{center}
\end{figure}

\section{Conclusions}

In this paper, we have studied gravitational collapse in K-essence models with additional shift symmetry. We have presented the various constraints for a well-defined problem at classical level and for its quantum completion which reduces to $K_{,X}>0$, $K_{,XX}>0$ and $K_{,X}+2XK_{,XX}>0$. For these theories, we generically have the formation of two horizons, an event horizon and a sonic horizon which define a limit for the propagation of the perturbations of the scalar field. For numerical purposes, we focused on a particular model defined by $K=X+\beta X^2$. We found that in the weak field regime, the scalar field disperses and spacetime is flat while in the strong field regime, we have the formation of a horizon. Two situations occur, either only a sonic horizon forms or both horizons form at the same time. In this last case, the exterior solution is always Schwarzschild and we never observed formation of caustics. In the cases where the sonic horizon formed first, we could have either a dynamics of the field showing the possible formation of a BH in the future or a loss of hyperbolicity of the equations. Very surprisingly, the lowest regime, corresponding to a situation were the field does not disperse to infinity, and which corresponds to the formation of a sonic horizon, reveals a universal behavior even if the hyperbolicity is rapidly lost after the formation of the sonic horizon. We found that in the critical limit of the formation of the sonic horizon $r_S$, a universal power-law scaling of $r_S$ appears with a critical exponent of order $0.51$ for any parameter $\beta \neq 0$. This result seems to indicate that the universal behavior is also encoded in the sonic horizon.

redpajama_set_name: RedPajamaArXiv


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