<p>This is a great question! Simply put, we do not know. However, I would say that the star in question would likely be pulled apart therefore leaving the star structure destroyed but the energy of the star still intact. Imagine a mirror being shattered! The pieces (energy) of that mirror (STAR) are still existent, however the mirror is shattered (destroyed). I hope this makes sense? The energy of the star would likely continue to exist, but the formation of the star would likely be altered.</p>

CC BY-SA 4.0
2019-04-12T03:14:30.950Z
2019-04-12T03:14:30.950Z
Doberg
<p>Yes, it is easily <em>possible</em>, but it depends critically on how massive the black hole is. A simple calculation will suffice.</p>

<p>If we take a Newtonian approximation for the tidal acceleration across a star of radius <span class="math-container">$R_*$</span> as it reaches the event horizon
<span class="math-container">$$ a_{\rm tidal} \sim 2\frac{GM_{\rm BH}R_*}{r_s^3}\ ,$$</span>
where <span class="math-container">$r_s = 2GM_{\rm BH}/c^2$</span> is the Schwarzschild radius.</p>

<p>The gravitational acceleration at the surface of the star, due to its own mass is just
<span class="math-container">$$a_* = \frac{GM_*}{R_*^2}\ .$$</span></p>

<p>If we take the ratio of the two, we can assume the star will survive being ripped up before it crosses the event horizon if this ratio is less than <span class="math-container">$\sim 1$</span>. i.e. when
<span class="math-container">$$\frac{a_{\rm tidal}}{a_*}= \frac{c^6 R_*^3}{4G^3 M_{\rm BH}^2 M_*} &lt;1$$</span></p>

<p>The tidal acceleration reduces markedly for high mass black holes. We can rearrange this inequality to give us the minimum black hole mass for survival:
<span class="math-container">$$ M_{\rm BH} &gt; \left(\frac{c^6 R_*^3}{4G^3 M_*}\right)^{0.5} = 1.5\times 10^{8} \left(\frac{M_*}{M_{\odot}}\right)^{-1/2} \left(\frac{R_*}{R_{\odot}}\right)^{3/2}\ M_{\odot}$$</span></p>

<p>To first order, this is almost independent of the type of star swallowed. It depends on the inverse square root of the average stellar density, which doesn't vary a lot.</p>

<p>This means that a star could fall into a black hole like that in M87 (<span class="math-container">$M_{\rm BH}\simeq 6\times 10^9 M_{\odot}$</span>), but  would not survive to the event horizon of Sgr A* (<span class="math-container">$M_{\rm BH}\simeq 4\times 10^6 M_{\odot}$</span>).</p>

<p>I think in practice this calculation can only be accurate to factors of a few. I have not taken into account shearing forces that would be present for a rotating black hole, or the compression due to tangential tidal forces, or any heating effects from hot gas near the black hole, or interaction with an accretion disk. A full hydrodynamic simulation is needed (and perhaps has been done?).</p>

<p>Also note, this calculation is just for getting past the event horizon. The tidal forces grow as <span class="math-container">$r^{-3}$</span>, so any normal star will be ripped up shortly after this, even for the most massive black holes we know of.</p>

<p>Please note: This answer is written from the point of view of the falling star. A distant observer will not see the star (or anything else) cross the event horizon.</p>

CC BY-SA 4.0
2019-04-19T17:53:18.187Z
In my thought experiment I assumed the event horizon area to be devoid of forces that could impact the star's fall - other than gravity.  In certain scenarios I can see how forces would destroy the star before it makes it past the event horizon.
Flood
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2019-04-19T18:11:21.850Z
I have to agree that simulations are needed.

Let's do it.

What do we do on stack exchange for questions that can't be answered until?
Flood
CC BY-SA 4.0
2019-05-29T01:22:48.130Z
I asked a Zachariah Etienne who's involved in the West Virginia University's BlackHoles@Home project whether they'd be interested in running the simulation and they responded, quote: "studied neutron stars (NSs) falling into much less massive black holes (BHs) for my PhD thesis..." providing a slide that "makes a back-of-the-envelope estimate (using Newtonian physics) of what quantities determine whether the NS plunges into the BH ("swallowed whole") or disrupts outside of the BH. Replace NS with "star" and BH with "supermassive BH".
Flood
CC BY-SA 4.0
2019-05-29T06:15:42.803Z
@Flood According to my formula, if $M_*/M_{\odot}\sim 1.4$ but $R_*/R_{\odot}\sim 10^{-8}$, then "swallowing whole" is easily possible for stellar-sized black holes if the other "star" is a neutron star. So what is it that can disrupt the NS in some cases?
ProfRob
CC BY-SA 4.0
2019-05-31T00:04:27.293Z
I would have to be a Physicist to give you a good answer.  I'm on here as an enthusiast who can ask questions and learn.  But the words in your own comment, quote: "shearing forces that would be present for a rotating black hole, or the compression due to tangential tidal forces, or any heating effects from hot gas near the black hole, or interaction with an accretion disk" could disrupt a NS, right?
Flood
CC BY-SA 4.0
2019-04-12T10:53:52.653Z
2019-05-29T06:18:35.397Z
2019-05-29T06:18:35.397Z
ProfRob
<p>This is the first of many similar questions I have to build up to a specific question or scenario that I want to explore and find an answer to.</p>

CC BY-SA 4.0
2019-04-12T01:55:22.957Z
Yes, it can. Probably no such event was found until now.
peterh
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2019-04-12T02:09:09.460Z
Good.  I'm no scientist, but this I thought was indeed possible given that some super massive black holes have been measured to be several Astronomical Units in size.  I would like to have more responses from other members and if we can all agree and even prove that the scenario outlined by my question is plausible; I will then pose my next question.
Flood
CC BY-SA 4.0
2019-04-12T02:28:33.340Z
See this question from the Physics stack about possible "orbits" inside charged spinning black holes: https://physics.stackexchange.com/q/365969/123208 Note that although it's easy for a black hole to have high angular momentum, getting high charge isn't very likely, as John's answer says. And you need both. Also, the trajectories are weird chaotic things, not at all like Keplerian orbits.
PM 2Ring
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2019-04-12T02:29:49.913Z
@peterh What do you mean? I haven't heard of such a thing being found now. That'd be big news!
PM 2Ring
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2019-04-12T02:43:19.013Z
@PM 2Ring If I may, I'm not asking whether it has happened, I'm asking whether it would be possible.
Flood
CC BY-SA 4.0
2019-04-12T02:53:45.490Z
Understood. And the answer by John that I linked says yes. And of course a star can easily cross the horizon of any SMBH without being destroyed before it crosses the horizon, but it *will* get destroyed shortly thereafter, unless the SMBH has enough spin & charge, and the star has the right trajectory.
PM 2Ring
CC BY-SA 4.0
2019-04-12T06:12:39.627Z
But note that even if there is an inner event horizon inside which there are stable orbits, the tidal forces inside that inner horizon would be intense.  Those tidal forces are weak at the outer event horizon for a supermassive black hole, but the inner event horizon is close to the singularity, so it seems unlikely a star could survive in there,and even less likely that any planets orbiting it could remain in orbit.
Ken G
<star><supermassive-black-hole>
Can a star fall in a super massive black hole without getting destroyed?
Flood
# Can a star fall in a super massive black hole without getting destroyed?

(Asked by: username_0 on 2019-04-12)

This is the first of many similar questions I have to build up to a specific question or scenario that I want to explore and find an answer to.

**Tags:** star, supermassive-black-hole
> **Comments:**
> **username_1**: Yes, it can. Probably no such event was found until now.  
> **username_0**: Good.  I'm no scientist, but this I thought was indeed possible given that some super massive black holes have been measured to be several Astronomical Units in size.  I would like to have more responses from other members and if we can all agree and even prove that the scenario outlined by my question is plausible; I will then pose my next question.  
> **username_2**: See this question from the Physics stack about possible "orbits" inside charged spinning black holes: https://physics.stackexchange.com/q/365969/123208 Note that although it's easy for a black hole to have high angular momentum, getting high charge isn't very likely, as John's answer says. And you need both. Also, the trajectories are weird chaotic things, not at all like Keplerian orbits.  
> **username_2**: @peterh What do you mean? I haven't heard of such a thing being found now. That'd be big news!  
> **username_0**: @PM 2Ring If I may, I'm not asking whether it has happened, I'm asking whether it would be possible.  
> **username_2**: Understood. And the answer by John that I linked says yes. And of course a star can easily cross the horizon of any SMBH without being destroyed before it crosses the horizon, but it *will* get destroyed shortly thereafter, unless the SMBH has enough spin & charge, and the star has the right trajectory.  
> **username_3**: But note that even if there is an inner event horizon inside which there are stable orbits, the tidal forces inside that inner horizon would be intense.  Those tidal forces are weak at the outer event horizon for a supermassive black hole, but the inner event horizon is close to the singularity, so it seems unlikely a star could survive in there,and even less likely that any planets orbiting it could remain in orbit.  

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## 2 answers

### Answer by username_5 on 2019-04-12. Score: 8 | Accepted answer

Yes, it is easily *possible*, but it depends critically on how massive the black hole is. A simple calculation will suffice.

If we take a Newtonian approximation for the tidal acceleration across a star of radius $R\_\*$ as it reaches the event horizon
$$ a\_{\rm tidal} \sim 2\frac{GM\_{\rm BH}R\_\*}{r\_s^3}\ ,$$
where $r\_s = 2GM\_{\rm BH}/c^2$ is the Schwarzschild radius.

The gravitational acceleration at the surface of the star, due to its own mass is just
$$a\_\* = \frac{GM\_\*}{R\_\*^2}\ .$$

If we take the ratio of the two, we can assume the star will survive being ripped up before it crosses the event horizon if this ratio is less than $\sim 1$. i.e. when
$$\frac{a\_{\rm tidal}}{a\_\*}= \frac{c^6 R\_\*^3}{4G^3 M\_{\rm BH}^2 M\_\*} <1$$

The tidal acceleration reduces markedly for high mass black holes. We can rearrange this inequality to give us the minimum black hole mass for survival:
$$ M\_{\rm BH} > \left(\frac{c^6 R\_\*^3}{4G^3 M\_\*}\right)^{0.5} = 1.5\times 10^{8} \left(\frac{M\_\*}{M\_{\odot}}\right)^{-1/2} \left(\frac{R\_\*}{R\_{\odot}}\right)^{3/2}\ M\_{\odot}$$

To first order, this is almost independent of the type of star swallowed. It depends on the inverse square root of the average stellar density, which doesn't vary a lot.

This means that a star could fall into a black hole like that in M87 ($M\_{\rm BH}\simeq 6\times 10^9 M\_{\odot}$), but would not survive to the event horizon of Sgr A\* ($M\_{\rm BH}\simeq 4\times 10^6 M\_{\odot}$).

I think in practice this calculation can only be accurate to factors of a few. I have not taken into account shearing forces that would be present for a rotating black hole, or the compression due to tangential tidal forces, or any heating effects from hot gas near the black hole, or interaction with an accretion disk. A full hydrodynamic simulation is needed (and perhaps has been done?).

Also note, this calculation is just for getting past the event horizon. The tidal forces grow as $r^{-3}$, so any normal star will be ripped up shortly after this, even for the most massive black holes we know of.

Please note: This answer is written from the point of view of the falling star. A distant observer will not see the star (or anything else) cross the event horizon.

> **Comments:**
> **username_0**: In my thought experiment I assumed the event horizon area to be devoid of forces that could impact the star's fall - other than gravity.  In certain scenarios I can see how forces would destroy the star before it makes it past the event horizon.  
> **username_0**: I have to agree that simulations are needed.  Let's do it.  What do we do on stack exchange for questions that can't be answered until?  
> **username_0**: I asked a Zachariah Etienne who's involved in the West Virginia University's BlackHoles@Home project whether they'd be interested in running the simulation and they responded, quote: "studied neutron stars (NSs) falling into much less massive black holes (BHs) for my PhD thesis..." providing a slide that "makes a back-of-the-envelope estimate (using Newtonian physics) of what quantities determine whether the NS plunges into the BH ("swallowed whole") or disrupts outside of the BH. Replace NS with "star" and BH with "supermassive BH".  
> **username_5**: @Flood According to my formula, if $M_*/M_{\odot}\sim 1.4$ but $R_*/R_{\odot}\sim 10^{-8}$, then "swallowing whole" is easily possible for stellar-sized black holes if the other "star" is a neutron star. So what is it that can disrupt the NS in some cases?  
> **username_0**: I would have to be a Physicist to give you a good answer.  I'm on here as an enthusiast who can ask questions and learn.  But the words in your own comment, quote: "shearing forces that would be present for a rotating black hole, or the compression due to tangential tidal forces, or any heating effects from hot gas near the black hole, or interaction with an accretion disk" could disrupt a NS, right?  

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### Answer by username_4 on 2019-04-12. Score: -5

This is a great question! Simply put, we do not know. However, I would say that the star in question would likely be pulled apart therefore leaving the star structure destroyed but the energy of the star still intact. Imagine a mirror being shattered! The pieces (energy) of that mirror (STAR) are still existent, however the mirror is shattered (destroyed). I hope this makes sense? The energy of the star would likely continue to exist, but the formation of the star would likely be altered.


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