# Can a star fall in a super massive black hole without getting destroyed?

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.

• Yes, it can. Probably no such event was found until now. – peterh - Reinstate Monica Apr 12 '19 at 1:55
• 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 Apr 12 '19 at 2:09
• See this question from the Physics stack about possible "orbits" inside charged spinning black holes: 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 Apr 12 '19 at 2:28
• @peterh What do you mean? I haven't heard of such a thing being found now. That'd be big news! – PM 2Ring Apr 12 '19 at 2:29
• 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 Apr 12 '19 at 6:12

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.

• 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 Apr 19 '19 at 17:53
• 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 Apr 19 '19 at 18:11
• 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 May 29 '19 at 1:22
• @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? – Rob Jeffries May 29 '19 at 6:15
• 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 May 31 '19 at 0:04

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.