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I am no physics major nor math major to this but merely an amateur cosmology enthusiast, so in my previous inquiries I wasn't able to find anything on the premise that if all black holes obviously have different masses (which we know they do, as all objects do), and we know that each black hole's gravitational pull exceeds the speed of light $c$ so my question being: is it possible the escape velocities of some black holes are quite possibly much greater than $c$ itself?

Let's say if there was "super light", light that goes $10c$ (10x the speed of normal light), is it possible that the gravity of some black holes could be so extreme that it would greatly exceed even $10c$? and beyond etc. Or do black holes only "defeat" light's escape velocity by just above $c$? If I am not understand it correctly, please feel free to correct, thanks.

Qmechanic
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Deadweed1
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    “Super light” has nothing to do with mainstream physics. – Ghoster Apr 14 '23 at 18:29
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    The OP is not proposing non-mainstream physics. The "super light" hypothetical is just an attempt to understand how escape velocity near a black hole works according to standard GR. – PM 2Ring Apr 15 '23 at 01:16
  • @PM2Ring We can incorporate all kinds of "magical devices" into our theories, but the only thing that comes out of that effort is intellectual nonsense. Th speed of light defines the geometry of causality in this universe. Breaking it means that causality breaks. What can a theory that behaves acausal tell us reliably about reality, which does not? – FlatterMann Apr 15 '23 at 05:40
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    @FlatterMann Ok, but Deadweed1 wasn't trying to incorporate some "magical device", they just wanted to talk about speeds > c. If you don't understand how spacetime geometry works, c just seems like some arbitrary mysterious restriction. FWIW, I have some relevant info on velocity in relativity here: https://physics.stackexchange.com/a/291346/123208 & https://physics.stackexchange.com/a/598415/123208 – PM 2Ring Apr 15 '23 at 07:00
  • @PM2Ring I can build a perpetual motion machine by violating any of the three laws of thermodynamics. So what, though? Neither is "just" an arbitrary "mysterious" restriction. They are defining pieces of the theoretical description of systems near thermal equilibrium. c is a direct consequence of relativity. What do I get if I give up on relativity? Certainly nothing that resembles reality. – FlatterMann Apr 15 '23 at 16:18
  • @FlatterMann Speeds beyond c are weird, but they don't exactly break relativity. Eg, see this recent question about an old paper on tachyonic orbits around a Schwarzschild black hole: https://physics.stackexchange.com/q/759758/123208 – PM 2Ring Apr 16 '23 at 08:24
  • @PM2Ring Has anybody observed a tachyonic orbit, yet? How about closed timelike curves? For all I know not even Schwarzchild black holes exist. Nature seems to prefer to give the real ones quite a bit of angular momentum, instead. Without any offense, but just because something can be done on paper doesn't mean that nature plays ball. – FlatterMann Apr 16 '23 at 11:11
  • @FlatterMann Of course we haven't seen tachyons, and they probably can't exist. But my point is that asking about tachyonic trajectories doesn't automatically make a question non-mainstream. FWIW, I prefer to parametrize relativistic motion using Bondi's k-factor (or its log, rapidity), rather than velocity. I suspect that if rapidity or the k-factor were introduced early when teaching SR, people would be less likely to wonder about transluminal velocities. ;) – PM 2Ring Apr 16 '23 at 13:02
  • @PM2Ring As an experimentalist I never had to wonder about transluminal velocities. I have never seen one. Having said that, I will read up on it. My GR is a little rusty. – FlatterMann Apr 16 '23 at 17:09
  • @PM2Ring Hehehe... what you call Bondi's k-factor is just the radial Doppler? Dudes, I have been telling people for decades that phenomenologically Doppler is the real deal. The other day plenty of people came at me because they didn't like my explanation of the twin-paradox with Doppler, which is trivial. That has nothing to do with transluminal velocities, though. A frequency shift is not a velocity, even if a fast ship coming at you MAY look like it's coming faster than the speed of light. That's just what it looks like. It doesn't really do that. – FlatterMann Apr 16 '23 at 17:14

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Escape velocity is position-dependent - the closer you are to a massive body, the faster you need to move to escape its gravitational field. We typically talk about the escape velocity at the "surface" of a body, but that's a bit of a tricky thing for a black hole.

The event horizon could be considered the "surface" of a black hole, and is the region from which light cannot escape. At positions outside the event horizon, the escape velocity is below c and light can escape. As you cross the event horizon, the escape velocity exceeds c - once it crosses the event horizon, even light cannot escape. Inside the event horizon, the escape velocity will continue to increase as you approach the singularity. By the time you are mere Planck lengths from a cosmic mass packed into a near-zero volume, the escape velocity will far exceed c.

All black holes have escape velocity equal to c at their event horizon by definition, and escape velocities much higher than c when approaching the singularity.

Nuclear Hoagie
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  • Thank you, that made perfect sense – Deadweed1 Apr 14 '23 at 20:05
  • A velocity has a magnitude and a direction. The escape velocity near a black hole does not have a single magnitude for any direction, unlike in Newtonian physics. – ProfRob Apr 14 '23 at 22:54
  • @ProfRob Please consider expanding that comment into an answer... – PM 2Ring Apr 16 '23 at 13:07
  • @ProfRob Wouldn't that imply that light actually can escape the event horizon of a black hole, so long as it's moving in the right direction? It suggests either that some light inside the event horizon can escape, or that some light outside the event horizon cannot escape. I'm not aware of the relativistic effect you're alluding to. – Nuclear Hoagie Apr 17 '23 at 13:50
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    @NuclearHoagie If you are just outside the event horizon, the only direction that light can escape is radially outwards. For all other directions it will end up "falling" back to the event horizon. As you move further away then the range of angles for which the light can escape will increase. Then for $r>3r_s/2$ light can escape in all directions that increase $r$, but not any for which $r$ decreases. This is completely un-Newtonian behaviour and is why talking about escape velocities or even escape speeds is hopeless/misleading for black holes. – ProfRob Apr 17 '23 at 15:39