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This question may seem a little naïve, but I need help with the basics of black hole physics. I'm having difficulty understanding the topology of the event horizon. Apologies for any errors in advance.

  1. I'm trying to come to grips with what the physical properties of an event horizon are. I understand that it is "...a mathematically defined demarcation boundary, and nothing prevents matter or radiation from entering a black hole, only from exiting one." However, I have some questions regarding how matter or energy can pass the boundary if $c$ is the fastest that anything material can move. Also, shouldn't relativistic effects cause the mass of any matter falling towards the event horizon to increase without bound as it approaches $c$?
  2. What thickness does the event horizon have? Is it thicker than 1 photon? Is there an analog of Roche's Limit to be applied to a photon in orbit at the event horizon (since the inner part is moving faster than the outer part, and the center has velocity $c$).
Níckolas Alves
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Spanki
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  • As with photons, there is no evidence that event horizons have any thickness at all. There is also no reason why matter travelling to an event horizon would have a speed of $c$ by the time it gets there. – Connor Behan Dec 09 '21 at 17:13
  • Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. – Michael Seifert Dec 09 '21 at 17:26
  • Here's my prob: Objects falling towards the black hole are accelerated due to the force of gravity, correct? So I assume that objects subjected to this acceleration for sufficient time will eventually be falling towards the black hole at a velocity of c. How does a proton get the energy required to accelerate it to c? Even if the proton's mass does not increase doesn't it take increasingly large amounts of energy to accelerate it all the way to c? Wouldn't the increasing energy requirements for accelerating the proton "drain" the energy from the black hole? Where does the energy come from? – Spanki Dec 10 '21 at 18:26
  • You may enjoy my answer about the photon sphere, which includes a link to my photon trajectory simulator which runs on the SageMath server. – PM 2Ring Feb 02 '22 at 05:32

1 Answers1

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how matter or energy can pass the boundary if c is the fastest that anything material can move

The event horizon is a lightlike surface. That means that in any local inertial frame the event horizon moves at the speed of light. Specifically, it is an outgoing lightlike surface.

With any lightlike surface you can cross it if it is going towards you, just not if it is going away from you. So, since it is outgoing if you are outside it is going towards you, and if you are inside it is going away. That is why matter and energy can go in but not out.

Also, shouldn't relativistic effects cause the mass of any matter falling towards the event horizon to increase without bound as it approaches c?

Relativistic mass is a generally discarded concept by professional scientists. It is pretty much only used in pop-sci sources. The mass that physicists use is invariant, it does not change as an object approaches or crosses the horizon.

Is there an analog of Roche's Limit to be applied to a photon in orbit at the event horizon (since the inner part is moving faster than the outer part, and the center has velocity c).

Photons don’t orbit at the event horizon. They orbit at the photon sphere, which is quite a bit outside the horizon.

https://en.wikipedia.org/wiki/Photon_sphere

The photon sphere is an unstable orbit, so any actual photon would either spiral in or escape.

Urb
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Dale
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