Bulging Black Hole caused by approaching object?

[philipp2020]

Hi

I just listened to Leonard Süsskind Lecture 7 on youtube about General Relativity in the following link.



At 1:28:00 he mentioned, that if a object is very close to the surface of a black hole, then the matter at this point would bulge out until it get completely absorbed.

I don't really understand why the surface would bulge out to reach the approaching object.

Thanks very much for an answer.

Philipp

 

[PAllen]

By surface, I think he means the event horizon, which is a mathematical surface not a physical surface. A BH has no physical surface.

As to why this would happen, it has to do with light trapping and the definition of the event horizon. The event horizon is surface from which light will never escape. Loosely, as an object gets very close to BH, some light from the object will ultimately never escape. As a result, the EH boundary is considered to engulf the object. Later, the BH will settle into a slightly larger sphere (or 'not quite' sphere if there is significant spin).

 

[mfb]

The event horizon encloses mass - if you add mass, the event horizon grows, and if you don't do that in a symmetric way the event horizon will be asymmetric as well (for a short period of time).

 

[philipp2020]

Thanks for the answers.

But what I still don't understand is the way he draws it. By the way he draws it, the surface of the black hole seems to "reach out" locally to the object, even before the object makes contact with the Event Horizon.

Does this mean the black hole's EH is expanding locally even before the object makes contact with it?

 

[George Jones]

Thanks for the answers.

But what I still don't understand is the way he draws it. By the way he draws it, the surface of the black hole seems to "reach out" locally to the object, even before the object makes contact with the Event Horizon.

Does this mean the black hole's EH is expanding locally even before the object makes contact with it?

See:

Here is the $64000 question: At what point does the Black Hole's event horizon increase its radius?

It is useful to look at the Vaidya metric. See Figure 5.7 on page 134 (pdf page 150) of Eric Poisson's notes,

http://www.physics.uoguelph.ca/poisson/research/agr.pdf,

which evolved into the excellent book, A Relativist's Toolkit: The Mathematics of black hole Mechanics.

Radiation falls into a black hole from v1 to v2, but the left diagram of Figure 5.7 shows that the event horizon starts to grow before the first radiation crosses the event horizon.

It is a remarkable property of the event horizon that the entire history of the spacetime before its position can be determined

Here, "history" means past and future.

 

[PAllen]

Thanks for the answers.

But what I still don't understand is the way he draws it. By the way he draws it, the surface of the black hole seems to "reach out" locally to the object, even before the object makes contact with the Event Horizon.

Does this mean the black hole's EH is expanding locally even before the object makes contact with it?

Yes. I am not sure this effect (bulging around an infalling body) was envisaged before numerical relativity; thus the real explanation is: that's what the math says. The best I can come up with for an intuitive justification is as follow:

When a new body is about to merge with an existing BH, and sufficiently close to the the horizon, light emitted from its far side - affected by the BH gravity plus body's gravity - will fail to escape. It will be drawn into the BH with the merging body. The boundary of where this happens is, by definition, part of the event horizon. Thus, event horizon, at very close approach, bulges out and engulfs the new body. Soon after, the body has made its way toward the singularity (or whatever is really there, assuming classical singularity is not the truth), the EH settles down into a new, slightly larger sphere. There can also be the phenomenon of 'ring down', where the horizon oscillates for a short while before settling down.

Quite generally, the event horizon, as formally defined, has the property of growing before the matter that will cause it to grow is arrives. Consider a photon almost trapped just above the horizon; so nearly trapped that if no matter fell in, it would take a year to make its way a millimeter further away from the horizon. Supposed some body is going to fall in a week later. That will grow the horizon enough to trap the photon. But since GR is a classical deterministic theory, the fact that that body is going to fall in means the horizon already includes this photon because it will never escape.

 

[philipp2020]

Thank you very much for the answers.

 

[Bill_K]

See this YouTube clip from the Caltech group, that follows the growing event horizon of two merging black holes.