All Questions
19
questions
-4
votes
2
answers
102
views
Are black holes 4-dimensional balls of spacetime? If so, will they have 3-sphere surfaces?
If black holes are 4-dimensional balls of spacetime, they will have a 3-sphere surface with a 3-dimensional volume. Would this allow infalling matter to remain within this surface?
- 371
2
votes
0
answers
101
views
What is the meaning of "The volume inside a black hole always increases"?
I have been following recent work by Susskind [1,2] where he talks about fact that the volume inside an eternal black hole increases with time. I am unsure how to obtain this result. I'll show my ...
- 4,827
2
votes
1
answer
224
views
Existence of a Trapped Surface to the Existence of a Black Hole
Does the existence of a trapped surface in a region of space (not necessarily either of the vacuum or symmetric spacetime) indicates (theoretically) the existence of a "black hole" there? ...
- 756
2
votes
0
answers
37
views
Change in Area of Event Horizon under Perturbation
It is known that if one perturbs Schwarzschild initial data and the perturbation corresponds to a massive particle following an ingoing geodesic which is close to null, then the perturbation can be ...
- 1,410
2
votes
1
answer
193
views
Why does Leonard Susskind draw constant time slices around a black hole as lines passing through the origin at zero?
In this video Inside Black Holes by Leonard Susskind,
why does he draw the constant time slice as lines passing through the origin at zero?
Something seems to be contradicting to have constant time ...
- 4,336
0
votes
1
answer
421
views
Surface gravity and affine parametrization
Consider a Killing vector $\chi^\mu$ with the Killing Horizon $\Sigma$. From Carroll's book (pg 245), along the Killing horizon, the Killing vector obeys the geodesic equation
$$\chi^\mu\,\nabla_\mu\,\...
- 964
2
votes
0
answers
364
views
How does the Hawking rigidity theorem follow from results in Hawking & Ellis?
I'm trying to find a statement and proof of the Hawking rigidity theorem for black holes, and I'm not having much success. The theorem basically says that given some assumptions, the event horizon of ...
- 28.3k
3
votes
1
answer
2k
views
What's the significance of a Killing horizon?
A Killing horizon is defined as a null hypersurface generated by a Killing vector, which is then null at that surface. Some often cited examples come from the Kerr spacetime, where the Killing vector $...
- 28.3k
1
vote
1
answer
300
views
Eddington-Finkelstein coordinates not well-defined?
Consider the Schwarschild solution $$d s^{2}=-\left(1-\frac{2 m}{r}\right) d t^{2}+\frac{d r^{2}}{1-\frac{2 m}{r}}+r^{2}\left(d \theta^{2}+\sin ^{2} \theta d \varphi^{2}\right) $$
and the radial null ...
- 344
6
votes
0
answers
122
views
Growth of apparent horizons and null convergence condition
An apparent horion ( S. W. Hawking & G. F. R. Ellis (1975). The large scale structure of space-time.) in General Relativity is a surface where all null vectors are pointing "inwards", i....
3
votes
1
answer
279
views
Why is $\chi_{[\mu}\nabla_\nu \chi_{\sigma ]} = 0$ at the Killing horizon?
Let $\chi$ be a Killing vector field that is null along a Killing horizon $\Sigma$
Why is $\chi_{[\mu}\nabla_\nu \chi_{\sigma ]} = 0$ at $\Sigma$?
- 669
2
votes
1
answer
430
views
Radius of Star, The Schwarzschild metric and Black Holes
From Section 9.1, in General Relativity by Woodhouse:
For a normal star, the Schwartzchild radius is well inside the star itself. As it is not in the vacuum region of space-time, the Ricci tensor ...
- 865
0
votes
1
answer
159
views
The $t$-coordinate bounds inside a black hole
In case of the Schwarzschild black hole, the $t$ coordinate inside the event horizon becomes spacelike. Hypothetically, if one had too much time inside a grand-super-massive black hole and decided to ...
- 12.7k
3
votes
1
answer
758
views
Two sphere - a spacelike hypersurface
Is the surface of a 2-sphere spacelike? What are the corresponding tangent vectors to the surface of a 2-sphere?
This question arises from the point of a trapped surface. In Schwarzschild spacetime ...
- 1,124
1
vote
1
answer
1k
views
Definition of trapped surface
The definition of a trapped surface in Sean Carroll's "Spacetime and Geometry" is as follows.
"A compact spacelike, two dimensional submanifold with the property that outgoing future directed light ...
- 1,124