All Questions
299
questions
3
votes
3
answers
182
views
Photonic black holes
"Can a photon turn into a black hole?" - usually the answer to this question is - it can't, because it has zero rest mass. However, when we derive the Schwarzchild Metric initially the $2M$ ...
- 1,161
0
votes
1
answer
66
views
Conformal equivalent to Schwarzschild metric
Consider Schwarzschild spacetime in Eddington-Finkelstein coordinates $(v,r,\theta,\phi)$
$$g \enspace = \enspace -f(r) \, dv^2 + 2 \, dv \, dr + r^2 \, d\Omega^2 \quad , \qquad f(r) = 1 - \frac{2m}{r}...
- 743
0
votes
1
answer
103
views
Interior Solution for Black Hole in Particular
This paper seems to suggest that the interior metric for a black hole in particular (a.k.a not a different kind of spherically symmetric non-rotating body) is just the exterior Schwarzschild metric ...
- 323
0
votes
2
answers
112
views
Event horizon is a null surface - what about the angular coordinates?
From the Schwarzschild metric $$ds^2=(1-2m/r)dt^2-(1-2m/r)^{-1}dr^2-r^2(dθ^2+\sin^2θ dϕ^2)$$ on the surface $r=2m$ (setting $dr=0$) we have $$ds^2=-r^2(dθ^2+\sin^2θ dϕ^2).$$
This looks spacelike ($...
- 366
0
votes
1
answer
77
views
Regularization of black hole singularities
Hi I have a question: when dealing with the gravitational Lorentz factor from schwarzchild solution to EFE, used in defining gravitaional time dilation and one encounters singularities at $r=0$ or $r=...
0
votes
1
answer
90
views
Length near the black hole
One meter rod at long distance is thrown to the Schwarzschild black hole. How its length near the black hole seems to distant observer?
- 626
2
votes
3
answers
245
views
Orbit description in Schwarzschild metric
Suppose to have a restricted 2-body system (BH + star with $M_{BH}\gg M_{\mathrm{star}}$) and you want to describe the orbit of the star relative to the BH, i.e. in the Schwarzschild metric.
Usually, ...
- 169
6
votes
1
answer
262
views
How to find that there is a conical singularity in the BTZ black hole?
Considering a non-rotating and non-charged 2+1 dimensional black hole, known as the BTZ black hole which obtained by adding a negative cosmological constant $\Lambda=-\frac{1}{l^2},l\ne0$ to the ...
0
votes
0
answers
59
views
Time dilatation of a free falling observer [duplicate]
I have two questions about time dilation near a black hole.
(I question) The relation $d\tau^2 = (1-\frac{r_s}{r}) dt^2$ between the proper time $d\tau$ of an observer near a B.H. and the time dt ...
- 21
1
vote
2
answers
68
views
Physical interpretation of the two possible roots for the isotropic Schwarzschild coordinate $r'$
I am trying to deep dive and study the isotropic Schwarzschild coordinates, whose line element is written for particles lying onto the equatorial plane $\theta=\pi/2$ as:
$$ds^2 = -\left(\dfrac{1-\...
- 382
1
vote
0
answers
83
views
What is the meaning to the switch $dt^2\to-dt^2$ and $dr^2\to-dr^2$ in the Schwarzschild metric?
What is the meaning of the change $dt^2\to-dt^2$ and $dr^2\to-dr^2$ in the Schwarzschild metric, leading to:
$$g=-c^{2}d\tau^{2}=(1-\frac{2GM}{c^{2}r})c^{2}dt^{2}-(1-\frac{2GM}{c^{2}r})^{-1}dr^{2}+r^{...
- 476
0
votes
1
answer
125
views
Event horizon in stationary spacetime
In the case of non-stationary spacetimes finding the event horizon is no easy task.
The stationary case should somehow be less involved or so it is in some well known cases, such as the Kerr spacetime....
- 1,989
1
vote
0
answers
86
views
Question on the transformation from Boyer-Lindquist to Kerr-Schild coordinates, for a modified Kerr metric
From Kerr metric, we do know that there exist a function with the form of:
$$\Delta = r^2 - 2 M r + a^2 \tag{1}.$$
Following $[1]$, I did understand the coordinate transformation from Boyer-Lindquist (...
- 3,085
1
vote
1
answer
85
views
Metric of Einstein static universe (ESU) black hole
The Einstein static universe (ESU) has metric
$$ g = - dt^2 + d\chi^2 + \sin^2 \chi d\Omega^2 $$
With
$$ t \in \mathbb{R}, \chi \in (0,\pi) .$$
Is there a metric that describes an eternal black hole ...
- 743
0
votes
0
answers
46
views
General relativity change of observer
I have a problem in calculating the module of the velocity of a particle measured by a static observer in a specific metric. This metric is
$$ds^2=(r^2-R^2)dt^2-\frac{dr^2}{r^2-R^2}-r^2d\varphi^2$$
...
- 86