All Questions
21
questions
0
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1
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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=...
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 ...
3
votes
2
answers
266
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How can we be sure that black hole's singularity is not a missunderstanding? [duplicate]
The Newtonian gravitational potential is given by:
$$\phi=-\dfrac{GM}{r}$$
Which appears in the Schwarzschild metric tensor with a so-called singularity at $r=0$. Nonetheless, I can't get why is it ...
- 495
6
votes
2
answers
1k
views
Schwarzschild metric with negative mass
Can mass be negative in Schwarzschild metric? If we use $M<0$, will it still be a solution to EFE? If not, why?
- 1,161
4
votes
2
answers
316
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Is $\theta=0$ a coordinate singularity in the Schwarzschild metric?
We often hear this example of coordinate singularity. We can describe the 3D Euclidean space using rectangular or spherical coordinates. But in the spherical coordinate, the north pole $(r,\theta=0, \...
- 339
2
votes
1
answer
380
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Understanding the Kruskal diagram for Schwarzschild spacetime
I am studying Kruskal coordinates for my General Relativity course. On the book Spacetime and Geometry: An introduction to General Relativity by Sean Carroll, the author gives the metric in Kruskal ...
- 308
0
votes
1
answer
270
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Identifying Black Hole Horizon from metric tensor
Suppose we have a spherically symmetric and static metric given by:
\begin{equation}
ds^2=-B(r)dt^2+A(r)dr^2+r^2d\theta^2 +r^2\sin^2(\theta)d\phi^2
\end{equation}
where:
\begin{equation}
B(r)=1-\...
- 73
2
votes
1
answer
214
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Why can't we use the line element to distinguish coordinate from gravitational singularities?
I am a bit confused as to why we can't use the line element to identify coordinate from gravitational singularities. My question stems from learning about the Schwarzschild Metric and the singularity ...
- 195
6
votes
4
answers
1k
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Schwarzschild solution, stress-energy side of Einstein's equation
The Schwarzschild solution in GR only has a singularity at the origin $r=0$: otherwise there is no matter content. The right-hand side of Einstein's equation is hence almost everywhere zero, but I ...
- 312
0
votes
0
answers
52
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Derivation of the Schwarzschild solution [duplicate]
For the Derivation of the Schwarzschild solution my Professor use:
$R_{\mu\nu} = 0$ since we are in vacuum.
I see that we are in vacuum, but we assume a mass at point $r = 0$.
Thus, the curvature is ...
- 339
5
votes
3
answers
2k
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What's the proper distance from the event horizon to the singularity?
How far away is the event horizon of a (Schwarzschild) black hole away from the central singularity for a radially infalling observer starting with $v=0$ somewhere outside the black hole? After ...
0
votes
1
answer
160
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Does metric stretching produce a physical force?
Here's a thought experiment: Say we have a cloud of theoretical test particles (no mass, no charge) that is far, far away from anything, with none of the particles moving with respect to any of the ...
- 513
0
votes
1
answer
131
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Does metric stretching show up in all coordinate systems?
The radial component of the Schwarzschild metric shows a dramatic metric stretching as the event horizon is approached from the outside and it shoots to infinity at the horizon.
Does this extreme ...
- 513
1
vote
1
answer
189
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Schwarzschild solution to Einstein's equation and singularities
In the book D'Inverno - Introducing Einstein's relativity, in the non-rotating black holes part, the following statement has been stated.
In Eddington-Finkelstein coordinates at $r=2m$ the ...
- 1,124
11
votes
2
answers
2k
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Schwarzschild coordinates beyond the event horizon
We can write down the metric of the Schwarzschild black hole in Schwarzschild coordinates.
On page 6 of the notes by Leonard Susskind of a course given at the Perimeter Institute titled 'Black Holes ...
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