All Questions
13
questions
0
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3
answers
186
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Equivalence principle near a black hole
At every spacetime point, there is a locally inertial frame in which the effect of gravitation is absent. Can this point be taken near the center of a black hole?
- 13
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
4
votes
1
answer
251
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Coordinate singularity in general relativity and smooth structure of a manifold
I'm a bit confused by the notion of coordinate singularity, or perhaps relatedly, the differential geometry behind GR.
In my elementary understanding of differential geometry, one starts with a ...
- 669
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
1
vote
0
answers
92
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Singularities of the Coordinate Systems
We know that, the singularity of the Schwarzschild metric at $r=2M$ can be removable via coordinate transformation to Kruskal-Szekers . Can we apply a similar argument to the Kerr metric? If so, what'...
- 3,122
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
2
votes
1
answer
66
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Black hole atlases
What sort of atlases of spaces that contain a black hole (that is, including the space inside the event horizon), if any, are there? Does the central singularity have to be excluded? Are there atlases ...
- 8,833
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
4
votes
3
answers
4k
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Physical interpretation of Kruskal-Szekeres coordinates
The Kruskal-Szekeres coordinates for Schwarzschild spacetime $(T,X,\theta,\phi)$ can be defined as is done in Wikipedia.
Now, what is the physical meaning of these coordinates? The standard ...
- 36.4k
2
votes
1
answer
1k
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Schwarzschild black hole spacetime in Kruskal-Szekeres coordinates
First, a brief introduction to provide the right context. I've been studying General Relativity with Ohanian and Ruffini's Gravitation and Spacetime. They introduce Kruskal-Szekeres coordinates for ...
- 643
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 ...
- 3,203
4
votes
1
answer
547
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Why is the natural singularity $r=0$ in Schwarzschild geometry a spacelike one?
Why is the natural singularity $r=0$ in Schwarzschild geometry a spacelike one?
- 7,720
4
votes
2
answers
3k
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Coordinate Singularity in Metric
Suppose I have some metric
$$ds^2=g(t)dt^2+\frac{1}{r}dr^2$$
which has a singularity at $r=0$.
However, if I make the coordinate transformation $u=\frac{1}{r}$, then I get:
$$ds^2=g(t)dt^2+r^3 du^...
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