All Questions
50
questions
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103
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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
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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
1
vote
2
answers
68
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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
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votes
1
answer
125
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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
2
votes
1
answer
135
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Event horizon of static black holes
I am interested in finding event horizon of static space times of the following forms :
\begin{equation}
ds^2=-f(r)dt^2+\frac{1}{g(r)}dr^2+r^2d\Omega^2,
\end{equation}
where we have $f(r)\neq g(r)$. ...
- 463
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
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votes
1
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85
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Is there no curvature due to mass when travelling along a sphere outside a black hole?
I'm trying to do actual Schwarzschild Metric calculations. In looking at this video Schwarzschild Proper Distance at 1:20 he shows the calculation for moving directly outward on a radius from the ...
- 4,783
3
votes
1
answer
279
views
Can we identify a given metric as a black hole solution?
Given a metric $g_{\mu \nu}(x)$, can we identify whether it corresponds to a black hole? To be more precise, can we perform some calculations or define certain parameters of the metric which can help ...
- 93
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votes
1
answer
219
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Physical properties of an event horizon
This question may seem a little naïve, but I need help with the basics of black hole physics. I'm having difficulty understanding the topology of the event horizon. Apologies for any errors in ...
- 1
8
votes
3
answers
1k
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Is there any *global* timelike Killing vector in Schwarzschild geometry?
I have been dealing with the following issue related to the Schwarzschild geometry recently. When expressed as:
$$
ds^{2}=-\left(1-\frac{2GM}{r}\right)dt^{2}+\frac{1}{1-\frac{2GM}{r}}dr^{2}+d\Omega_{2}...
- 503
1
vote
1
answer
97
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Can you modify the surrounding curvature of a black hole while keeping the Schwarzschild radius constant?
TL;DR: I'm attempting to make a black hole rendering, and I like the current size of the event-horizon but I want to reduce the curvature further away from it. But it seems like $g_{uv}$ only depends ...
- 45
3
votes
2
answers
356
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How does time become space inside a black hole? What is the space the old time variable "becomes"?
The Schwarzschild metric is
$$
ds^2 = - (1 - r_s/r) dt^2 + (1 - r_s/r)^{-1}dr^2 + r^2 d\Theta^2,
$$
where $d \Theta^2 = \sin^2 \varphi\, d \theta + d\varphi^2$ is the metric on the sphere and $r_s$ is ...
- 396
1
vote
1
answer
114
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Distances in General Relativity, near massive bodies
I've been studying the basics of General Relativity, and my question is: does it make sense to say that near a black hole (or any massive body), distances increase, the way on a topographical map the ...
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