All Questions
33
questions
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
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
2
votes
1
answer
320
views
Why cant a repulsive event horizon of negative mass be theoretically constructed?
An event horizon appears in the Schwarzschild metric when considering a positive point mass in General Relativity.
But for a negative point mass in the negative mass Schwarzschild metric, which ...
- 476
3
votes
2
answers
297
views
Time in the negative mass Schwarzschild solution
I have read that for the Schwarzschild metric solution with $M<0$, something odd happens with the time coordinate. For the constants of motion, $dt/d\tau=e(1 - 2GM/r)^{-1}$ with $M<0$ and $e$ a ...
- 476
3
votes
1
answer
90
views
Kruskal Diagram: 2D projection?
Is a Kruskal diagram a 2D flat space projection of Schwarzschild space-time diagram? If not, isn't it true that one could not draw one accurately on a paper?
BTW, I am not referring to Penrose ...
- 1,161
3
votes
2
answers
158
views
About the temporal coordinate $t_*$ in Eddinton-Finkelstein coordinate
For the Schwarzschild solution $ds^2=-(1-\frac{2GM}{r})dt^2+(1-\frac{2GM}{r})^{-1}dr^2+r^2(d\theta^2+sin^2\theta d\phi^2)$, if we set $dr^2_*=(1-\frac{2GM}{r})^{-2}dr^2$(in other words, $r_*=r+2GMlog{|...
- 77
2
votes
0
answers
568
views
How to derive the Kerr killing vector?
The Kerr metric have two killing vectors:
$$t^{\mu} \equiv (k_{t})^{\mu} = (1,0,0,0)\hspace{5mm} \mathrm{and}\hspace{5mm} \phi^{\mu} \equiv (k_{\phi})^{\mu} = (0,0,0,1). \tag{1}$$
In general, it is ...
- 3,085
1
vote
1
answer
187
views
Schwarzschild geometry
In the text "Exploring Black Holes" by Taylor ,Wheeler I came across the following thought experiment
"We consider two imaginary concentric spherical shells and suppose we measure the &...
0
votes
1
answer
147
views
Schwarzschild with cosmic strings: How can I visualize the string?
Geometrically, you can talk about a cosmic string in Schwarzschild black hole with this metric $[1]$:
$$ds^{2} = -\Big(1- \frac{r_{s}}{r}\Big) dt^{2} + \frac{1}{\Big(1- \frac{r_{s}}{r}\Big)}dr^{2} + ...
- 3,085
2
votes
2
answers
262
views
How do I deal with the radius-coordinate of the schwarzschild-metric in this numerical problem?
It is well known that if a black hole fulfills certain conditions, it's tidal forces will rip incoming objects apart even before they cross the event horizon. So at some point, the curvature of space ...
- 101
1
vote
1
answer
123
views
Visualization of time curvature of spacetime
The Flamm's paraboloid is a slice of the Schwarzschild metric by two spatial dimensions. This shows the space dilation, but without the time component doesn't really give much insight into the ...
- 1,601
2
votes
1
answer
567
views
A doubt on the Topology of Einstein-Rosen Bridges (or Schwarzschild/Kruskal Wormholes)
Well, one of the "mantras" of General Relativity is:
Einstein Field Equations concerns about the local geometrical structure of spacetime (the metric tensor) and tell you nothing about the ...
- 3,085
4
votes
1
answer
394
views
Penrose diagram for two black holes
There are well-known Penrose diagrams for black holes:
And for collapsing star:
Diagram for collapsing star is obtained by joining two Penrose diagrams:
Is it possible to join diagrams for two ...
- 5,707
0
votes
2
answers
59
views
Replacing the $M$ coefficient in Schwarzschild metric with a distribution $M(r)$
Consider the Schwarzschild metric
$$ds^2 = -f(r)dt^2 + \frac{1}{f(r)}dr^2+r^2 d\Omega^2,$$
where $f(r)=1-\frac{2M}{r}$. I take it that $M$, although not really the mass of a black hole, is the ...
- 595
0
votes
1
answer
102
views
Existence of parallel vector field
Is there any known parallel vector field in a Schwarzschild spacetime? Or any method to identify parallel vector fields in any spacetime, given the metric $g$?
- 1