All Questions
125
questions
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Orthogonal complement of null vector [closed]
I am trying to solve excercise 8.5 d) from Straumanns book on general relativity (here V is an n-dimensional Minkowski vector space):
Prove that the orthogonal complement of a null vector is an $(n-1)$...
- 11
1
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1
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46
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The Expansion of a Congruence of Outgoing Light Rays in Schwarzschild Metric - Kruskal Coordinates
Background:
The Schwarzschild metric expressed in Kruskal coordinates is $$ds^2=-\frac{32M^3}{r}e^{-r/2M} dU dV + r^2 d\Omega^2,$$ where $r=r(U,V)$ is defined through the implicit relation $$e^{-r/2M}\...
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0
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What is tangential and radial velocity of light in Schwarzschild metric at distance $r$ for observer that is infinitely far away?
What i have learned from Schwarzschild metric is that the time dilation at
radius $r$ compared to distant observers time is:
$$ \frac{\tau_r }{t_\infty } = \sqrt{1 - \frac{r_s}{r}} $$
and i have heard ...
- 385
2
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1
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163
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Why domain of Kerr black hole includes negative values for $r$ coordinate?
I understand the domain of $t$ is all real numbers but mathematically, how to prove the domain of $r$ coordinate is also all real numbers except $r=0$ when $\theta = \pi/2$. I know that we get two ...
- 59
0
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1
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150
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Black holes, singularities and topology in relativity
General relativity is defined on a base manifold which, viewed as a topological space, is simply connected (which means there's no holes). However, we know that inside a black hole there's a ...
- 309
1
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1
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95
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Reaching a turning point in photon trajectory
Given the geodesic equations for a photon in a Schwarzchild or Kerr metric (provided by a near BH for example), the radial equation has usually two possible signs:
\begin{equation}
\dfrac{dr}{d\tau}= ...
- 169
6
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1
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350
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Are worldlines towards the origin with the Schwarzschild metric finite in time and length?
A recent spacetime video about Kerr's objection to the existence of singularities has made want to clear up something about geodesics towards the origin in the Schwarzschild solution.
It is said that ...
- 462
3
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88
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Intuition for the interior Killing vector fields in Schwarzschild?
The Schwarzschild metric represents a stationary (and static), spherically-symmetric, spacetime. These characteristics are manifested by the four Killing vector fields: one for time translation and ...
- 1,290
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37
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Application of Fermi-Walker derivative to specific problem
I am now reading about the tetrad formalism in GR and I am starting (how not) with the Wikipedia Article:
Frame fields in general relativity.
In this article, as an example, they show how tetrads can ...
- 533
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1
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142
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The Komar mass of the second Killing vector in the Schwarzschild metric
In David Tong's lectures on general relativity the interpretation of the $M$ which appears in Schwarschild metric:
$$ds^2=-\left(1-\frac{2GM}{r}\right)dt^2+\left(1-\frac{2GM}{r}\right)^{-1}dr^2+r^2\...
-4
votes
2
answers
102
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Are black holes 4-dimensional balls of spacetime? If so, will they have 3-sphere surfaces?
If black holes are 4-dimensional balls of spacetime, they will have a 3-sphere surface with a 3-dimensional volume. Would this allow infalling matter to remain within this surface?
- 371
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1
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115
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Obtaining Geodesic equation for Massive particles using Schwarzschild metric
Geodesic equations for the metric $$dS^2 = \left(1 - \dfrac{2GM}{r}\right)\dot t^2 - \dfrac{\dot r^2}{\left(1-\dfrac{2GM}{r}\right)} - r^2\left(\dot \phi^2\right),$$ would be
$$\left(1 - \frac{2GM}{r}\...
user385554
4
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44
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Eigenvalues of the geodesic deviation equation, curvature invariants, and singularities
The geodesic deviation equation tells us what tidal forces freely falling observers experience in a local Lorentz reference frame. The tidal deformation tensor is
$$E^{\alpha}_{\gamma}=R^{\alpha}_{\...
- 572
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1
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76
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Constant determinant of metric tensor of Schwarzschild solution in $(x, y, z, t)$ coordinates?
In spherical Schwarzschild coordinates, it's $A \cdot B$
= constant. Is there something similar in the Schwarzschild solution in $(x, y, z, t)$ coordinates? For example in Droste coordinates $g_{tt} \...
- 63
1
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2
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230
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Can the Schwarzschild orbit equation be solved exactly?
The Schwarzschild orbit is
$U'' + U = 1 + \varepsilon \cdot U^2$.
I've only seen turning-point analysis that demonstrates shift of perihelion.
Is there an exact solution?
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