All Questions
Tagged with black-holes vector-fields
24
questions
-1
votes
1
answer
56
views
Why does the timelike killing vector become spacelike inside the ergoregion?
Why does the timelike killing vector become spacelike inside the ergoregion?
Some textbooks make this claim and move on to explain negative energy, but I could not find any proof for this claim. I can'...
- 63
4
votes
3
answers
667
views
What is the proof that the Schwarzschild metric is not static inside the horizon?
In Lecture Notes on General Relativity, Sean M. Carroll shows that the Schwarzschild metric is not only stationary but also static (Chapter 7, page 169, Eq. 7.20 and following interpretation). On the ...
- 1,948
0
votes
0
answers
36
views
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
9
votes
1
answer
806
views
Defining Surface gravity of a black hole
For a Killing horizon associated with a Killing vector $K$, the surface gravity $\kappa$ can be computed by various methods, like
$$
\kappa^2 = - \frac{1}{2} \nabla^\mu K^\nu \nabla_\mu K_\nu \ .
$$
...
- 669
1
vote
1
answer
121
views
Calculating divergence and flux of geodesic word lines
Given a family of neighbouring geodesic word lines, is there a way of calculating properties such as their divergence or flux? maybe by converting the tangent vectors of the world lines to a vector ...
- 633
4
votes
1
answer
1k
views
I'm confused about the number of Killing vectors in Schwarzschild metric
I'm trying to perform a calculation to derive the Killing vectors of a spherically symmetric metric (so I use the Schwarzschild metric without loss of generality because the Birkhoff theorem tells me ...
- 180
0
votes
1
answer
68
views
Tensor Manipulation in Wald's General Relativity by Robert M. Wald at page 334
I don't understand the example, just after the "i.e.", at the end of the paragraph in the image. Why is it zero when the condition is fulfilled?
- 37
1
vote
0
answers
86
views
Rotating Observers in Kerr Spacetime
I am learning about the Kerr metric and I am using the book Gravitation - Foundations and Frontiers by T. Padmanabhan.
While discussing a 'static limit' he considers an observer rotating with an ...
- 593
1
vote
0
answers
307
views
Killing Horizons in the Kerr Metric
I seem to be quite confused with Killing vector fields, Killing horizons and null horizons, especially in the context of the Kerr metric. I have a couple of questions regarding this, and the text I am ...
- 593
0
votes
1
answer
101
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
0
votes
0
answers
339
views
Killing vectors of Schwarzschild: Solution
In the solution of the Killing equations for Schwarzschild metric, $\nabla_\mu\xi_\nu+\nabla_\nu\xi_\mu=0$ for rotational part of symmetry participate Christoffel symbols with purely angular ...
- 626
3
votes
1
answer
2k
views
What's the significance of a Killing horizon?
A Killing horizon is defined as a null hypersurface generated by a Killing vector, which is then null at that surface. Some often cited examples come from the Kerr spacetime, where the Killing vector $...
- 28.3k
1
vote
0
answers
102
views
Systematic way of finding the Killing vector of a specific mass
I have a specific black hole solution (in AdS space) with a particular energy given. The energy was computed in the paper by assuming the validity of the first law ($dE = T dS + \Omega dJ + \Phi dQ$) ...
- 700
3
votes
1
answer
276
views
Why is $\chi_{[\mu}\nabla_\nu \chi_{\sigma ]} = 0$ at the Killing horizon?
Let $\chi$ be a Killing vector field that is null along a Killing horizon $\Sigma$
Why is $\chi_{[\mu}\nabla_\nu \chi_{\sigma ]} = 0$ at $\Sigma$?
- 669
8
votes
2
answers
789
views
Puzzle concerning the Divergence Theorem
Something is puzzling me concerning the divergence theorem. Usually, one writes the divergence theorem as
\begin{equation}
\int_\mathcal{M} d^4x \sqrt{-g} \nabla_\mu v^\mu=\int_{\partial \mathcal{M}} ...
- 511