Recent content by off-diagonal

Wow, thank you WannabeNewton for the proof of the first statement that helps me a lot. About the second statement, I am sure because I just copy+paste from the original textbook.

Hi, everyone I'm now reading A Relativist's Toolkit by Eric Poisson. In chapter 3, he say something about stationary and static spacetime. For static spacetime, it's just like stationary (admits timelike Killing vector t^{\alpha} ) with addition that metric should be invariant under...

oh thank you very much. now I think I understand it more clearer. Could you suggest me books or articles where the Penrose diagram is discussed in very neat detail?

Thank, LAHLH that's a great answer but, I'm still doubt about the boundary of causal past of future null infinitiy which Carroll said in his book (ch6). What is its physical meaning? He said it is an equivalent definition of an event horizon. One more question, if we begin with the...

I've got two questions here 1a What is the definition of an event horizon of black hole? In Carroll, he defines an event horizon as a boundary of causal past of future null infinitiy. What is the physical interpretation of that? 1b What is the difference between event horizon and Killing...

I've read about Schwarzschild and Kerr metric, I confused about the spacelike singularity(occur in non-rotating metric) and timelike singularity (Kerr, RN). In Schwarzschild case, when we cross and event horizon r=2M metric component switch sign between time and radial component of metric...

So , according to your comment when I apply the prescription in P.248 to the metric in Kruskal Coordinates (p,r,\theta,\phi). ds^{2}=\left(1-\frac{2M}{r}\right)dp dq-r^{2}d\Omega^{2}_{s^{2}} then as dq=d\theta=d\phi=0 so we conclude that p is null coordinate. Am I right? If that...

"vectors represented by partial derivative operators" like this? V=V^{\mu}\partial_{\mu} sorry, but I have no idea about what you are said. Could you please tell me more about it?

Now I'm study the Schwarzschild geometry from "General Relativity (M.P. Hobson)". Since the Schwarzschild metric has coordinate singularity at r=2M so to remove this singularity they use the Eddington-Finkelstein coordinate, first they begin with introduces new time parameter "p" p=ct+r+2M...

Now I'm just start to study the Kaluza-Klein theory from http://arxiv.org/abs/grqc/9805018. I try to calculate the Einstein Field equations in 5 dimensional vacuum space-time. we start with 5D metric tensor, \hat{g}_{AB}=\begin{pmatrix}...

What is it? and How different between intrinsic(absolute) derivative and covariant derivative? What is its geometric interpretation?

Thank you for your answer but after I perform calculation. I found a problem that may cause from my misunderstand about Killing vector equation. Here's the detail from these metric \displaystyle ds^2=d\theta^2 + sin^2\theta d\phi^2 I can read out metric tensor component as...

The metric on S^2 is given by, \displaystyle ds^2=d\theta^2 + sin^2\theta d\phi^2 Here's the answer \displaystyle \xi ^{\mu}_{(1)}\partial _{\mu} = \partial_{\phi} \displaystyle \xi^{\mu}_{(2)}\partial_{\mu} = \ -(cos\phi \partial_{\theta} - cot\theta sin\phi \partial_{\phi})...

"jerk" 4-vector?? What is jerk four vector? and what is its definition or a form? as far as I know it is a rate of change of 4-acceleration. Could anyone clarify me?

Hi, every one I'm newbie here. I have a few problem with my study about GR. Here's a problem \partial_a(g^{ad})g_{cd}-\partial_d(g^{ad})g_{ac}=\\0 Could I prove these relation by change index (in 1st term ) from a -> d and also d -> a? and let's defined {g}=det{\\g_{ab}\\}...