Recent content by atrahasis

Ok finally I got it.

Hi, I have a question concerning the Wald's book: General Relativity. In the appendix E, he derived the Einstein equation by considering the surface term (GHY). I do not understand what he said after the equation (E.1.38). Actually he considers that h^{bc}\nabla_c(\delta g_{ab})=0...

There are maybe all wrong, for example \Gamma_{00}^1=-\frac{1}{2}g^{11}\partial_r g_{00}=\frac{c^2 r_s (r-r_s)}{2 r^3} So maybe something is wrong when you define the inverse, e.g. g^{11}=-(1-r_s/r)

Thanks for the reply, I checked on Poisson's book and also Gourgoulhon's review but I couldn't found the reason. I finally understood my mistake, h_{\mu\nu} is not the induced metric but only the projection tensor. For to have the induced metric we have to look to the tangential components...

Ok I have half of the answer, the normal vector is wrong, because r=a(t), we have dr-\dot a dt=0, which gives for the normal vector n^\mu=n(-\dot a,1,0,0) with n a normalization factor in the goal to have g_{\mu\nu}n^\mu n^\nu=+1. But I still don't have the right induced metric

You have to replace the Riemann by it's decomposition into Weyl tensor ... which is given by the eq. 3.2.28 in Wald's book.

Hello, I have a problem to understand what people say by "induced metric". In many papers, it is written that for brane models, if we consider the metric on the bulk as g_{\mu\nu} hence the one in the brane is h_{\mu\nu}=g_{\mu\nu}-n_\mu n_{\nu} where n_{\mu} is the normalized spacelike...

thanks

Hi, Do you know the name of this kind of singularity at A ? The function is finite but the left derivative is +\infty and the right derivative is -\infty. http://shareimage.org/viewer.php?file=mt79897bbpxxse1v8pzb.jpg Thanks

Ok, finally I have it.

Hi, I was wondering about something a friend told me. He said that we can regularize this product in this form sgn(x)^2 \delta(x)=\frac{\delta(x)}{3} Any guess on how to derive it Thanks.