1
vote
1answer
88 views

Normal to the Hypersurfaces

I am trying to understand the derivation of the Hilbert-Einstein action. However it requires a knowledge about hyper-surfaces for the boundaries of the integrals and also about the normal to the ...
12
votes
1answer
361 views

Asymptotic symmetry algebra

So after a lot of research, and tons and tons of papers that I've went through, I finally have some idea how to solve the equations that will give me candidates for the asymptotic symmetry group for ...
2
votes
1answer
57 views

Getting diffeomorphisms from boundary conditions in $AdS_3$

As usual I'm asking a question about boundary conditions for AdS${}_3$, based on the thesis by Porfyriadis. He is solving equations $\mathcal{L}_\xi g_{\mu\nu}$ for AdS${}_3$ metric, with a given ...
2
votes
1answer
59 views

Finding superpotentials and central charges in $AdS_3$

In text "Covariant theory of asymptotic symmetries, conservation laws and central charges" is given an example of finding central charges and superpotential (among other things). I am interested in ...
1
vote
1answer
59 views

Maximum aging and path of rock

When a rock falls from a ledge, why does it head to the surface and not up to where time runs faster? If a rock, free from forces, follows a worldline of maximum aging, why would that rock approach ...
5
votes
1answer
104 views

Help with the understanding of boundary conditions on $AdS_3$

So I am trying to reproduce results in this article, precisely the 3rd chapter 'Virasoro algebra for AdS$_3$'. I have the metric in this form: ...
6
votes
1answer
343 views

Diffeomorphisms and boundary conditions

I am trying to find out how did the authors in this paper (arXiv:0809.4266) found out the general form of the diffeomorphism which preserve the boundary conditions in the same paper. I found this ...
6
votes
1answer
155 views

Einstein's equations as a Dirichlet boundary problem

Can Einstein's equations in vacuum $R_{ab} - \frac{1}{2}Rg_{ab} + \Lambda g_{ab}= 0$ be treated as a Dirichlet problem? I am thinking of something along those lines: Consider a compact manifold $M$ ...
6
votes
1answer
352 views

Do spacelike junctions in the Thin-Shell Formalism imply energy nonconservation and counterintuitive wormholes?

The Thin Shell Formalism (MTW 1973 p.551ff) is used to properly paste together different vacuum solutions to the Einstein equations. At the junction of the two solutions is a hypersurface of matter – ...