AdS spacetimes and isometric embeddings

An algebraic global isometric embedding of the nonrotating BTZ black hole is presented. The ambient spacetime is $\mathbb{M}^{2,3}$, the 3+2 dimensional flat spacetime. We also present the analogous embedding for the Euclidean BTZ spacetime and by performing a kind of double analytic continuation construct a 1-parameter family of embeddings of cosmological AdS spacetime into $\mathbb{M}^{2,3}$ which coincide asymptotically with the embedded BTZ manifold of the appropriate mass. Finally we note that the family of embeddings of cosmological AdS$_{n}$ into $\mathbb{M}^{2,n}$ generalises to higher dimensions.Comment: To appear in the proceedings of the conference: "Relativity and Gravitation, 100 Years after Einstein in Prague." We give a brief review of the results obtained in [arXiv:1011.3883[gr-qc]]. Lemma 2.2, is a new resul

Inaugural Session, Institute of English Studies Seminar in the History of Libraries

Text of the inaugural session of the Institute of English Studies seminar in the History of Libraries held on 27/2/08

Israel conditions for the Gauss-Bonnet theory and the Friedmann equation on the brane universe

Assuming an Einstein-Gauss-Bonnet theory of gravitation in a ($D \geq 5$)-dimensional spacetime with boundary, we consider the problem of the boundary dynamics given the matter Lagrangian on it. The resulting equation is applied in particular on the derivation of the Friedmann eq. of a 3-brane, understood as the non-orientable boundary of a 5d spacetime. We briefly discuss the contradictory conclusions of the literature.Comment: 8 pages, published versio