Relativity and Cosmology

   

N-Dimensional Ads Related Spacetime and Its Transformation

Authors: Thomas Heiko Günther

Recently, anti-de Sitter spaces are used in promising theories of quantum gravity like the anti-de Sitter/conformal field theory correspondence. The latter provides an approach to string theorie, which includes more than four dimensions. Unfortunately, the anti-de Sitter model contains no mass and is not able to describe our universe adequately. Nevertheless, the rising interest in higherdimensional theories motivates to take a deeper look at the n-dimensional AdS Spacetime. In this paper, a solution of Einstein's field equations is constructed from a modified anti-de Sitter metric in n dimensions. The idea is based on the connection between Schwarzschild- and McVittie metric: McVittie's model, which interpolates between a Schwarzschild Black Hole and an expanding global Friedmann–Lemaître–Robertson–Walker spacetime, can be constructed by a simple coordinate replacement in Schwarzschild's isotropic intervall, where radial coordinate and it's differential is multiplied by a time dependent scale factor a(t). In a previous work I showed, that an exact solution of Einstein's equations can analogously be generated from a static transformation of de Sitter's metric. The present article is concerned with the application of this method on an AdS (Anti de Sitter) related spacetime in n dimensions. It is shown that the resulting isotropic intervall is a solution of the n-dimensional Einstein equations. Further, it is transformed into a spherical symmetric but anisotropic form, analogously to the transformtion found by Kaloper, Kleban and Martin for McVittie's metric.

Comments: 4 Pages.

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Submission history

[v1] 2019-01-26 05:35:32

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