Relativity and Cosmology


An Ads Related Spacetime with Time Dependent Scale Factor

Authors: Thomas Heiko Günther

McVittie's model [10], which interpolates between a Schwarzschild Black Hole and an expanding global (FLRW) spacetime, can be constructed by a simple coordinate replacement in Schwarzschild's isotropic intervall. Analogously, one gets a similarly generated exact solution of Einstein's equations based on a static transformation of de Sitter's metric, cf. [6]. The present article is concerned with the application of this method on the AdS (Anti de Sitter) spacetime. Multiplying the radial coordinate and it's differential by a function a(t) gives the basic line element. Einstein's equations for the modified interval reduce to a system of two differential equations, which are solved in the article. The resulting solution is classified depending on the value of the cosmological constant. Several promising theories like String theorie and AdS/CFT correspondence [11] include spacetimes with higher dimensions. Thereby motivated, the previous results of this article are generalized to D dimensions in the last section.

Comments: 7 Pages.

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Submission history

[v1] 2018-06-27 17:28:19

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