Constructing New Asymptotically de-Sitter Cosmological Solutions in (2+1)-Dimensions

Rajak, Debobrata and Roy, Shubho Ranjan (2017) Constructing New Asymptotically de-Sitter Cosmological Solutions in (2+1)-Dimensions. Masters thesis, Indian Institute of Technology Hyderabad.

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Abstract

In this work we find novel warped Kerr-de Sitter cosmological solution to the Einsteins field equa- tions in ( 2 + 1 ) − dimensions, modified by a Chern-Simons term. To start with we review the exact solutions of Einsteins field equations including the Penrose diagrams for highly symmetric space- times like that of Minkowski, de Sitter, anti-de Sitter and FLRW spacetimes. Next we review BTZ Black hole and their geometry for both rotating and non-rotating black holes. Balasubramanian and et. al. had found topologically non-trivial de Sitter (dS) solutions in (2 + 1)- dimensions, which are dubbed Kerr de Sitter and singular de Sitter quotients with Big bang/big crunch type singularities are also reviewed. Gravity in ( 2 + 1 ) − dimensions is reviewed as a simpler warm up problem to the ( 3 + 1 ) − dimensional case. In ( 2 + 1 ) − dimensions an additional Chern-Simon term is added to the Einstein-Hilbert action, this produces new interesting solutions. The introduction of the Chern-Simons term results in the non-zero mass of the graviton, thus giving us topologically massive gravity solutions. The warped AdS 3 and warped dS 3 spaces are also reviewed together with spacelike stretched warped AdS 3 black holes. Finally we write down the war ped Kerr − dS 3 solutions to the topological massive gravity(TMG) equation of motion.

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