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Exact solutions of Einstein and Einstein-scalar equations in 2 + 1 dimensions

K. S. Virbhadra
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Abstract

A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant $Λ$ and null fluid) in $2+1$ dimensions is given. This is a nonstatic generalization of the uncharged spinless BTZ metric. For $Λ= 0 $, the spacetime is though not flat, the Kretschmann invariant vanishes. The energy, momentum, and power output for this metric are obtained. Further a static and circularly symmetric exact solution of the Einstein-massless scalar equations is given, which has a curvature singularity at $r =0$ and the scalar field diverges at $r=0$ as well as at infinity .

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K. S. Virbhadra. 1994-08-29. Exact solutions of Einstein and Einstein-scalar equations in 2 + 1 dimensions. https://doi.org/10.1007/bf02847608

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