Abstract
One of the most important achievements in general relativity has been discovery of the (2 + 1)-dimensional black hole solutions of Einstein gravity in anti-de Sitter (AdS) spacetime [7]. In this paper, we construct, for the first time, the (2 + 1)-dimensional solutions of mimetic theory of gravity. These solutions may provide a powerful background to investigate the physical properties of mimetic gravity and examine its viability in lower spacetime dimensions. In particular, some physical properties of stationary black hole solutions of this theory in the presence of charge or angular momentum are investigated.
Highlights
Field equations and solutionsOur aim here is to derive static (2 + 1)-dimensional black hole solutions of the above field equations
JHEP01(2021)043 the quantum gravity in three dimensions
We study the effects of the mimetic field on the casual structure and physical properties of the solutions and disclose that, in contrast to the three dimensional solution of general relativity, in mimetic gravity a curvature singularity emerges at r = 0 even in the absence of Maxwell field
Summary
Our aim here is to derive static (2 + 1)-dimensional black hole solutions of the above field equations. Where b is the constant of integration which incorporates the impact of the mimetic field into the solutions. The asymptotic behavior of the solutions is still AdS since the constant 1 + b can be absorbed by redefinition of the time at the asymptotic region This confirms that in large r limit, we have −gtt = grr. The spacetime has an essential singularity at r = 0 This is in contrast to the (2 + 1)-dimensional black holes of Einstein gravity where r = 0 is not a curvature singularity but, rather, a singularity in the causal structure [15]. We shall consider the (2 + 1)-dimensional charged black hole of mimetic gravity
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