Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

Solutions of generalized supergravity equations with the BTZ black hole metric

Document Type : Original Article

Authors
Department of Physics, Azarbaijan Shahid Madani University, Tabriz, Iran
Abstract
We proceed to investigate the solutions of generalized supergravity equations (GSE) in three dimensions.
Our candidate is the metric of BTZ black hole. It is shown that only the cases with J=M=0 and J=0, M\neq 0 of the BTZ metric satisfy the GSE.
In the former, we find a family of solutions including the field strength H_r t=2r/l,
the cosmological constant Lambda=-1/l times l, one-form Z_mu and a vector field which is obtained to be a linear combination of the directions of the time translation and rotational symmetries. In the latter, the solutions possess the same field strength as before, while the cosmological constant Lambda,
one-form Z_mu and vector field I will be different from the previous case.
Finally, we show that the charged black string solution
found by Horne and Horowitz, which is Abelian T-dual to the the BTZ black hole solution, can be considered as a solution for the GSE.
Keywords
Subjects

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Volume 1, Issue 2
Spring 2024
Pages 33-38

  • Receive Date 19 November 2023
  • Accept Date 03 February 2024
  • First Publish Date 01 May 2024
  • Publish Date 01 May 2024