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 $H_{_{r \varphi t}}=2r/l$,
the cosmological constant $\Lambda=-1/l^2$, 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

Main Subjects


Volume 1, Issue 2
May 2024
Pages 33-38
  • Receive Date: 19 November 2023
  • Accept Date: 03 February 2024
  • First Publish Date: 11 February 2024
  • Publish Date: 01 May 2024