Solutions of generalized supergravity equations with the BTZ black hole metric

Eghbali, Ali; Ghasemi-Sorkhabi, Simin; Rezaei-Aghdam, Adel

doi:10.30511/ttmp.2024.2016004.1019

Solutions of generalized supergravity equations with the BTZ black hole metric

Document Type : Original Article

Authors

Ali Eghbali

Simin Ghasemi-Sorkhabi

Adel Rezaei-Aghdam

Department of Physics, Azarbaijan Shahid Madani University, Tabriz, Iran

10.30511/ttmp.2024.2016004.1019

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

Generalized supergravity equations

Standard supergravity

BTZ metric

Subjects