(2+1)-dimensional f(R) gravity solutions via Hojman symmetry

TL;DR

This paper employs the Hojman symmetry method to discover new (2+1)-dimensional f(R) gravity solutions, including BTZ black holes, highlighting the role of symmetry in deriving cosmological constants.

Contribution

It introduces the Hojman symmetry approach to find gravity solutions, providing an alternative to Noether symmetry and revealing the cosmological constant as a symmetry manifestation.

Findings

Recovered (2+1)-dimensional BTZ black hole solutions

Generalized BTZ black hole solutions obtained

Cosmological constant emerges from Hojman symmetry

Abstract

In this paper, we use the Hojman symmetry approach to find new $(2+1)$-dimensional $f(R)$ gravity solutions, in comparison to Noether symmetry approach. In the special case of Hojman symmetry vector $X=R$, we recover $(2+1)$-dimensional BTZ black hole and generalized $(2+1)$-dimensional BTZ black hole solutions, obtained by Noether symmetry approach, and the interesting point is that the cosmological constant is appeared as the direct manifestation of Hojman symmetry.