Three-dimensional black holes via Noether symmetries

TL;DR

This paper explores Noether symmetries in three-dimensional rotating BTZ-type black holes within $f(R)$ gravity, deriving new solutions and analyzing their thermodynamic properties, including mass, angular momentum, and adherence to thermodynamic laws.

Contribution

It introduces a Noether symmetry approach to find exact rotating BTZ-type black hole solutions in $f(R)$ gravity, which is a novel application in this context.

Findings

Derived new (2+1)-dimensional rotating BTZ-type black hole solutions.

Confirmed thermodynamic quantities satisfy the first law and Smarr-like formulas.

Analyzed physical implications of the new solutions.

Abstract

We investigate the Noether symmetries of the Lagrangian for the stationary rotating BTZ-type three-dimensional spacetimes in $f(R)$ theory of gravity. A detailed analysis of Noether symmetries of (2+1)-dimensional rotating BTZ-type black hole spacetime model is presented. Applying the Noether symmetry approach, the first integrals (constants of motion) for each of Noether symmetries are obtained to look for the exact solutions. After solving the first integral equations depending on the form of the function $f(R)$, we derived some new (2+1)-dimensional rotating BTZ-type black hole solutions. We discussed the physical implications of the derived exact solutions. The thermodynamical properties of the obtained BTZ-type black hole solutions are analyzed by making use of the mass $M$ and the angular momentum $J$ in terms of $r_{\pm}$, where $r_+$ is the event horizon and $r_{-}$ is the inner horizon. Further, it is shown that thermodynamic quantities obey the first law, and the Smarr-like formulas of the solutions we found are obtained.