Three-dimensional black holes via Noether symmetries

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.

29 pages, 1 table, no figures, to appear in Physical Review D

References in corpus (7)

• Black holes in asymptotically Lifshitz spacetime
• Scalar-Tensor Teleparallel Wormholes by Noether Symmetries
• Two dimensional dynamical systems which admit Lie and Noether symmetries
• Exact solutions of three dimensional black holes: Einstein gravity vs F(R) gravity
• Black holes and gravitational waves in three-dimensional f(R) gravity
• Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes
• Radiation in (2+1)-dimensions

Cited by in corpus (1)

• Black holes of $(2+1)$-dimensional $f(R)$ gravity coupled to a scalar field