Thermodynamic Interpretation of Field Equations at Horizon of BTZ Black Hole

Abstract

A spacetime horizon comprising with a black hole singularity acts like a boundary of a thermal system associated with the notions of temperature and entropy. In case of static metric of BTZ black hole, the field equations near horizon boundary can be expressed as a thermal identity $dE=TdS+P_{r}dA$, where $E=M$ is the mass of BTZ black hole, $dA$ is the change in the area of the black hole horizon when the horizon is displaced infinitesimally small, $P_r$ is the radial pressure provided by the source of Einstein equations, $S=4\pi a$ is the entropy and $T=\kappa /2\pi$ is the Hawking temperature associated with the horizon. This approach is studied further to generalize it for non-static BTZ black hole and show that it is also possible to interpret the field equation near horizon as a thermodynamic identity $dE=TdS+P_{r}dA+{\Omega }_{+}dJ$, where ${\Omega }_{+}$ is the angular velocity and $J$ is the angular momentum of BTZ black hole. These results indicate that the field equations for BTZ black hole possess intrinsic thermodynamic properties near horizon.

8 pages

References in corpus (2)

• Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics
• Thermodynamic route to Field equations in Lanczos-Lovelock Gravity

Cited by in corpus (8)

• Friedmann Equations from Entropic Force
• Lessons from Classical Gravity about the Quantum Structure of Spacetime
• Notes on Entropy Force in General Spherically Symmetric Spacetimes
• Generalized Second Law of Thermodynamics in Extended Theories of Gravity
• Deformation of Codimension-2 Surface and Horizon Thermodynamics
• Quantum corrections to the entropy of Einstein-Maxwell dilaton-axion black holes
• Corrected entropy of the rotating black hole solution of the new massive gravity using the tunneling method and Cardy formula
• Thermodynamic approach to field equations in Lovelock gravity and f(R) gravity revisited