Thermodynamic Interpretation of Field Equations at Horizon ofBTZ Black Hole

Abstract

A spacetime horizon comprising with a black hole singularity acts like aboundary of a thermal system associated with the notions of temperatureand entropy. In the case of static metric ofBanados–Teitelboim–Zanelli (BTZ) black hole, the field equations near the horizon boundary can be expressed as a thermal identity dE = TdS+PrdA, where E = M is the mass of BTZ black hole, dA is thechange in the area of the black hole horizon when the horizon isdisplaced infinitesimally small, Pr is the radial pressure providedby the source of Einstein equations, S = 4πa is the entropy and T = κ/2π is the Hawking temperature associated with the horizon.This approach is studied further to generalize it for non-static BTZblack hole, showing that it is also possible to interpret thefield equation near horizon as a thermodynamic identity dE = TdS+PrdA+Ω+dJ, where Ω+ is the angularvelocity and J is the angular momentum of BTZ black hole. Theseresults indicate that the field equations for BTZ black holepossess intrinsic thermodynamic properties near the horizon.