Entropy Product Formula for spinning BTZ Black Hole
Abstract
We investigate the thermodynamic properties of inner and outer horizons in the background of spinning BTZ(Ba\~{n}ados,Teitelboim and Zanelli) black hole. We compute the \emph{horizon radii product, the entropy product, the surface temperature product, the Komar energy product and the specific heat product} for both the horizons. We observe that the entropy product is \emph{universal}(mass-independent), whereas the surface temperature product, Komar energy product and specific heat product are \emph{not universal} because they all depends on mass parameter. We also show that the \emph{First law} of black hole thermodynamics and \emph {Smarr-Gibbs-Duhem } relations hold for inner horizon as well as outer horizon. The Christodoulou-Ruffini mass formula is derived for both the horizons. We further study the \emph{stability} of such black hole by computing the specific heat for both the horizons. It has been observed that under certain condition the black hole possesses \emph{second order phase transition}.
Keywords
Cite
@article{arxiv.1509.00626,
title = {Entropy Product Formula for spinning BTZ Black Hole},
author = {Parthapratim Pradhan},
journal= {arXiv preprint arXiv:1509.00626},
year = {2015}
}
Comments
9 Pages, Accepted in JETP Letters, 20/08/2015. arXiv admin note: text overlap with arXiv:1506.03173