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(Bañados,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}.

9 Pages, Accepted in JETP Letters, 20/08/2015. arXiv admin note: text overlap with arXiv:1506.03173

References in corpus (3)

• Universal Area Product Formulae for Rotating and Charged Black Holes in Four and Higher Dimensions
• Inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory
• Thermodynamic Product Formula for Hořava Lifshitz Black Hole

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• Universal entropy relations: entropy formulae and entropy bound
• Hawking radiation of rotating BTZ Black hole based on modified dispersion relation and Rarita-Schwinger equation
• Entropy Product Formula for Gravitational Instanton
• Thermodynamic Volume Product in Spherically Symmetric and Axisymmetric Spacetime
• Entropy product of rotating black holes in three-dimensions