Thermodynamic Product Formula for Taub-NUT Black Hole

Abstract

We derive various important thermodynamic relations of the inner and outer horizon in the background of Taub-NUT(Newman-Unti-Tamburino) black hole in four dimensional \emph{Lorentzian geometry}. We compare these properties with the properties of Reissner Nordstrøm black hole. We compute \emph{area product, area sum, area minus and area division} of black hole horizons. We show that they all are not universal quantities. Based on these relations, we compute the area bound of all horizons. From area bound, we derive entropy bound and irreducible mass bound for both the horizons. We further study the stability of such black hole by computing the specific heat for both the horizons. It is shown that due to negative specific heat the black hole is thermodynamically unstable. All these calculations might be helpful to understanding the nature of black hole entropy both \emph{interior} and exterior at the microscopic level.

10 Pages, Accepted in Journal of Experimental and Theoretical Physics(JETP), 05/08/2015

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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• Energy Formula for Newman-Unti-Tamburino class of Black Holes
• Entropy Product Function and Central charges in NUT Geometry
• Entropy Product Formula for Gravitational Instanton
• Circular Orbits in the Taub-NUT and mass-less Taub-NUT Space-time
• Bekenstein-Hawking Entropy Products for NUT class of Black Holes in AdS Space