Surface Area Products for Kerr-Taub-NUT Space-time

Abstract

We examine properties of the inner and outer horizon thermodynamics of Taub-NUT (Newman-Unti-Tamburino) and Kerr-Taub-NUT (KTN) black hole (BH) in four dimensional \emph{Lorentzian geometry}. We compare and contrasted these properties with the properties of Reissner Nordstrøm (RN) BH and Kerr BH. We focus on "area product", "entropy product", "irreducible mass product" of the event horizon and Cauchy horizons. Due to mass-dependence, we speculate that these products have no beautiful quantization feature. Nor does it has any universal property. We further observe that the \emph{First law} of BH thermodynamics and \emph {Smarr-Gibbs-Duhem} relations do not hold for Taub-NUT (TN) and KTN BH in Lorentzian regime. The failure of these aforementioned features are due to presence of the non-trivial NUT charge which makes the space-time to be asymptotically non-flat, in contrast with RN BH and Kerr BH. The another reason of the failure is that Lorentzian TN and Lorentzian KTN geometry contains \emph{Dirac-Misner type singularity}, which is a manifestation of a non-trivial topological twist of the manifold. The black hole \emph{mass formula} and \emph{Christodoulou-Ruffini mass formula} for TN and KTN BHs are also computed. This thermodynamic product formulae gives us further understanding to the nature of BH entropy (inner and outer) at the microscopic level.

Version accepted for publication in EPL

References in corpus (8)

• 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
• Statistical Origin of Gravity
• Black Hole Interior Mass Formula
• Thermodynamic Product Formula for Hořava Lifshitz Black Hole
• The "universal property" of Horizon Entropy Sum of Black Holes in Four Dimensional Asymptotical (anti-)de-Sitter Spacetime Background
• Kerr-Taub-NUT Spacetime with Maxwell and Dilaton Fields
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Cited by in corpus (8)

• Thermodynamical hairs of the four-dimensional Taub-Newman-Unti-Tamburino spacetimes
• Consistent mass formulas for the four-dimensional dyonic NUT-charged spacetimes
• Remarks on the Taub-NUT solution in Chern-Simons modified gravity
• Area (or entropy) products for Newman-Unti-Tamburino class of Black Holes
• Energy Formula for Newman-Unti-Tamburino class of Black Holes
• Upper limit on NUT charge from the observed terrestrial Sagnac effect
• Entropy Product Function and Central charges in NUT Geometry
• Entropy Product Formula for Gravitational Instanton