Entropy product function and central charges in NUT geometry

Abstract

We define an entropy product function (EPF) for Taub–Newman–Unti–Tamburino (TNUT) black hole (BH) following the prescription suggested by Wu et al. [Phys. Rev. D 100, 101501(R) (2019)]. The prescription argues that a generic four-dimensional TNUT space–time might be expressed in terms of three or four different types of thermodynamic hairs. They can be defined as the Komar mass ([Formula: see text]), the angular momentum ([Formula: see text]), the gravitomagnetic charge ([Formula: see text]), the dual (magnetic) mass [Formula: see text]. Taking this prescription and using the EPF, we derive the central charges of dual conformal field theory (CFT) via Cardy’s formula. Remarkably, we find that for TNUT BH there exists a relation between the central charges and EPF as [Formula: see text], where [Formula: see text] is EPF and [Formula: see text] is one of the integer-valued charges i.e. the NUT charges ([Formula: see text]) or any new conserved charges ([Formula: see text]). We reverify these results by calculating the exact values of different thermodynamic parameters. We define the EPF [Formula: see text] from the first law of thermodynamics of both horizons. Moreover, we write the first laws of both the horizons for left-moving and right-moving sectors. Introducing the Bézout’s identity, we show that for TNUT BH one can generate more holographic descriptions described by a pair of integers [Formula: see text]. More holographic pictures have a great significance towards understanding the holographic nature of quantum gravity. Furthermore, using the EPF we derive the central charges for Reissner–Nordström–NUT (RNNUT) BH, Kerr–Taub–NUT (KNUT) BH and Kerr–Newman–NUT (KNNUT) BH. Finally we prove that they are equal in both sectors provided that the EPF is mass-independent (or universal).