Speaker
Description
We define an entropy product function (EPF) for Taub-Newman-Unti-Tamburino(TNUT) black hole(BH) following the prescription suggested by Wu et al. [PRD 100, 101501(R) (2019)].
The prescription argues that a generic four-dimensional TNUT spacetime might be expressed in terms of three or four different types of thermodynamic hairs. They can be defined as the Komar mass($M=m$), the angular momentum($J_{n}=mn$), the gravitomagnetic charge ($N=n$), the dual (magnetic) mass $(\tilde{M}=n)$. Taking this prescription and
using the EPF, we derive the central charges of dual CFT (conformal field theory) via Cardy's formula. Remarkably, we find that for TNUT
BH there exists a relation between the central charges and EPF as $c=6\left(\frac{\partial {\cal F}}{\partial {\cal N}_{i}}\right)$,
where ${\cal F}$ is EPF and ${\cal N}_{i}$ is one of the integer-valued
charges i.e. the NUT charges($N$) or any new conserved charges($J_{N}$).
We reverify these results by calculating the exact values of different thermodynamic parameters. We define the EPF ${\cal F}$ 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 B\'{e}zout's identity, we show that for TNUT BH one
can generate more holographic descriptions described by a pair of integers $(a,b)$. More holographic pictures have
a great significance in understanding the holographic nature of quantum gravity. Furthermore, using the EPF we derive the central charges for Reissner-Nordstr\"{o}m-NUT(RNNUT) BH, Kerr-Taub-NUT~(KNUT) BH and Kerr-Newman-NUT~(KNNUT) BH proved that they are equal in both
sectors provided that the EPF is mass-independent(or universal).
