Area (or entropy) products for Newman-Unti-Tamburino class of Black Holes

Abstract

We compute area (or entropy) product formula for Newman-Unti-Tamburino (NUT) class of black holes. Specifically, we derive the area product of outer horizon and inner horizon (${ \mathcal{H}}^{\pm }$) for Taub-NUT, Euclidean Taub-NUT black hole, Reissner-Nordstr\"{o}m--Taub-NUT black hole, Kerr-Taub-NUT black hole and Kerr-Newman-Taub-NUT black hole under the formalism developed very recently by Wu et al. \cite{wu} [PRD 100, 101501(R) (2019)]. The formalism is that a generic four dimensional Taub-NUT spacetime should be described completely in terms of three or four different types of thermodynamic hairs. They are defined as the Komar mass ($M=m$), the angular momentum ($J_{n}=m\,n$), the gravitomagnetic charge ($N=n$), the dual (magnetic) mass $(\tilde{M}=n)$. After incorporating this formalism, we show that the area (or entropy) product of both the horizons for NUT class of black holes are \emph{mass-independent}. Consequently, the area product of ${\mathcal{H}}^{\pm }$ for these black holes are \emph{universal}. Which was previously known in the literature that the area product of said black holes are \emph{mass-dependent}. Finally, we can say that this universality is solely due to the presence of \emph{new conserved charges $J_{N}=M\,N$} which is closely analogue to the Kerr like angular momentum $J=a\,M$.