Bekenstein–Hawking entropy products for NUT class of black holes in AdS space

Abstract

In this paper, we derive the entropy product rule for Taub–Newman–Unti–Tamburino (Taub–NUT)–de Sitter black hole (BH) and Taub–NUT–anti-de Sitter BH. We show that the entropy products in terms of both the physical horizons are mass-independent. Both perturbative approximation and direct method have been considered. By introducing the cosmological horizon, we show that for Taub–NUT–de Sitter BH, there exists a mass-independent entropy functional relation in terms of three horizons namely event horizon (EH), Cauchy horizon (CH) and cosmological horizon (CHH) which depends on cosmological parameter ([Formula: see text]) and the NUT parameter (N). For Taub–NUT–anti-de Sitter BHs, we determine the mass-independent entropy functional relations in terms of two physical horizons (namely EH and CH) which depends on only NUT parameter. Sometimes some complicated functions of EH entropy and CH entropy are also strictly mass-independent. This is plausible only due to the new formalism developed in [S. Wu and D. Wu, Phys. Rev. D 100, 101501(R) (2019)] for NUT class of BHs. The formalism states that a generic four dimensional Taub–NUT spacetime should be described completely in terms of three or four different types of thermodynamic hairs. They could 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]. Finally, we could say that this universality is mainly due to the presence of new conserved charges [Formula: see text] which is closely analogue to the Kerr-like angular momentum [Formula: see text].