Eur. Phys. J. Plus (2021) 136: 1169
https://doi.org/10.1140/epjp/s13360-021-02119-y

Regular Article

Joule–Thomson expansion of the torus-like black hole

¹ Physics Teaching and Research Section, College of Medical Technology, Chengdu University of Traditional Chinese Medicine, 611137, Chengdu, People’s Republic of China
² Center for Theoretical Physics, College of Physics, Sichuan University, 610064, Chengdu, People’s Republic of China

^c benrongmu@cdutcm.edu.cn

Received: 12 March 2021
Accepted: 25 October 2021
Published online: 22 November 2021

Abstract

In this paper, we study the Joule–Thomson expansion of the torus-like black hole in extended phase space, where the cosmological constant is determined by the pressure. It is noteworthy that the torus-like black hole has a horizon of toroidal topology, rather than a horizon of spherical topology. We study both the inversion and isenthalpic curves of the torus-like black holes in the $T-P$ plane and find that their intersection coincides with the inversion point that distinguishes the heat in the cooling process. Compared to the Van der Waals fluid, the inversion curves of torus-like black holes do not end at any point and only lower inversion curves are available. Most importantly, we find that the $P-V$ diagram of the torus-like black hole has no inflection point, i.e., the torus-like black hole is always thermally stable. Therefore, the torus-like black hole has no critical point and critical temperature, and there is no ratio between the minimum inversion temperature and the critical temperature. This is completely different from the black hole with the horizon of spherical topology.