Consistent thermodynamics and topological classes for the four-dimensional Lorentzian charged Taub-NUT spacetimes

• Published in: The European physical journal. C, Particles and fields Vol. 83; no. 7; pp. 589 - 12
• Main Author: Wu, Di
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-07-2023; Springer; Springer Nature B.V; SpringerOpen
• Subjects: Astronomy; Astrophysics and Cosmology; Asymptotic properties; Black holes; Elementary Particles; Free energy; Hadrons; Heavy Ions; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Phase transitions; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; Spacetime; String Theory; Thermodynamics; Topology
• ISSN: 1434-6052; 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-023-11782-7

In this paper, we derive the consistent thermodynamics of the four-dimensional Lorentzian Reissner-Nordström-NUT (RN-NUT), Kerr–Newman-NUT (KN-NUT), and RN-NUT-AdS spacetimes in the framework of the (
ψ
-
N
)-pair formalism, and then investigate their topological numbers by using the uniformly modified form of the generalized off-shell Helmholtz free energy. We find that these solutions can be included into one of three categories of those well-known black hole solutions, which implies that these spacetimes should be viewed as generic black holes from the perspective of the topological thermodynamic defects. In addition, we demonstrate that although the existence of the NUT charge parameter seems to have no impact on the topological number of the charged asymptotically locally flat spacetimes, it has a remarkable effect on the topological number of the charged asymptotically locally AdS spacetime.