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

TL;DR

This paper develops a consistent thermodynamic framework for four-dimensional Lorentzian charged NUT spacetimes and explores their topological classifications, revealing how NUT charge influences topological numbers in different asymptotic regimes.

Contribution

It introduces a unified thermodynamic approach for various charged NUT spacetimes and analyzes their topological classes, highlighting the impact of NUT charge on topological numbers.

Findings

Charged NUT spacetimes can be categorized into known black hole classes.

NUT charge affects topological numbers in AdS spacetimes but not in flat spacetimes.

All studied solutions are classified as generic black holes topologically.

Abstract

In this paper, we derive the consistent thermodynamics of the four-dimensional Lorentzian charged Reissner-Nordstr\"om-NUT (RN-NUT), Kerr-Newman-NUT (KN-NUT), and RN-NUT-AdS spacetimes in the framework of the ($\psi-\mathcal{N}$)-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.