Classifying topology of consistent thermodynamics of the four-dimensional neutral Lorentzian NUT-charged spacetimes

TL;DR

This paper uses a topological approach to classify the thermodynamics of four-dimensional neutral Lorentzian NUT-charged spacetimes, revealing they are akin to known black hole solutions.

Contribution

It introduces a modified off-shell Helmholtz free energy method to classify the topology of NUT-charged spacetimes, showing their similarity to standard black holes.

Findings

NUT-charged spacetimes share topological properties with known black holes

These solutions can be classified into three types of black hole solutions

The approach confirms the thermodynamic universality of these spacetimes

Abstract

In this paper, via employing the uniformly modified form of the generalized off-shell Helmholtz free energy, we investigate the topological numbers for the four-dimensional neutral Lorentzian Taub-NUT, Taub-NUT-AdS and Kerr-NUT spacetimes, and find that these solutions can also be classified into one of three types of those well-known black hole solutions, which implies that these spacetimes should be viewed as generic black holes from the viewpoint of the thermodynamic topological approach.