Regularization of Kerr-NUT spacetimes and their thermodynamical quantities

TL;DR

This paper calculates the energy, momentum, and thermodynamic properties of Kerr-NUT spacetimes within TEGR, using multiple methods and Lorentz transformations to regularize results, and explores their thermodynamic laws and quantum relations.

Contribution

It introduces a regularization approach using local Lorentz transformations in TEGR to accurately compute energy, momentum, and thermodynamic quantities of Kerr-NUT spacetimes.

Findings

Consistent energy and momentum values obtained via three methods.

Verification of the first law of thermodynamics for Kerr-NUT spacetime.

Establishment of quantum statistical relations in this context.

Abstract

In the context of the teleparallel equivalent of general relativity (TEGR) theory, continues calculations of the total energy and momentum for Kerr-NUT spacetimes using three different methods, the gravitational energy-momentum, the Riemannian connection 1-form, ${\widetilde{\Gamma}_\alpha}^\beta$ and the Euclidean continuation method, have been achieved. Many local Lorentz transformations, that play the role of regularizing tool, are given to get the commonly known form of energy and momentum. We calculate the thermodynamic quantities of Kerr-NUT spacetime. We also investigate the first law of thermodynamics and quantum statistical relation.