On the Regularization of Kerr-NUT spacetime: I

TL;DR

This paper investigates the calculation of energy and momentum in Kerr-NUT spacetimes within TEGR, revealing divergences and proposing a local Lorentz transformation as a regularization method to obtain meaningful results.

Contribution

It introduces a regularization technique using local Lorentz transformations to address divergences in energy-momentum calculations in Kerr-NUT spacetimes within TEGR.

Findings

Two methods yield divergent energy-momentum results.

A local Lorentz transformation regularizes the energy-momentum calculations.

The regularized spacetime remains a solution of TEGR equations.

Abstract

Within the framework of teleparallel equivalent of general relativity (TEGR) theory, calculation of the total energy and momentum of Kerr-NUT spacetimes have been employed using two methods of the gravitational energy-momentum, which is coordinate independent, and the Riemannian connection 1-form, ${\widetilde{\Gamma}_\alpha}^\beta$. It has been shown that the two methods give the same an unacceptable result, i.e., divergent value. Therefore, a local Lorentz transformation that plays a role of a regularizing tool, which subtracts the inertial effects without distorting the true gravitational contribution, has been suggested. This transformation keeps the resulting spacetime to be a solution of the equations of motion of TEGR.