Regularizing role of teleparallelism

TL;DR

This paper explores how covariant teleparallelism regularizes gravitational energy calculations, ensuring finite, meaningful results by subtracting inertial effects, and reanalyzes Schwarzschild and Kerr solutions for validation.

Contribution

It demonstrates the role of the teleparallel connection as a regularizing tool in covariant teleparallel gravity, improving energy computation consistency.

Findings

Energy in covariant teleparallelism is finite and nontrivial.

The teleparallel connection effectively subtracts inertial effects.

Reanalysis confirms the approach's validity for Schwarzschild and Kerr solutions.

Abstract

The properties of the gravitational energy-momentum 3-form and of the superpotential 2-form are discussed in the covariant teleparallel framework, where the Weitzenb\"ock connection represents inertial effects related to the choice of the frame. Due to its odd asymptotic behavior, the contribution of the inertial effects often yields unphysical (divergent or trivial) results for the total energy of the system. However, in the covariant teleparallel approach, the energy is always finite and nontrivial. The teleparallel connection plays a role of a regularizing tool which subtracts the inertial effects without distorting the true gravitational contribution. As a crucial test of the covariant formalism, we reanalyze the computation of the total energy of the Schwarzschild and the Kerr solutions.