Spin Connection and Renormalization of Teleparallel Action

TL;DR

This paper demonstrates how the spin connection in teleparallel gravity can isolate inertial effects from gravitation, enabling a renormalization of the action to obtain physically meaningful energy-momentum values.

Contribution

It introduces a method to associate a spin connection with each tetrad that removes inertial effects, improving the calculation of energy and momentum in teleparallel gravity.

Findings

The spin connection can be used to renormalize the teleparallel action.

A self-consistent method for solving field equations and determining the spin connection is proposed.

The approach yields physically relevant energy-momentum values free from inertial contamination.

Abstract

In general relativity, inertia and gravitation are both included in the Levi-Civita connection. As a consequence, the gravitational action, as well as the corresponding energy-momentum density, are in general contaminated by spurious contributions coming from inertial effects. In teleparallel gravity, on the other hand, because the spin connection represents inertial effects only, it is possible to separate inertia from gravitation. Relying on this property, it is shown that to each tetrad there is naturally associated a spin connection that locally removes the inertial effects from the action. The use of the appropriate spin connection can be viewed as a renormalization process in the sense that the computation of energy and momentum naturally yields the physically relevant values. A self-consistent method for solving field equations and determining the appropriate spin connection is presented.