Schwarzschild Solution within a new renormalizable SO(1,3) Gauge Field Theory of Gravitation

TL;DR

This paper demonstrates the existence of the Schwarzschild solution within a new renormalizable SO(1,3) gauge field theory of gravitation, which is classically equivalent to General Relativity but formulated with a gauge field approach.

Contribution

It introduces a renormalizable SO(1,3) gauge field theory of gravity that reproduces the Schwarzschild solution and is classically equivalent to GR.

Findings

Schwarzschild solution exists within the new gauge theory.

The gauge field action parallels the Einstein-Hilbert action.

The theory is classically equivalent to General Relativity.

Abstract

The existence of the Schwarzschild solution is demonstrated within a new SO(1,3) gauge field theory whose fundamental gauge field B is of dimension one allowing for the renormalizability of the full quantum theory. On the other hand the classically dominant term of the gauge field action can be expressed in terms of a naturally emerging Vierbein of dimension zero. In fact this action term is the same functional of the emerging Vierbein e[B] as is the Einstein-Hilbert action of the Vierbein in General Relativity (GR), albeit with e[B] subject to a constraint. To solve the Einstein equations a spherically symmetric Ansatz for e[B] respecting the constraint is determined and transformed into the standard metric used to calculate the Schwarzschild solution. This allows to prove the latter's existence making the present theory a perfectly viable theory of gravitation equivalent to GR at the classical level.