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

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.