Gravity, Gauge Theories and Geometric Algebra

TL;DR

This paper introduces a novel gauge theory of gravity formulated in flat spacetime, deriving field equations from an action principle, and explores its applications to cosmology, black holes, and quantum effects like Hawking radiation.

Contribution

It presents a new gauge theory of gravity in flat spacetime with a unique action principle and spin-torsion interaction, and develops methods to solve the resulting field equations.

Findings

Derived a gauge-invariant set of gravitational field equations.

Applied the theory to cosmology and black hole physics.

Connected the Dirac equation in black hole backgrounds to Hawking temperature.

Abstract

A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the positions and orientations of the matter fields. In this manner all properties of the background spacetime are removed from physics, and what remains are a set of `intrinsic' relations between physical fields. The properties of the gravitational gauge fields are derived from both classical and quantum viewpoints. Field equations are then derived from an action principle, and consistency with the minimal coupling procedure selects an action that is unique up to the possible inclusion of a cosmological constant. This in turn singles out a unique form of spin-torsion interaction. A new method for solving the field equations is outlined and applied to the case of a time-dependent, spherically-symmetric perfect fluid. A gauge is found which reduces the physics to a set of essentially Newtonian equations. These equations are then applied to the study of cosmology, and to the formation and properties of black holes. The existence of global solutions enables one to discuss the properties of field lines inside the horizon due to a point charge held outside it. The Dirac equation is studied in a black hole background and provides a quick derivation of the Hawking temperature.