A Maxwell Like Formulation of Gravitational Theory in Minkowski Spacetime

TL;DR

This paper develops a Maxwell-like Lagrangian formulation of gravity within Minkowski spacetime using Clifford algebra, showing equivalence to Einstein's equations under certain geometric interpretations.

Contribution

It introduces a novel gauge-theoretic approach to gravity in flat spacetime, connecting it to Lorentzian and teleparallel geometries.

Findings

Field equations are equivalent to Einstein's equations in Lorentzian interpretation.

Uses Clifford bundle formalism for a gauge theory of gravity.

Provides a new perspective on gravitational dynamics in flat spacetime.

Abstract

In this paper using the Clifford bundle formalism a Lagrangian theory of the Yang-Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski spacetime is presented. It is shown how two simple hypothesis permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory the field equations are shown to be equivalent to Einstein's equations.