(2,2)-Formalism of General Relativity: An Exact Solution

TL;DR

This paper introduces a (2,2)-formalism of general relativity that reformulates Einstein's equations as a Yang-Mills gauge theory on a 2D base, successfully deriving the Schwarzschild solution and exploring potential applications.

Contribution

It presents a novel (2,2)-formalism of general relativity, framing it as a Yang-Mills gauge theory on a 2D base manifold, and provides an exact spherically symmetric solution.

Findings

Derivation of Einstein's equations in (2,2)-formalism

Exact Schwarzschild solution within this formalism

Discussion of potential applications of the formalism

Abstract

I discuss the (2,2)-formalism of general relativity based on the (2,2)-fibration of a generic 4-dimensional spacetime of the Lorentzian signature. In this formalism general relativity is describable as a Yang-Mills gauge theory defined on the (1+1)-dimensional base manifold, whose local gauge symmetry is the group of the diffeomorphisms of the 2-dimensional fibre manifold. After presenting the Einstein's field equations in this formalism, I solve them for spherically symmetric case to obtain the Schwarzschild solution. Then I discuss possible applications of this formalism.