New Geometric Formalism for Gravity Equation in Empty Space

TL;DR

This paper introduces a complex daor field formalism that models gravity as a gauge theory related to SU(1,3), providing a new mathematical framework consistent with Einstein's theory.

Contribution

It proposes a novel complex daor field approach to describe gravity, linking it to gauge fields and extending geometric formalism.

Findings

Daor field equations are first-order differential equations.

The formalism is compatible with Einstein's gravity.

Establishes a connection between gravity and SU(1,3) gauge symmetry.

Abstract

In this paper, a complex daor field which can be regarded as the square root of space-time metric is proposed to represent gravity. The locally complexified geometry is set up, and the complex spin connection constructs a bridge between gravity and SU(1,3) gauge field. Daor field equations in empty space are acquired, which are one-order differential equations and not conflict with Einstein's gravity theory.