New Geometric Formalism for Gravity Equation in Empty Space
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.
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