Matrix theory of gravitation

TL;DR

This paper introduces a novel matrix-based classical gravitation theory within general relativity, utilizing complex tetrads and a trace Lagrangian, which aligns with Einstein's theory in standard tests but offers new vacuum solutions.

Contribution

It presents a new matrix formulation of gravitation that differs from traditional curvature scalar approaches and may resolve longstanding issues in teleparallel theories.

Findings

No differences from Einstein theory in standard tests

Derives a new geometrical stress-energy tensor

Provides novel vacuum solutions

Abstract

A new classical theory of gravitation within the framework of general relativity is presented. It is based on a matrix formulation of four-dimensional Riemann-spaces and uses no artificial fields or adjustable parameters. The geometrical stress-energy tensor is derived from a matrix-trace Lagrangian, which is not equivalent to the curvature scalar R. To enable a direct comparison with the Einstein-theory a tetrad formalism is utilized, which shows similarities to teleparallel gravitation theories, but uses complex tetrads. Matrix theory might solve a 27-year-old, fundamental problem of those theories (sec. 4.1). For the standard test cases (PPN scheme, Schwarzschild-solution) no differences to the Einstein-theory are found. However, the matrix theory exhibits novel, interesting vacuum solutions.