Matrix theory of gravitation

Details Matrix theory of gravitation Matrix theory of gravitation

2011-03-23

arxiv.org/abs/1103.4482v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages

Scientific paper

10.1007/s10714-011-1158-x

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.

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