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Matrix theory of gravitation

Matrix theory of gravitation,10.1007/s10714-011-1158-x,General Relativity and Gravitation,Wolfgang Köhler

Matrix theory of gravitation  
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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 (Sect. 4.1). For the standard test cases (PPN scheme, Schwarz schild-solution) no differences to the Einstein-theory are found. However, the matrix theory exhibits novel, interesting vacuum solutions.
Journal: General Relativity and Gravitation - GEN RELATIV GRAVIT , vol. 43, no. 6, pp. 1787-1825, 2011
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