Einstein vs. Maxwell: Is gravitation a curvature of space, a field in flat space, or both?T. M. Nieuwenhuizen
Institute for Theoretical Physics, University of Amsterdam - Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands
received 12 October 2006; accepted in final form 12 February 2007; published April 2007
published online 22 March 2007
Starting with a field theoretic approach in Minkowski space, the gravitational energy momentum tensor is derived from the Einstein equations in a straightforward manner. This allows to present them as acceleration tensor = const. total energy momentum tensor. For flat space cosmology the gravitational energy cancels the material energy. In the relativistic theory of gravitation a bimetric coupling between the Riemann and Minkowski metrics breaks general coordinate invariance. The case of a positive cosmological constant is considered. A singularity free version of the Schwarzschild black hole is solved analytically. In the interior the components of the metric tensor quickly die out, but do not change sign, leaving the role of time as usual. For cosmology the CDM model is covered, while there appears a form of inflation at early times. Here both the total energy and the zero point energy vanish.
04.20.Cv - Fundamental problems and general formalism.
04.20.Fy - Canonical formalism, Lagrangians, and variational principles.
98.80.Bp - Origin and formation of the Universe.
© Europhysics Letters Association 2007