Einstein vs. Maxwell: Is gravitation a curvature of space, a field in flat space, or both?

Institute for Theoretical Physics, University of Amsterdam - Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands

Received: 12 October 2006
Accepted: 12 February 2007

Abstract

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.