Einstein Vs Maxwell: Is Gravitation a Curvature of Space, a Field in Flat Space, or Both?

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 is negative and 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 ΛCDM model is covered, while there appears a form of inflation at early times. Here both the total energy and the zero point energy vanish. It is said that in introducing the general theory of relativity (GTR), Einstein made the step that Lorentz and Poincaré had failed to make: to go from flat space to curved space. Technically, this arises from the group of general coordinate transformations [1, 2]. One fundamental difficulty is then how to deal with the physics of gravitation itself, since there is only a quasi energy-momentum tensor [3]. For gravitational wave detection, e.g., this leaves open the question as to how energy can be faithfully transferred from the wave to the detector. The proper energy momentum tensor of gravitation was derived only recently by Babak and Grishchuk [4], who start with a field theoretic approach to gravitation, in terms of a tensor field h in a Minkowski background space-time. The metric of the latter, ημν = diag(1,−1,−1,−1), is denoted in arbitrary coordinates by γμν = (γ ). The Riemann metric tensor gμν = (g ), is then defined by