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

## TL;DR

This paper explores whether gravitation is best described as space curvature, a field in flat space, or both, by deriving gravitational energy tensors and analyzing cosmological and black hole solutions within different frameworks.

## Contribution

It presents a field theoretic derivation of gravitational energy in Minkowski space and examines implications for cosmology and black holes, including a singularity-free Schwarzschild solution.

## Key findings

- Gravitational energy can be derived as an acceleration tensor from Einstein equations.
- In flat space cosmology, gravitational energy cancels material energy.
- A singularity-free black hole solution is analytically obtained.

## 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 {\it acceleration tensor} = const. $\times$ {\it 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 $\Lambda$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.