On the field theoretic description of gravitation

Maxwell started to describe gravitation as a field in Minkowski space. Such an approach brought Babak and Grishchuk in 1999 the gravitational energy-momentum tensor. Simple manipulations allow the Einstein equations to take the form Aµν = (8πG/c4)Θµν, where A is the acceleration tensor and Θ, the total energy momentum tensor, is conserved in Minkowski space. For non-curved cosmology, the total energy density vanishes: the gravitational part is negative and cancels the one of matter due to the Friedman equation.

In 1989 Logunov added to the Lagrangian a bimetric coupling between the Minkowski and Riemann metrics. The case of a positive cosmological constant allows a regularization of the interior of the Schwarzschild black hole: The components of the metric tensor donot change sign, so, inside the black hole, time keeps its usual role. Cosmology generalizes the ΛCDM model, while gravitational and matter energy cancel again at all times.