Abstract

In this review paper, general relativity (GR) is presented in the field theoretical form, where gravitational field (metric perturbations) together with other physical fields are propagated in an auxiliary either curved, or flat background spacetime. Such a reformulation of GR is exact and equivalent to GR in the standard geometrical description. It is actively used for study of theoretical problems and in applications. Conserved currents are constructed on the basis of a symmetrical (with respect to a background metric) total energy-momentum tensor and are expressed through divergences of anti-symmetrical tensor densities (superpotentials). This form connects local properties of perturbations with the academic imagination on the quasi-local nature of the conserved quantities in GR. The gauge invariance is studied, its properties allow to consider the problem of non-localization of energy in GR in exact mathematical expressions. The Friedmann solution for a closed world and the Schwarzschild solution are presented as field configurations in Minkowski space, properties of which are analyzed. An original modification of the field formulation of GR is given by Babak and Grishchuk. Basing on this they have modified GR itself. The resulting theory includes \massive terms" describing spin-2 and spin-0 gravitons with non-zero masses. We present and discuss their results. It is shown that all the local weak-field predictions of the massive theory are in agreement with experimental data. Otherwise, the exact non-linear equations of the new theory eliminate the black hole event horizons and replace a permanent power-law expansion of the homogeneous isotropic universe with an oscillator behavior.