New theory of gravitation

Abstract

A new theory of gravity is proposed in which the geometry of space-time is determined by a nonsymmetric field structure. The theory satisfies the following requirements: (1) general covariance, (2) (weak) principle of equivalence, (3) the field equations are derivable from a Lagrangian action principle, (4) the theory agrees with all the classical (weak gravitational field) tests of Einstein's general relativity. The field equations for the nonsymmetric Hermitian ${g}_{\ensuremath{\mu}\ensuremath{\nu}}$ lead to a rigorous static spherically symmetric solution for the gravitational field in empty space that excludes the essential singularity at $r=0$ from physical space-time. It is expected that the predictions of the theory will differ significantly from Einstein's theory of gravitation for compact sources or supermassive stars. Matter undergoing gravitational collapse is prevented from forming a black hole (in physical space-time) of the kind predicted in Einstein's theory, when a new gravitational parameter $l$ that appears as a constant of integration in the solution satisfies $l>2m$.