Inertial and Gravitational Mass in General Relativity and Their Cosmological Consequences

Abstract

We revise the concept of mass of a particle in general relativity initiated by Einstein, Brans, and Rosen in the fifties, using the results of P. Havas and J.N. Goldberg on the equations of motion for point-like particles. We show how one can define a constant inertial mass, and a variable gravitational mass dependent on their gravitational interaction with the rest of particles. The introduced gravitational mass allows us to construct a cosmological model that satisfactorily accounts for the observed deficit of mass, the dark energy and the cosmological constant, without the assumption of new forms of matter or energy: dark matter and dark energy can be explained as a gravitational effect in the framework of the standard general theory of relativity.