Inertial and Gravitational Mass in General Relativity and Their Cosmological Consequences

Miguel Portilla

doi:10.4236/jmp.2021.1213101

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.

Highlights

We interpret in this paper the cosmological dark matter and energy present in the epoch of galactic dominance as a pure gravitational effect, using primarily baryonic matter and standard general relativity.In a Minkowski spacetime, a fluid is the result of a statistical average of the dynamical properties of a system of particles; in a curved space, as it is the case when the particles are self gravitating, one needs to revise the concept of mass
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
In subsection IIIC, where we study the Milne’s universe with mass and prove the equality active and passive gravitational mass, we shall find that the quotient M a (τ a ) ma is the same for all the particles, and all them with the same initial conditions move equal in the gravitational field in accord with the WEPkin, but the quotient of masses is a monotonous increasing function of the expansion factor (see Equation (23)) and the WEPdyn does not imply the equality of inertial and gravitational mass by choosing appropriated units

Summary

Introduction

We interpret in this paper the cosmological dark matter and energy present in the epoch of galactic dominance as a pure gravitational effect, using primarily baryonic matter and standard general relativity. Serious problems of convergence over the particle world lines were overcome in the first approximation [2], and needed of more efforts in the second one [5] These results were useful to interpret in the eighties the first indirect proves of gravitational radiation by compact bodies [6]. We have obtained [9] a maximal extension of this metric that is regular and has, as hoped, a distribution with tridimensional support as source, in accordance to the Geroch-Traschen theorem These results has not been extended to more than one particle, and we must use the approximated solutions [2] [5].

Inertial and Passive Gravitational Mass of Point-Like Particles

A Cosmological Model Built with Point-Like Particles

Gravitational Mass Density in the Galactic Dominance Epoch

Findings

Conclusions