About the mass problem

TL;DR

This paper examines the distinction between active and proper gravitational mass in General Relativity, comparing new and traditional definitions and analyzing their impact on mass ratios.

Contribution

It introduces a new definition of proper mass and discusses its implications for the active-to-proper mass ratio in gravitational fields.

Findings

The new proper mass definition alters the active-to-proper mass ratio.

Comparison shows differences between traditional and new mass concepts.

Clarifies the conceptual understanding of mass in General Relativity.

Abstract

The concept of {\it active gravitational mass}, its definition and its relation with the sources of a gravitational field, was clearly established by Tolman in 1934. On the contrary, and surprisingly in our opinion, the concept of {\it proper mass} has remained obscure in General relativity. We compare a new definition to an apparent more obvious one and discuss how each choice modifies the ratio of active to proper gravitational mass.