Does Pressure Increase or Decrease Active Gravitational Mass Density?

TL;DR

This paper challenges the conventional understanding of how pressure affects active gravitational mass density in general relativity, showing that globally it decreases with pressure, contrary to local interpretations, and linking it to the Ricci scalar.

Contribution

It reveals that the global active gravitational mass density decreases with pressure, opposite to the local view, and connects it to the Ricci scalar, providing a new perspective on gravitational mass in GR.

Findings

AGMD is proportional to the Ricci scalar.

Globally, pressure decreases active gravitational mass density.

The GR virial theorem is derived using proper energies.

Abstract

It is known that, for a static fluid sphere, the GeneralRelativistic (GR) Effective Mass Energy Density (EMD) appears to be (rho + 3 p), where rho is the bare mass density, p is the isotropic pressure, from a purely localized view point. But since there is no truly local definition of ``gravitational field'', such a notion could actually be misleading. On the other hand, by using the Tolman mass formula, we point out that, from a global perspective, the Active Gravitational Mass Energy Density (AGMD) is sqrt{g_{00}} (rho + 3 p) and which is obviously smaller than (rho + 3p) because g_{00} < 1. Then we show that the AGMD eventually is (rho - 3p), i.e., exactly opposite to what is generally believed. We further identify the AGMD to be proportional to the Ricci Scalar. By using this fundamental and intersting property, we obtain the GR virial theorem in terms of appropriate ``proper energies''.