Pressure as a Source of Gravity

TL;DR

This paper investigates whether pressure contributes to gravitational mass by analyzing exact solutions of Einstein's equations in static perfect fluids, highlighting the role of pressure in active gravitational mass.

Contribution

It provides a detailed analysis of pressure's contribution to gravitational mass using exact solutions in Einstein's theory, clarifying its role in static cases.

Findings

Pressure adds to active gravitational mass in static solutions

The study confirms the proportionality of active mass to density and pressure

Results support the theoretical relation involving pressure in Einstein's equations

Abstract

The active mass density in Einstein's theory of gravitation in the analog of Poisson's equation in a local inertial system is proportional to $\rho+3p/c^2$. Here $\rho$ is the density of energy and $p$ its pressure for a perfect fluid. By using exact solutions of Einstein's field equations in the static case we study whether the pressure term contributes towards the mass.