On the role of pressure in generating the gravitational field

TL;DR

This paper explores how pressure influences gravitational fields in Einstein's equations, questioning why classical solutions depend only on mass despite linearized theories indicating pressure's role.

Contribution

It highlights the discrepancy between classical and linearized solutions regarding pressure's role, suggesting a potential need for alternative gravitational theories.

Findings

Schwarzschild solution depends only on mass parameter

Linearized Einstein equations include pressure analogue

Implication for phenomenological gravity models

Abstract

The Einstein equations for static gravitational field depend on energy density and pressure. So one may expect that solutions should depend on two parameters: mass and its analogue originated from pressure. Yet the Schwarzschild solution have only mass parameter. So does its linear approximation. On the other hand the solutions of linearized Einstein equations, obtained using graviton propagator, contain mass and its pressure analogue. This suggests that a phenomenological approach to gravity, using propagators and many graviton vertices, should lead to a theory different from general relativity.