On the dynamics of perfect fluids in non-minimally coupled gravity

TL;DR

This paper investigates how non-minimal coupling between geometry and matter affects perfect fluid dynamics, revealing pressure mimicking effects, altered spacetime structures, and implications for black hole environments.

Contribution

It introduces the impact of non-minimal coupling on perfect fluids, showing deviations from General Relativity and proposing a generalized Newtonian potential.

Findings

Static, axially symmetric pressureless fluids do not imply Minkowski spacetime.

In equilibrium, fluid mass around a black hole can be twice the black hole mass.

A generalized Newtonian potential for fluid elements is proposed.

Abstract

In this work we explore the consequences that a non-minimal coupling between geometry and matter can have on the dynamics of perfect fluids. It is argued that the presence of a static, axially symmetric pressureless fluid does not imply a Minkowski space-time like as is in General Relativity. This feature can be atributed to a pressure mimicking mechanism related to the non-minimal coupling. The case of a spherically symmetric black hole surrounded by fluid matter is analyzed, and it is shown that under equilibrium conditions the total fluid mass is about twice that of the black hole. Finally, a generalization of the Newtonian potential for a fluid element is proposed and its implications are briefly discussed.