What makes a shear-free spherical perfect fluid be inhomogeneous with tidal effects?

TL;DR

This paper investigates the conditions under which shear-free, inhomogeneous, perfect fluid spacetimes with tidal effects can exist, revealing that such scenarios are limited to specific equations of state governed by complex differential equations.

Contribution

It introduces a novel geometrical classification of shear-free LRS-II perfect fluids and derives the governing differential equation for their equations of state.

Findings

Limited classes of equations of state allow shear-free inhomogeneous fluids with tidal effects.

A covariant semitetrad decomposition facilitates the classification of these systems.

The governing differential equation constrains possible matter configurations.

Abstract

This is an important and natural question as the spacetime shear, inhomogeneity and tidal effects are all intertwined via the Einstein field equations. However, as we show in this paper, such scenarios are possible for limited classes of equations of state that are solutions to a highly non-linear and fourth order differential equation. To show this, we use a covariant semitetrad spacetime decomposition and present a novel geometrical classification of shear-free Locally Rotationally Symmetric (LRS-II) perfect fluid self-gravitating systems, in terms of the covariantly defined fluid acceleration and the fluid expansion. Noteworthily, we deduce the governing differential equation that gives the possible limited equations of state of matter.