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

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 a...

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Bibliographic Details
Published in:arXiv.org 2023-08
Main Authors: Hakata, Jonathan, Goswami, Rituparno, Hansraj, Chevarra, Maharaj, Sunil D
Format: Article
Language:English
Subjects:
Equations of state
Gravitation
Mathematical analysis
Nonlinear differential equations
Shear
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2306.14581