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Spherically symmetric steady states of John elastic bodies in general relativity

Journal article
Authors Håkan Andreasson
Simone Calogero
Published in Classical and quantum gravity
Volume 31
Issue 16
Pages Art. no. 165008
ISSN 0264-9381
Publication year 2014
Published at Department of Mathematical Sciences, Mathematics
Pages Art. no. 165008
Language en
Links dx.doi.org/10.1088/0264-9381/31/16/...
Keywords spherical symmetry, elasticity, static solutions
Subject categories Physical Sciences

Abstract

We study some properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The materials considered belong to the class of John elastic materials and reduce to perfect fluids when the rigidity parameter is set to zero. We find numerical support that such elastic bodies exist with different possible shapes (balls, single shells and multiple shells) and that their gravitational redshift can be very large (z approximate to 2.8) without violating the dominant energy condition. Moreover we show that the elastic body has finite radius even in the case when the constitutive equation of the elastic material is a perturbation of a polytropic fluid without finite radius, thereby concluding that such fluids are structurally unstable within the larger class of elastic matter models under study.

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