Spherically symmetric steady states of John elastic bodies in general relativity

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 ($z\approx 2.8$) 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.

arXiv comment25 pages, 11 figures. The title has been changed to match the published version. References added

References in corpus (16)

• Sharp bounds on $2m/r$ of general spherically symmetric static objects
• The Einstein-Vlasov System/Kinetic Theory
• Relativistic Elasticity
• Gravitational collapse with non-vanishing tangential stresses II: a laboratory for cosmic censorship experiments
• Spherically symmetric relativistic stellar structures
• On the steady states of the spherically symmetric Einstein-Vlasov system
• Anisotropic Models for Globular Clusters, Galactic Bulges and Dark Halos
• Spherically symmetric equilibria for self-gravitating kinetic or fluid models in the non-relativistic and relativistic case - A simple proof for finite extension
• Existence of axially symmetric static solutions of the Einstein-Vlasov system
• Analytical families of 2-component anisotropic polytropes and their relativistic extensions
• Rotating, stationary, axially symmetric spacetimes with collisionless matter
• Static Solutions of the Einstein Equations for Spherically Symmetric Elastic Bodies
• Rotating elastic bodies in Einstein gravity
• Relativistic Elastostatics I: Bodies in Rigid Rotation
• General spherically symmetric elastic stars in Relativity
• Ground states of self-gravitating elastic bodies

Cited by in corpus (8)

• Spherically symmetric elastic bodies in general relativity
• Scale invariant elastic stars in General Relativity
• Relativistic elasticity of rigid rods and strings
• Rotating elastic string loops in flat and black hole spacetimes: stability, cosmic censorship and the Penrose process
• Multi-body spherically symmetric steady states of Newtonian self-gravitating elastic matter
• Elastic shocks in relativistic rigid rods and balls
• Rigid elastic solids in relativity
• Compact elastic objects in general relativity