Spherically symmetric elastic bodies in general relativity

Abstract

The purpose of this review it to present a renewed perspective of the problem of self-gravitating elastic bodies under spherical symmetry. It is also a companion to the papers [Phys. Rev. D105, 044025 (2022)], [Phys. Rev. D106, L041502 (2022)], and [arXiv:2306.16584 [gr-qc]], where we introduced a new definition of spherically symmetric elastic bodies in general relativity, and applied it to investigate the existence and physical viability, including radial stability, of static self-gravitating elastic balls. We focus on elastic materials that generalize fluids with polytropic, linear, and affine equations of state, and discuss the symmetries of the energy density function, including homogeneity and the resulting scale invariance of the TOV equations. By introducing invariant characterizations of physical admissible initial data, we numerically construct mass-radius-compactness diagrams, and conjecture about the maximum compactness of stable physically admissible elastic balls.

arXiv commentv2: Published version. 132 pages, 18 figures; Invited review for the Special Issue of Class. Quantum Gravity on 'Focus on the Mathematics of Gravitation in the Non-Vacuum Regime'

References in corpus (58)

• Color superconductivity in dense quark matter
• The Physics of Neutron Stars
• Neutron Star Observations: Prognosis for Equation of State Constraints
• Testing the nature of dark compact objects: a status report
• Constraints on a phenomenologically parameterized neutron-star equation of state
• Is the gravitational-wave ringdown a probe of the event horizon?
• Gravitational Vacuum Condensate Stars
• Physics of Neutron Star Crusts
• The observational evidence for horizons: from echoes to precision gravitational-wave physics
• Light ring stability in ultra-compact objects
• Tests for the existence of horizons through gravitational wave echoes
• Approximate Universal Relations for Neutron Stars and Quark Stars
• Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects
• On the gravitational field of a mass point according to Einstein's theory
• Critical phenomena in gravitational collapse
• Sharp bounds on $2m/r$ of general spherically symmetric static objects
• Phenomenological aspects of black holes beyond general relativity
• Anisotropic stars as ultracompact objects in General Relativity
• The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models
• General Relativistic Stars : Polytropic Equations of State
• Tidal deformability and I-Love-Q relations for gravastars with polytropic thin shells
• The Crystallography of Three-Flavor Quark Matter
• Relativistic Elasticity
• I-Love-Q relations for a gravastar and the approach to the black-hole limit
• Exotic Compact Objects and the Fate of the Light-Ring Instability
• Light rings of stationary spacetimes
• On gravitational echoes from ultracompact exotic stars
• Slowly rotating thin shell gravastars
• On gravitational-wave echoes from neutron-star binary coalescences
• General Relativistic Stars: Linear Equations of State
• Spherically symmetric relativistic stellar structures
• Elastic Stars in General Relativity: II. Radial perturbations
• Sharp bounds on 2m/r for static spherical objects
• Bounds on 2m/R for static spherical objects
• Compactness bounds in General Relativity
• Influence of the crust on the neutron star macrophysical quantities and universal relations
• Spherically symmetric equilibria for self-gravitating kinetic or fluid models in the non-relativistic and relativistic case - A simple proof for finite extension
• Elastic Stars in General Relativity: III. Stiff ultrarigid exact solutions
• Static Solutions of the Einstein Equations for Spherically Symmetric Elastic Bodies
• Newtonian Stellar Models
• Stability and instability of self-gravitating relativistic matter distributions
• Axisymmetric deformations of neutron stars and gravitational-wave astronomy
• Testing the nature of dark compact objects with gravitational waves
• Elasticity Theory in General Relativity
• The static spherically symmetric body in relativistic elasticity
• The Crystallography of Strange Quark Matter
• (In)finiteness of Spherically Symmetric Static Perfect Fluids
• Spherically symmetric steady states of John elastic bodies in general relativity
• Scale invariant elastic stars in General Relativity
• On self-gravitating polytropic elastic balls
• On "hard stars" in general relativity
• A stellar model with diffusion in general relativity
• Static self-gravitating Newtonian elastic balls
• Multi-body spherically symmetric steady states of Newtonian self-gravitating elastic matter
• Static spherical perfect fluid stars with finite radius in general relativity: a review
• Elastic shocks in relativistic rigid rods and balls
• Expansion and collapse of spherically symmetric isotropic elastic bodies surrounded by vacuum
• Naked singularities in the Einstein-Euler system

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