Compact elastic objects in general relativity

Abstract

We introduce a rigorous and general framework to study systematically self-gravitating elastic materials within general relativity, and apply it to investigate the existence and viability, including radial stability, of spherically symmetric elastic stars. We present the mass-radius ($M-R$) diagram for various families of models, showing that elasticity contributes to increase the maximum mass and the compactness up to $\approx 22\%$, thus supporting compact stars with mass well above two solar masses. Some of these elastic stars can reach compactness as high as $GM/(c^{2}R)\approx 0.35$ while remaining stable under radial perturbations and satisfying all energy conditions and subluminal wave propagation, thus being physically realizable models of stars with a light ring. We provide numerical evidence that radial instability occurs for central densities larger than that corresponding to the maximum mass, as in the perfect-fluid case. Elasticity may be a key ingredient to build consistent models of exotic ultracompact objects and black-hole mimickers, and can also be relevant for a more accurate modelling of the interior of neutron stars.

5 pages, 3 figures; v3: Inclusion of discussion regarding missing sound speed. Updated plot of Fig. 2 with previously missing velocity. Conclusions and results unchanged

References in corpus (19)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• GW190814: Gravitational Waves from the Coalescence of a 23 M${}_{\odot }$ Black Hole with a 2.6 M${}_{\odot }$ Compact Object
• Color superconductivity in dense quark matter
• Constraints on a phenomenologically parameterized neutron-star equation of state
• Light ring stability in ultra-compact objects
• Tests for the existence of horizons through gravitational wave echoes
• Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects
• Fundamental photon orbits: black hole shadows and spacetime instabilities
• Tidal deformability and I-Love-Q relations for gravastars with polytropic thin shells
• The Crystallography of Three-Flavor Quark Matter
• Light rings of stationary spacetimes
• Sharp bounds on 2m/r for static spherical objects
• Influence of the crust on the neutron star macrophysical quantities and universal relations
• Slowly rotating gravastars
• Gravitational wave echoes from interacting quark stars
• The static spherically symmetric body in relativistic elasticity
• The Crystallography of Strange Quark Matter
• Spherically symmetric steady states of John elastic bodies in general relativity
• On self-gravitating polytropic elastic balls