Compact elastic objects in general relativity

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 increasing the maximum mass and the compactness up to ≈22%, thus supporting compact stars with mass well above two solar masses. Some of these elastic stars can reach compactness as high as GM/(c2R)≈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 building consistent models of exotic ultracompact objects and black hole mimickers, and can also be relevant for a more accurate modeling of the interior of neutron stars.