Spherically symmetric steady states of John elastic bodies in general relativity. (English) Zbl 1298.83034
Summary: 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.
MSC:
83C35 | Gravitational waves |
83C75 | Space-time singularities, cosmic censorship, etc. |
85A15 | Galactic and stellar structure |
83-08 | Computational methods for problems pertaining to relativity and gravitational theory |
83C15 | Exact solutions to problems in general relativity and gravitational theory |
83C40 | Gravitational energy and conservation laws; groups of motions |
83C55 | Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) |