Analytic study of self-gravitating polytropic spheres with light rings. (arXiv:1811.04948v1 [gr-qc])

Analytic study of self-gravitating polytropic spheres with light rings. (arXiv:1811.04948v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Hod_S/0/1/0/all/0/1">Shahar Hod</a>

Ultra-compact objects describe horizonless solutions of the Einstein field
equations which, like black-hole spacetimes, possess null circular geodesics
(closed light rings). We study {it analytically} the physical properties of
spherically symmetric ultra-compact isotropic fluid spheres with a polytropic
equation of state. It is shown that these spatially regular horizonless
spacetimes are generally characterized by two light rings
${r^{text{inner}}_{gamma},r^{text{outer}}_{gamma}}$ with the property
${cal C}(r^{text{inner}}_{gamma})leq{cal C}(r^{text{outer}}_{gamma})$,
where ${cal C}equiv m(r)/r$ is the dimensionless compactness parameter of the
self-gravitating matter configurations. In particular, we prove that, while
black-hole spacetimes are characterized by the lower bound ${cal
C}(r^{text{inner}}_{gamma})geq1/3$, horizonless ultra-compact objects may be
characterized by the opposite dimensionless relation ${cal
C}(r^{text{inner}}_{gamma})leq1/4$. Our results provide a simple analytical
explanation for the interesting numerical results that have recently presented
by Novotn’y, Hlad’ik, and Stuchl’ik [Phys. Rev. D 95, 043009 (2017)].

Ultra-compact objects describe horizonless solutions of the Einstein field
equations which, like black-hole spacetimes, possess null circular geodesics
(closed light rings). We study {it analytically} the physical properties of
spherically symmetric ultra-compact isotropic fluid spheres with a polytropic
equation of state. It is shown that these spatially regular horizonless
spacetimes are generally characterized by two light rings
${r^{text{inner}}_{gamma},r^{text{outer}}_{gamma}}$ with the property
${cal C}(r^{text{inner}}_{gamma})leq{cal C}(r^{text{outer}}_{gamma})$,
where ${cal C}equiv m(r)/r$ is the dimensionless compactness parameter of the
self-gravitating matter configurations. In particular, we prove that, while
black-hole spacetimes are characterized by the lower bound ${cal
C}(r^{text{inner}}_{gamma})geq1/3$, horizonless ultra-compact objects may be
characterized by the opposite dimensionless relation ${cal
C}(r^{text{inner}}_{gamma})leq1/4$. Our results provide a simple analytical
explanation for the interesting numerical results that have recently presented
by Novotn’y, Hlad’ik, and Stuchl’ik [Phys. Rev. D 95, 043009 (2017)].

http://arxiv.org/icons/sfx.gif