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- Title
Analytic study of self-gravitating polytropic spheres with light rings.
- Authors
Hod, Shahar
- Abstract
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 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 {rγinner,rγouter}<inline-graphic></inline-graphic> with the property C(rγinner)≤C(rγouter)<inline-graphic></inline-graphic>, where C≡m(r)/r<inline-graphic></inline-graphic> 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 C(rγinner)≥1/3<inline-graphic></inline-graphic>, horizonless ultra-compact objects may be characterized by the opposite dimensionless relation C(rγinner)≤1/4<inline-graphic></inline-graphic>. Our results provide a simple analytical explanation for the interesting numerical results that have recently presented by Novotný et al. (Phys Rev D 95:043009, <xref>2017</xref>).
- Subjects
BLACK holes; NUMERICAL solutions to Einstein field equations; POLYTROPIC processes; CURVED spacetime; DARK matter; GRAVITATIONAL fields
- Publication
European Physical Journal C -- Particles & Fields, 2018, Vol 78, Issue 5, p1
- ISSN
1434-6044
- Publication type
Article
- DOI
10.1140/epjc/s10052-018-5905-y