Analytic study of self-gravitating polytropic spheres with light rings

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 {\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 $\{r_{\gamma }^{\text{inner}},r_{\gamma }^{\text{outer}}\}$ with the property $\mathcal{C}(r_{\gamma }^{\text{inner}})\le \mathcal{C}(r_{\gamma }^{\text{outer}})$, where $\mathcal{C}\equiv m(r)/r$ 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 $\mathcal{C}(r_{\gamma }^{\text{inner}})\ge 1/3$, horizonless ultra-compact objects may be characterized by the opposite dimensionless relation $\mathcal{C}(r_{\gamma }^{\text{inner}})\le 1/4$. Our results provide a simple analytical explanation for the interesting numerical results that have recently presented by Novotný, Hladík, and Stuchlík [Phys. Rev. D 95, 043009 (2017)].

7 pages

References in corpus (16)

• Are eikonal quasinormal modes linked to the unstable circular null geodesics?
• Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects
• Connection between black-hole quasinormal modes and lensing in the strong deflection limit
• Slow relaxation of rapidly rotating black holes
• Universal Bound on Dynamical Relaxation Times and Black-Hole Quasinormal Ringing
• The Quasinormal Mode Spectrum of a Kerr Black Hole in the Eikonal Limit
• Unstable circular null geodesics of static spherically symmetric black holes, Regge poles and quasinormal frequencies
• Upper bound on the radii of black-hole photonspheres
• General relativistic polytropes with a repulsive cosmological constant
• Extremal Kerr-Newman black holes with extremely short charged scalar hair
• Near-Extreme Black Holes and the Universal Relaxation Bound
• A no-short scalar hair theorem for rotating Kerr black holes
• Polytropic spheres containing regions of trapped null geodesics
• Self-gravitating field configurations: The role of the energy-momentum trace
• Ultra-spinning exotic compact objects supporting static massless scalar field configurations
• On the number of light rings in curved spacetimes of ultra-compact objects

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• Topological charge and black hole photon spheres in massive gravity
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