Analytic study of self-gravitating polytropic spheres with light rings

• Main Author: Shahar Hod
• Format: Article
• Language: English
• Published: SpringerOpen 2018-05-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-018-5905-y

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 $$\{r^{\text {inner}}_{\gamma },r^{\text {outer}}_{\gamma }\}$$ {rγinner,rγouter} with the property $$\mathcal{C}(r^{\text {inner}}_{\gamma })\le \mathcal{C}(r^{\text {outer}}_{\gamma })$$ C(rγinner)≤C(rγouter) , where $$\mathcal{C}\equiv m(r)/r$$ C≡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 $$\mathcal{C}(r^{\text {inner}}_{\gamma })\ge 1/3$$ C(rγinner)≥1/3 , horizonless ultra-compact objects may be characterized by the opposite dimensionless relation $$\mathcal{C}(r^{\text {inner}}_{\gamma })\le 1/4$$ C(rγinner)≤1/4 . 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, 2017).