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 analytically the physical properties of spherically symmetric ultra-compact isotropic fluid spheres with a p...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-05-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-018-5905-y |
| Summary: | 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). |
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| ISSN: | 1434-6044 1434-6052 |