https://doi.org/10.1140/epjc/s10052-018-5905-y
Regular Article - Theoretical Physics
Analytic study of self-gravitating polytropic spheres with light rings
1
The Ruppin Academic Center, Emeq Hefer, 40250, Israel
2
The Hadassah Academic College, Jerusalem, 91010, Israel
* e-mail: shaharhod@gmail.com
Received:
23
March
2018
Accepted:
18
May
2018
Published online:
26
May
2018
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 
with the property 
, where 
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 
, horizonless ultra-compact objects may be characterized by the opposite dimensionless relation 
. 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).
© The Author(s), 2018
