Polytropic spheres containing regions of trapped null geodesics

Publication date: Feb 2017

Abstract:
We demonstrate that in the framework of standard general relativity, polytropic spheres with properly fixed polytropic index n and relativistic parameter σ , giving a ratio of the central pressure p_c to the central energy density ρ_c , can contain a region of trapped null geodesics. Such trapping polytropes can exist for n >2.138 , and they are generally much more extended and massive than the observed neutron stars. We show that in the n – σ parameter space, the region of allowed trapping increases with the polytropic index for intervals of physical interest, 2.138 0.677 from the allowed region. In order to relate the trapping phenomenon to astrophysically relevant situations, we restrict the validity of the polytropic configurations to their extension r_extr corresponding to the gravitational mass M ∼2 M_⊙ of the most massive observed neutron stars. Then, for the central density ρ_c∼1 0¹⁵ g cm^-3 , the trapped regions are outside r_extr for all values of 2.138 c∼5 ×1 0¹⁵ g cm^-3 , the whole trapped regions are located inside r_extr for 2.138 c∼1 0¹⁶ g cm^-3 , the whole trapped regions are inside r_extr for all values of 2.138 Authors:
Novotný, Jan; Hladík, Jan; Stuchlík, Zdeněk;

https://ui.adsabs.harvard.edu/abs/2017PhRvD..95d3009N