Polytropic spheres containing regions of trapped null geodesics

Understand

We demonstrate that in the framework of standard general relativity polytropic spheres with properly fixed polytropic index $n$ and relativistic parameter $\sigma$, giving ratio of the central pressure $p_\mathrm{c}$ to the central energy density $\rho_\mathrm{c}$, can contain 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 $n$--$\sigma$ parameter space the region of allowed trapping increase with polytropic index for interval of physical interest $2.138 < n < 4$.
• Space extension of the region of trapped null geodesics increases with both increasing $n$ and $\sigma > 0.677$ from the allowed region.