Podrobný výpis o publikaci

We demonstrate that in the framework of standard general relativity, polytropic spheres with properly fixed polytropic index n and relativistic parameter sigma, giving a ratio of the central pressure p_(c) to the central energy density rho_(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-sigma parameter space, the region of allowed trapping increases with the polytropic index for intervals 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. In order to relate the trapping phenomenon to astrophysically relevant situations, we restrict the validity of the polytropic configurations to their extension rextr corresponding to the gravitational mass M similar to 2M_(circle dot) of the most massive observed neutron stars. Then, for the central density rho(c) similar to 10^(15) g cm^(-3), the trapped regions are outside r_extr for all values of 2.138 < n < 4; for the central density rho_(c) similar to 5 x 10^(15) g cm^(-3), the whole trapped regions are located inside r_(extr) for 2.138 < n < 3.1; while for rho_(c) similar to 10^(16) g cm^(-3), the whole trapped regions are inside r_(extr) for all values of 2.138 < n < 4, guaranteeing astrophysically plausible trapping for all considered polytropes. The region of trapped null geodesics is located close to the polytrope center and could have a relevant influence on the cooling of such polytropes or binding of gravitational waves in their interior.