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• W2594587480 abstract "We demonstrate that in the framework of standard general relativity, polytropic spheres with properly fixed polytropic index $n$ and relativistic parameter $ensuremath{sigma}$, giving a ratio of the central pressure ${p}_{mathrm{c}}$ to the central energy density ${ensuremath{rho}}_{mathrm{c}}$, 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 $n--ensuremath{sigma}$ 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 $ensuremath{sigma}>0.677$ 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 ${r}_{mathrm{extr}}$ corresponding to the gravitational mass $Mensuremath{sim}2{M}_{ensuremath{bigodot}}$ of the most massive observed neutron stars. Then, for the central density ${ensuremath{rho}}_{mathrm{c}}ensuremath{sim}1{0}^{15}text{ }text{ }mathrm{g}text{ }{mathrm{cm}}^{ensuremath{-}3}$, the trapped regions are outside ${r}_{mathrm{extr}}$ for all values of $2.138<n<4$; for the central density ${ensuremath{rho}}_{mathrm{c}}ensuremath{sim}5ifmmodetimeselsetexttimesfi{}1{0}^{15}text{ }text{ }mathrm{g}text{ }{mathrm{cm}}^{ensuremath{-}3}$, the whole trapped regions are located inside ${r}_{mathrm{extr}}$ for $2.138<n<3.1$; while for ${ensuremath{rho}}_{mathrm{c}}ensuremath{sim}1{0}^{16}text{ }text{ }mathrm{g}text{ }{mathrm{cm}}^{ensuremath{-}3}$, the whole trapped regions are inside ${r}_{mathrm{extr}}$ 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." @default.
• W2594587480 created "2017-03-16" @default.
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• W2594587480 date "2017-02-28" @default.
• W2594587480 modified "2023-09-27" @default.
• W2594587480 title "Polytropic spheres containing regions of trapped null geodesics" @default.
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• W2594587480 doi "https://doi.org/10.1103/physrevd.95.043009" @default.
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