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    Polytropic spheres containing regions of trapped null geodesics

    Zdeněk Stuchlík · Únor 01, 2017 · Fyzika · 0 comments
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    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
    pc to the central energy density ρc , 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 <n <4 . Space
    extension of the region of trapped null geodesics increases with both
    increasing n and σ >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 ̃2
    M☉ of the most massive observed neutron stars. Then, for the
    central density ρc̃1 015 g cm-3 , the
    trapped regions are outside rextr for all values of 2.138
    <n <4 ; for the central density ρc̃5 ×1 015
    g cm-3 , the whole trapped regions are located inside
    rextr for 2.138 <n <3.1 ; while for ρc̃1
    016 g cm-3 , the whole trapped regions are inside
    rextr 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.

    Authors:
    Novotný, Jan; Hladík, Jan; Stuchlík, Zdeněk;

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

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