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    Gravitational instability of polytropic spheres containing region of trapped null geodesics: a possible explanation of central supermassive black holes in galactic halos

    Zdeněk Stuchlík · Červen 01, 2017 · Fyzika · 0 comments
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    Publication date: Jun 2017

    Abstract:
    We study behaviour of gravitational waves in the recently introduced
    general relativistic polytropic spheres containing a region of trapped
    null geodesics extended around radius of the stable null circular
    geodesic that can exist for the polytropic index N > 2.138 and the
    relativistic parameter, giving ratio of the central pressure
    pc to the central energy density ρc, higher than σ
    = 0.677. In the trapping zones of such polytropes, the effective
    potential of the axial gravitational wave perturbations resembles those
    related to the ultracompact uniform density objects, giving thus similar
    long-lived axial gravitational modes. These long-lived linear
    perturbations are related to the stable circular null geodesic and due
    to additional non-linear phenomena could lead to conversion of the
    trapping zone to a black hole. We give in the eikonal limit examples of
    the long-lived gravitational modes, their oscillatory frequencies and
    slow damping rates, for the trapping zones of the polytropes with N in
    (2.138,4). However, in the trapping polytropes the long-lived damped
    modes exist only for very large values of the multipole number l >
    50, while for smaller values of l the numerical calculations indicate
    existence of fast growing unstable axial gravitational modes. We
    demonstrate that for polytropes with N >= 3.78, the trapping region
    is by many orders smaller than extension of the polytrope, and the mass
    contained in the trapping zone is about 10-3 of the total
    mass of the polytrope. Therefore, the gravitational instability of such
    trapping zones could serve as a model explaining creation of central
    supermassive black holes in galactic halos or galaxy clusters.

    Authors:
    Stuchlík, Zdeněk; Schee, Jan; Toshmatov, Bobir; Hladík, Jan; Novotný, Jan;

    https://ui.adsabs.harvard.edu/abs/2017JCAP…06..056S

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