Gravitational instability of polytropic spheres containing region of trapped null geodesics: a possible explanation of central supermassive black holes in galactic halos
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.
- Publication:
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Journal of Cosmology and Astroparticle Physics
- Pub Date:
- June 2017
- DOI:
- 10.1088/1475-7516/2017/06/056
- arXiv:
- arXiv:1704.07713
- Bibcode:
- 2017JCAP...06..056S
- Keywords:
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- General Relativity and Quantum Cosmology
- E-Print:
- 28 pages, 8 figures, 2 tables