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 p_{c} to the central energy density ρ_{c}, 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 longlived axial gravitational modes. These longlived linear perturbations are related to the stable circular null geodesic and due to additional nonlinear phenomena could lead to conversion of the trapping zone to a black hole. We give in the eikonal limit examples of the longlived 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 longlived 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:

Journal of Cosmology and Astroparticle Physics
 Pub Date:
 June 2017
 DOI:
 10.1088/14757516/2017/06/056
 arXiv:
 arXiv:1704.07713
 Bibcode:
 2017JCAP...06..056S
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 28 pages, 8 figures, 2 tables