Radial instability of trapping polytropic spheres

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19630%2F20%3AA0000041" target="_blank" >RIV/47813059:19630/20:A0000041 - isvavai.cz</a>
Result on the web
<a href="https://www.worldscientific.com/doi/abs/10.1142/S0218271820500303" target="_blank" >https://www.worldscientific.com/doi/abs/10.1142/S0218271820500303</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0218271820500303" target="_blank" >10.1142/S0218271820500303</a>

Result language
angličtina
Original language name
Radial instability of trapping polytropic spheres
Original language description
We complete the stability study of general-relativistic spherically symmetric polytropic perfect fluid spheres, concentrating our attention on the newly discovered polytropes containing region of trapped null geodesics. We compare the methods of treating the dynamical stability based on the equation governing infinitesimal radial pulsations of the polytropes and the related Sturm-Liouville eigenvalue equation for the eigenmodes governing the pulsations, to the methods of stability analysis based on the energetic considerations. Both methods are applied to determine the stability of the polytropes governed by the polytropic index n in the whole range 0 < n < 5, and the relativistic parameter sigma given by the ratio of the central pressure and energy density, restricted by the causality limit. The critical values of the adiabatic index for stability are determined, together with the critical values of the relativistic parameter sigma. For the dynamical approach, we implemented a numerical method which is independent on the choice of the trial function, and compare its results with the standard trial function approach. We found that the energetic and dynamic method give nearly the same critical values of sigma. We found that all the configurations having trapped null geodesics are unstable according to both methods.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10308 - Astronomy (including astrophysics,space science)

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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