Dynamical instability of polytropic spheres in spacetimes with a cosmological constant
Abstract
The dynamical instability of relativistic polytropic spheres, embedded in a spacetime with a repulsive cosmological constant, is studied in the framework of general relativity. We apply the methods used in our preceding paper to study the trapping polytropic spheres with Λ =0 , namely, the critical point method and the infinitesimal and adiabatic radial perturbations method developed by Chandrasekhar. We compute numerically the critical adiabatic index, as a function of the parameter σ =p_{c}/(ρ_{c}c^{2}), for several values of the cosmological parameter λ giving the ratio of the vacuum energy density to the central energy density of the polytrope. We also determine the critical values for the parameter σ_{cr}, for the onset of instability, by using both approaches. We found that for large values of the parameter λ , the differences between the values of σ_{cr} calculated by the critical point method differ from those obtained via the radial perturbations method. Our results, given by both applied methods, indicate that large values of the cosmological parameter λ have relevant effects on the dynamical stability of the polytropic configurations.
 Publication:

Physical Review D
 Pub Date:
 July 2020
 DOI:
 10.1103/PhysRevD.102.024056
 arXiv:
 arXiv:2005.14072
 Bibcode:
 2020PhRvD.102b4056P
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 15 pages, 8 figures. Minor typos corrected, accepted for publication in PRD