The impact of spheroidicity on the stability of polytropic spheres

Abstract

We investigate the stability of polytropic spheres in classical general relativity influenced by a departure from homogeneous spherical symmetry. We utilize the Vaidya–Tikekar ansatz to generate models of superdense stars obeying a polytropic equation of state of the form pr=κρ1+1n−β. Models with polytropic index n=1 (quadratic equation of state) and n=2 are generated for the general spheroidal parameter. We investigate the physical viability of these models and show that they describe strange star candidates such as SAX J1808.4-3658 to a good approximation. An interesting finding of this work shows that these models become unstable as the spheroidal parameter is decreased which leads us to conclude that stability is compromised with departure from homogeneous spherical symmetry.