Numerical analysis for relativistic stars with nonlinear equation of state in AdS

Abstract

It is known that for self-gravitating radiation stars in anti-de Sitter (AdS) spacetime, there is a critical dimension, larger than it, the stars always maintain stability with any central energy density [Formula: see text]; smaller than it, there is a maximal mass for the [Formula: see text] and when the [Formula: see text] continues to increase, the total mass of stars becomes a function of the [Formula: see text], and the function appears as an oscillation behavior and therefore the stars become unstable. In this paper we extend this study to the nonlinear case, in this case the equation of state is [Formula: see text], in AdS spacetime, where a and b are two constant parameters. For the nonlinear case,the equations of gravitational field are more complicated, so the relation of total mass to the central energy density is numerically investigated. In particular, the effect of the two parameters a and b and the relation between spacetime dimension d, mass and [Formula: see text] are analyzed. We find that the critical dimension changes when the parameters a and b vary, namely the equation of state. In particular, the critical dimension decreases when b decreases.