Slowly rotating thin shell gravastars

Abstract

We construct the solutions of slowly rotating gravastars with a thin shell. In the zero-rotation limit, we consider the gravastar composed of a de Sitter core, a thin shell, and Schwarzschild exterior spacetime. The rotational effects are treated as small axisymmetric and stationary perturbations. The perturbed internal and external spacetimes are matched with a uniformly rotating thin shell. We assume that the angular velocity of the thin shell, $\Omega$, is much smaller than the Keplerian frequency of the nonrotating gravastar, ${\Omega }_k$. The solutions within an accuracy up to the second order of $\Omega /{\Omega }_k$ are obtained. The thin shell matter is assumed to be described by a perfect fluid and to satisfy the dominant energy condition in the zero-rotation limit. In this study, we assume that the equation of state for perturbations is the same as that of the unperturbed solution. The spherically symmetric component of the energy density perturbations, $\delta {\sigma }_0$, is assumed to vanish independently of the rotation rate. Based on these assumptions, we obtain many numerical solutions and investigate properties of the rotational corrections to the structure of the thin shell gravastar.

36 pages, 32 figures

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