How to tell a gravastar from a black hole

TL;DR

The paper addresses whether gravastars can be stable and observationally distinguished from black holes by analyzing axial perturbations of thick-shell gravastar models with anisotropic pressures. It develops a general thick-shell framework that reproduces a de-Sitter interior and Schwarzschild exterior, derives the anisotropic TOV equations, and imposes physically motivated EOS and continuity conditions. Through numerical integration of the axial perturbation equation and QNM extraction, the study shows all models are dynamically stable ($\mathrm{Im}(\omega)<0$) and demonstrates that gravastar QNM spectra differ from Schwarzschild black holes, even when $\omega_R$ coincides, due to differences in $\omega_I$; this provides a robust gravitational-wave-based discriminator. The results extend the original Mazur-Mottola construction to finite-thickness shells and highlight gravitational radiation as a practical probe to distinguish gravastars from black holes in astrophysical observations.

Abstract

Gravastars have been recently proposed as potential alternatives to explain the astrophysical phenomenology traditionally associated to black holes, raising the question of whether the two objects can be distinguished at all. Leaving aside the debate about the processes that would lead to the formation of a gravastar and the astronomical evidence in their support, we here address two basic questions: Is a gravastar stable against generic perturbations? If stable, can an observer distinguish it from a black hole of the same mass? To answer these questions we construct a general class of gravastars and determine the conditions they must satisfy in order to exist as equilibrium solutions of the Einstein equations. For such models we perform a systematic stability analysis against axial-perturbations, computing the real and imaginary parts of the eigenfrequencies. Overall, we find that gravastars are stable to axial perturbations, but also that their quasi-normal modes differ from those of a black hole of the same mass and thus can be used to discern, beyond dispute, a gravastar from a black hole.

Figures (8)

• Figure 1: Limits in the compactness and thickness of a gravastar in the MM model. The curve shows the maximum compactness for a given thickness $\delta$ of the shell, that is, in the light gray area below the curve we have the possible solutions, while in the area above the curve solutions are no longer possible. The dark gray area highlights the typical compactnesses for neutron stars. The inset shows a comparison between the numerical solution of the TOV equations with the analytical solution in the thin-shell limit.
• Figure 2: Left panel: Behaviour of the functions $\rho(r)$, $p_r(r)$ and $p_t(r)$ for a representative gravastar model with $M = 1$, $r_1 = 1.8$ and $r_2 = 2.2$. The function $p_t(r)$ is scaled by 0.1 for better visualization but provides the dominant contribution in eq. (\ref{['aTOV']}). Right panel: Behaviour of the mass function $m(r)$ and of the metric coefficient $g_{rr}$ for the same solution shown in the left panel.
• Figure 3: Left panel: Behaviour of $1-2m(r)/r$ for $M = 1$ and different values of $r_1$ and $r_2 = 2.2$. Right panel: Dependence on $\delta$ of the minimum value of $1-2m(r)/r$ for gravastars with $M = 1$ and different values of $r_2$. Note that for sufficiently large models, the minimum is always positive.
• Figure 4: Limit on the compactness $\mu$ of the gravastar with the thickness of the shell $\delta$. This figure compares the results obtained for the MM model in the lower curve (see figure \ref{['graf_novo']}) and the results obtained for our model in the upper curve.
• Figure 5: Diagram of the numerical grid and the domain of interest. The black points represent the grid points where the value of the field is known. The red points represent the grid points to be calculated.