On the ergoregion instability in rotating gravastars

TL;DR

The paper reexamines the ergoregion instability in rotating gravastars, challenging the notion that rapid rotation necessarily leads to instability. Using a finite-thickness, slowly rotating gravastar with anisotropic pressure and a scalar perturbation analyzed via a WKB method, it derives conditions for ergoregion formation and estimates growth times of unstable modes. The authors demonstrate that not all rotating gravastars develop ergoregions; stable configurations can occur even for J/M^2 ~ 1 and they establish μ_max(J) bounds that constrain the compactness of stable models. These results imply that some ultra-compact, rapidly spinning objects could masquerade as black holes less strictly than previously thought, offering new observational avenues beyond quasi-normal-mode analysis to distinguish gravastars from black holes.

Abstract

The ergoregion instability is known to affect very compact objects that rotate very rapidly and do not possess a horizon. We present here a detailed analysis on the relevance of the ergoregion instability for the viability of gravastars. Expanding on some recent results, we show that not all rotating gravastars are unstable. Rather, stable models can be constructed also with J/M^2 ~ 1, where J and M are the angular momentum and mass of the gravastar, respectively. The genesis of gravastars is still highly speculative and fundamentally unclear if not dubious. Yet, their existence cannot be ruled out by invoking the ergoregion instability. For the same reason, not all ultra-compact astrophysical objects rotating with J/M^2 <~ 1 are to be considered necessarily black holes.

Figures (7)

• Figure 1: Typical example for the dragging of inertial frames $\omega(r)$, for a gravastar with $\mu = 0.45$, $\delta/M = 0.4$ and $J/M^2 = 1$ ($\Omega/\Omega_K = 0.82$). We can see that $\omega = {\rm const.}$ in the interior ($r < r_1$) and $\omega \to 0$ in the exterior region ($r > r_2$).
• Figure 2: Typical example for the potentials $V_{\pm}$, for a gravastar with $\mu = 0.45$, $\delta/M = 0.4$ and $J/M^2 = 1$ ($\Omega/\Omega_K = 0.82$). The first three unstable modes with negative energy "trapped" in the potential well are depicted, as well as the points $r_a$, $r_b$ and $r_c$ for the $\ell=m=1$ mode.
• Figure 3: Left panel: Change in the size of the ergoregion for fixed compactness $\mu = 0.45$, several different values for $\delta/M$ (from top to bottom $\delta/M = 0.1,\,0.2,\,0.3\,$ and 0.4) and increasing angular velocity $\Omega$, until the Keplerian limit $\Omega_K$. A given value of $\Omega$ on the vertical axis determines the inner and outer radii of the ergoregion, while the vertical line shows the location of the radius of the gravastar for all the models: the ergoregion generally starts in the interior of the gravastar and goes up to a radius exterior to the radius $r_2$ of the gravastar. Right panel: Same as the left panel, but for fixed thickness of the shell $\delta/M = 0.4$ and different values for $\mu$ (from top to bottom $\mu = 0.42,\,0.43,\,0.45$ and 0.47). In this case we do not show the surface radius, since each model has a different radius $r_2$.
• Figure 4: Minimum angular velocity necessary for the existence of an ergoregion, as a function of both $\mu$ and $\delta$. If an ergoregion is present, the instability will set in for a high enough value of $m$. In the grey area at the bottom, an angular velocity $\Omega$ larger than the mass shedding limit $\Omega_K$ would be required for an ergoregion to develop. The grey area at the top shows a constraint on the possible (nonrotating) gravastar solutions found in ref. Chirenti.
• Figure 5: Minimum angular momentum necessary for the existence of an ergoregion, as a function of both $\mu$ and $\delta$. Gravastars with parameters $(\mu,\delta)$ given below a curve labeled with some value of $J_{\rm min}/M^2$ will be stable if rotating with angular momentum smaller or equal to $J_{\rm min}$. Note that the $\Omega$ is not constant along the lines, and increases in the direction of the region labeled $\Omega_{\rm min}(J_{\rm min}) > \Omega_K$.