Ergoregion instability of ultra-compact astrophysical objects

TL;DR

The paper demonstrates that horizonless ultra-compact objects like gravastars and boson stars develop strong ergoregion instabilities when rapidly spinning, with growth times ranging from $\tau \sim 0.1\ \mathrm{s}$ to $7\times10^{5}\ \mathrm{s}$ for $M\sim 1-10^{6}M_\odot$ and $J>0.4M^2$. Using a WKB framework for scalar perturbations (with axial gravitational perturbations mapping to the scalar case in the large-$l$ limit), it provides semi-analytic growth rates and compares them to full numerical Klein–Gordon results, finding good frequency agreement and order-of-magnitude accuracy for growth times. The instability is stronger for more compact, rapidly rotating gravastars and boson stars, suggesting that highly spinning horizonless objects are unlikely BH mimics. The work also assesses detectability of the resulting gravitational waves with ground- and space-based detectors, showing that LISA could readily observe supermassive cases while LIGO-type detectors could detect sufficiently massive stellar remnants, provided the instability saturates and radiates efficiently. Overall, the study argues that rapid rotation plus the absence of an event horizon leaves identifiable gravitational-wave signatures, offering a robust test of BH horizons and a constraint on alternative ultra-compact objects.

Abstract

Most of the properties of black holes can be mimicked by horizonless compact objects such as gravastars and boson stars. We show that these ultra-compact objects develop a strong ergoregion instability when rapidly spinning. Instability timescales can be of the order of 0.1 seconds to 1 week for objects with mass M=1-10^6 solar masses and angular momentum J> 0.4 M^2. This provides a strong indication that ultra-compact objects with large rotation are black holes. Explosive events due to ergoregion instability have a well-defined gravitational-wave signature. These events could be detected by next-generation gravitational-wave detectors such as Advanced LIGO or LISA.

Figures (8)

• Figure 1: Top panel: Metric coefficients for the thin-shell model gravastar with $r_2=1.05$, $r_1=1$, $w_1=350$ and $w_2=1$, corresponding to $M\sim 0.485\,r_2$. Bottom panel: Anisotropic pressure model for $r_2=2.2$, $r_1=1.8$ and $M=1$, corresponding to $M\sim 0.45r_2$.
• Figure 2: Top panel: Size of the ergoregion for three different gravastars in the thin-shell limit. The vertical axis gives the angular momentum of the gravastar in units of its total mass. The horizontal axis gives the locations of the ergoregion boundaries in units of the gravastar radius $r_2$. Each curve refers to a different gravastar. The minima of the curves determine the existence and extent of ergoregions. The size of an ergoregion can be found by drawing a horizontal line at a given value of $J/M^2$; its intersections with the curves give the radii of the ergoregion boundaries. From top to bottom the three curves refer to $r_2=1.3$, $r_1=1$, $w_1=50$ and $w_2=1$, corresponding to $M\sim 0.39\,r_2$; $r_2=1.2$, $r_1=1$, $w_1=150$ and $w_2=1$, corresponding to $M\sim 0.44\,r_2$; $r_2=1.05$, $r_1=1$, $w_1=350$ and $w_2=1$, corresponding to $M\sim 0.49\,r_2$. Bottom panel: $J/M^2$ and angular frequency $\Omega$ for the anisotropic pressure model with $r_2=2.2$, $r_1=1.8$ and $M=1$. The angular frequency is always very small, thus the slow-rotation formalism applies. These results extend up to the Keplerian frequency $\Omega_K$.
• Figure 3: Left panel: Metric coefficients for a rotating boson star along the equatorial plane, with parameters $n=2$, $b=1.1$, $\lambda=1.0$, $a=2.0$, $J/(GM^2)\sim 0.566$. Right panel: Fractional difference of the metric potentials between $\theta=\pi/2$ and $\theta=\pi/4$ for the same star. The plot gives the maximum possible fractional difference between these quantities.
• Figure 4: The $g_{tt}$ metric coefficient for a boson star with $J/(GM^2)\sim 0.566$ at its equator. The ergoregion is identified by the region inside the dotted vertical lines and extends from $r/(GM)\sim 0.047$ to $0.770$.
• Figure 5: Top panel: Potentials $V_{\pm}$ for the thin-shell gravastar with $r_2=1.3$, $r_1=1$, $w_1=50$ and $w_2=1$. The ergoregion extends from $r\sim 0.247r_2$ to $0.832r_2$ and corresponds to a gravastar with $J\sim 0.333M^2$ and $M\Omega\sim 0.105$. Bottom panel: Potentials for the anisotropic pressure gravastar with $r_2=2.2$, $r_1=1.8$ and $M=1$. The ergoregion extends from $r\sim 0.270r_2$ to $r\sim 1.055r_2$ and rotates with angular momentum $J/M^2=1.00$, corresponding to $\Omega\sim 0.250$.