Ergoregion instability of ultracompact astrophysical objects

Most of the properties of black holes can be mimicked by horizonless compact objects such as gravastars and boson stars. We show that these ultracompact objects develop a strong ergoregion instability when rapidly spinning. Instability time scales can be of the order of 0.1 seconds to 1 week for objects with mass $M=1-{10}^6{M}_{\odot }$ and angular momentum $J>0.4M^2$. This provides a strong indication that ultracompact 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.

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 $M\sim 0.485r_2$. 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 $r_2=1.3$, $r_1=1$, $w_1=50$n and $w_2=1$, corresponding to $M\sim 0.39r_2$; $r_2=1.2$, $r_1=1$, $w_1=150$, and $w_2=1$, corresponding to $M\sim 0.44r_2$; $r_2=1.05$, $r_1=1$, $w_1=350$, and $w_2=1$, corresponding to $M\sim 0.49r_2$. 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 $n=2$, $b=1.1$, $\lambda =1.0$, $a=2.0$, $J/({\mathrm{GM}}^2)\sim 0.566$. 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 $J/({\mathrm{GM}}^2)\sim 0.566$ at its equator. The ergoregion is identified by the region inside the dotted vertical lines and extends from $r/(\mathrm{GM})\sim 0.047$ 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 $\Omega \sim 0.250$.

Figure 6

Details of the ergoregion instability ($m=1$ and $m=4$) for the thin-shell gravastar of Sec. 2a1 with $r_2=1.3$, $r_1=1$, $w_1=50$, and $w_2=1$. The plot shows the logarithm of the dimensionless instability time scale $\tau /M$, the dimensionless angular velocity $M\Omega$, and the oscillation frequency $\Sigma$ vs the angular momentum per unit mass, $J/M^2$. The $m=2$, 3 modes follow a similar pattern and are in between the $m=1$, 4 results.

Figure 7

Potentials $V_{\pm }$ for the boson star model with $J/({\mathrm{GM}}^2)=0.566$. The ergoregion extends from $r/(\mathrm{GM})\sim 0.0478$ to 0.779.

Figure 8

Evolution of mass, angular velocity, and waveform of a thin-shell gravastar with $h_0={10}^{-4}$, $M{\Omega }_0=0.25$, and $\tau /M=0.041$ during the linear perturbation phase. The mass difference is rescaled by a factor 10 for better visualization.