Gravitational instabilities of superspinars

TL;DR

This work analyzes the dynamical stability of superspinars, compact objects that violate the Kerr bound ($a/M>1$), by solving spin-2 perturbations in a Kerr background with two external boundary prescriptions at an excision radius $r_0$: a perfectly reflecting surface and a perfectly absorbing (stringy horizon) surface. Using the Teukolsky formalism and careful treatment of the angular eigenvalues ${}_sA_{lm}$, the authors show that both boundary conditions yield unstable gravitational modes on dynamical timescales, with the strongest low-$\ell$ instability occurring for $l=m=2$ around $a/M\sim 1.1$, and additional $m=0$ instabilities in certain parameter ranges. Higher-$\ell$ modes are also generally unstable, especially as the ergoregion becomes more oblate for large $a/M$, suggesting that superspinars are not viable astrophysical alternatives to black holes. The results hold across a broad class of gravity theories, implying that stabilizing such objects would require substantial departures from standard Kerr geometry or the incorporation of more complex internal/external structure. Consequently, due to rapid spin-down by accretion and ubiquitous gravitational instabilities, superspinars are unlikely to form or persist in nature as black-hole mimickers.

Abstract

Superspinars are ultracompact objects whose mass M and angular momentum J violate the Kerr bound (cJ/GM^2>1). Recent studies analyzed the observable consequences of gravitational lensing and accretion around superspinars in astrophysical scenarios. In this paper we investigate the dynamical stability of superspinars to gravitational perturbations, considering either purely reflecting or perfectly absorbing boundary conditions at the "surface" of the superspinar. We find that these objects are unstable independently of the boundary conditions, and that the instability is strongest for relatively small values of the spin. Also, we give a physical interpretation of the various instabilities that we find. Our results (together with the well-known fact that accretion tends to spin superspinars down) imply that superspinars are very unlikely astrophysical alternatives to black holes.

Figures (9)

• Figure 1: Top: Real (left) and imaginary part (right) of unstable gravitational modes of a superspinar as a function of the spin parameter, $a/M$, for $l=m=2$ and several fixed values of $r_0$. Bottom: Real (left) and imaginary part (right) of unstable gravitational modes of a superspinar as a function of the mirror location, $r_0/M$, for $l=m=2$ and different fixed values of the spin parameter. Large dots indicate purely imaginary modes.
• Figure 2: Proper volume of the ergoregion as a function of the spin $a/M$. The volume increases monotonically when $a<M$, is infinite at $a=M$ and decreases monotonically when $a>M$. The proper volumes for $a\sim2M$ and $a\sim0.3M$ are roughly the same. In the inset we show the azimuthal section of the ergoregion for selected values of the spin. These spins are marked by filled circles and capital Latin letters in the main plot; their numerical value is indicated in parentheses in the figure. In the limit $a/M\to\infty$ the ergoregion becomes so oblate that its proper volume shrinks to zero.
• Figure 3: Left: Imaginary part of unstable gravitational modes of a superspinar as a function of the mirror location, $r_0/M$, for $a=1.1M$, $l=2$ and $m=0,\,1,\,2$. Right: Imaginary part of unstable gravitational modes of a superspinar as a function of the mirror location, $r_0/M$, for $l=2$, $m=0$ and several values of the spin parameter, $a$.
• Figure 4: Left: Purely imaginary unstable mode as a function of the mirror location, $r_0/M<0$, for $a=1.4M$, $s=l=2$ and $m=0$. In the limit $r_0\to-\infty$, $M\omega_I\sim7.07$, which perfectly agrees with results in Ref. Dotti:2008yr. Right: Purely imaginary unstable mode as a function of the spin, $a/M$, for $r_0=-3M$, $s=l=2$, $m=0$. Numerical results (black straight line) are consistent with the quadratic fit of Eq. (\ref{['fitdotti']}) (red dashed line). The dot marks the case considered in the left panel.
• Figure 5: Top: Real (left) and imaginary part (right) of unstable gravitational modes of a superspinar as a function of the spin parameter, $a/M$, for $l=m=2$ and several fixed values of the horizon location $r_0/M$. Bottom: Real (left) and imaginary part (right) of unstable gravitational modes of a superspinar as a function of the horizon location, for $l=m=2$ and fixed values of the spin parameter. Large dots indicate purely imaginary modes.