Instability of hyper-compact Kerr-like objects

TL;DR

The paper investigates the ergoregion instability of horizonless, Kerr-like hyper-compact objects (superspinars and Kerr-like wormholes) by modeling them as Kerr spacetimes bounded by a reflective surface. Using analytic treatments in slow- and fast-rotation limits and comprehensive numerical Teukolsky-based stability analyses, it shows that such objects exhibit rapid ergoregion-driven instabilities across a wide range of spins and masses, with gravitational perturbations typically the most unstable. It also identifies algebraically special modes that can trigger instabilities even without an ergoregion. Collectively, the results strengthen the case that observed rapidly rotating hyper-compact objects are black holes, imposing strong constraints on horizonless alternatives in astrophysical settings.

Abstract

Viable alternatives to astrophysical black holes include hyper-compact objects without horizon, such as gravastars, boson stars, wormholes and superspinars. The authors have recently shown that typical rapidly-spinning gravastars and boson stars develop a strong instability. That analysis is extended in this paper to a wide class of horizonless objects with approximate Kerr-like geometry. A detailed investigation of wormholes and superspinars is presented, using plausible models and mirror boundary conditions at the surface. Like gravastars and boson stars, these objects are unstable with very short instability timescales. This result strengthens previous conclusions that observed hyper-compact astrophysical objects with large rotation are likely to be black holes.

Figures (4)

• Figure 1: Imaginary and real parts of the characteristic gravitational frequencies for an object with $a=0.998M$, according to the analytic calculation for rapidly-spinning objects. The mirror location is at $r_0=(1+\epsilon)r_+$. The real part is approximately constant and close to $m\Omega$, in agreement with the assumptions used in the analytic approach.
• Figure 2: Details of the instability for scalar perturbations, from a numerical solution of Teukolsky equation. Top panels: Numerical results for the imaginary part (left panel) and real part (right panel) of the fundamental mode frequency vs. the mirror position $r_0=r_+(1+\epsilon)$ for different $l=m$ values. The angular momentum is $a=0.998M$. The instability grows monotonically with $l=m$. Bottom panels: Zoomed-in version of the upper panels, where numerical results (solid lines) are compared to the analytic solutions in the near-extremal regime (\ref{['extremal zero equation2']}) (dotted lines). The agreement between numerical and analytic values of the resonant frequency is remarkable. The analytic results for the imaginary part (bottom left panel) agree with the numerical results within a factor $\sim 3$.
• Figure 3: Details of the instability for gravitational perturbations, for different $l=m$ modes and $a/M=0.998$ (top panels) and for $l=m=2$ and different $a/M<1$.
• Figure 4: The fundamental $l=m=2,3,4$ modes of an object spinning above the Kerr bound as function of rotation. The surface is located at $r_0/M=0.001$.