Onset of superradiant instabilities in rotating spacetimes of exotic compact objects

Abstract

Abstract Exotic compact objects, horizonless spacetimes with reflective properties, have intriguingly been suggested by some quantum-gravity models as alternatives to classical black-hole spacetimes. A remarkable feature of spinning horizonless compact objects with reflective boundary conditions is the existence of a discrete set of critical surface radii, {r c(ā; n)} n = 1 n = ∞ , which can support spatially regular static (marginally-stable) scalar field configurations (here ā≡J/M 2 is the dimensionless angular momentum of the exotic compact object). Interestingly, the outermost critical radius r c max ≡ max n {r c(ā; n)} marks the boundary between stable and unstable exotic compact objects: spinning objects whose reflecting surfaces are situated in the region r c > r c max (ā) are stable, whereas spinning objects whose reflecting surfaces are situated in the region r c < r c max (ā) are superradiantly unstable to scalar perturbation modes. In the present paper we use analytical techniques in order to explore the physical properties of the critical (marginally-stable) spinning exotic compact objects. In particular, we derive a remarkably compact analytical formula for the discrete spectrum {r c max (ā)} of critical radii which characterize the marginally-stable exotic compact objects. We explicitly demonstrate that the analytically derived resonance spectrum agrees remarkably well with numerical results that recently appeared in the physics literature.

Keywords

• Black Holes
• Classical Theories of Gravity
• Models of Quantum Gravity