Onset of superradiant instabilities in rotating spacetimes of exotic compact objects

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 {\it discrete} set of critical surface radii, $\{r_{\text{c}}(\bar{a};n){\}}_{n=1}^{n=\infty }$, which can support spatially regular static ({\it marginally-stable}) scalar field configurations (here $\bar{a}\equiv J/M^2$ is the dimensionless angular momentum of the exotic compact object). Interestingly, the outermost critical radius $r_{\text{c}}^{\text{max}}\equiv {\text{max}}_n\{r_{\text{c}}(\bar{a};n)\}$ marks the boundary between stable and unstable exotic compact objects: spinning objects whose reflecting surfaces are situated in the region $r_{\text{c}}>r_{\text{c}}^{\text{max}}(\bar{a})$ are stable, whereas spinning objects whose reflecting surfaces are situated in the region $r_{\text{c}}<r_{\text{c}}^{\text{max}}(\bar{a})$ 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 {\it analytical} formula for the discrete spectrum $\{r_{\text{c}}^{\text{max}}(\bar{a})\}$ 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.

9 pages

References in corpus (23)

• The fuzzball proposal for black holes
• Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects
• How to tell a gravastar from a black hole
• Kerr-Newman scalar clouds
• Not quite a black hole
• Weak Cosmic Censorship: As Strong as Ever
• Kerr-Newman black holes with stationary charged scalar clouds
• Tidal deformability and I-Love-Q relations for gravastars with polytropic thin shells
• A new spin on black hole hair
• Non-linear Q-clouds around Kerr black holes
• Scalarized Hairy Black Holes
• Iron K$\alpha$ line of Kerr black holes with scalar hair
• Myers-Perry black holes with scalar hair and a mass gap
• Gravitational echoes from macroscopic quantum gravity effects
• The large-mass limit of cloudy black holes
• Extremal Kerr-Newman black holes with extremely short charged scalar hair
• Rotating black holes can have short bristles
• Myers-Perry black holes with scalar hair and a mass gap: unequal spins
• Wiggly tails: a gravitational wave signature of massive fields around black holes
• A no-short scalar hair theorem for rotating Kerr black holes
• Spinning Kerr black holes with stationary massive scalar clouds: The large-coupling regime
• Eigenvalue spectrum of the spheroidal harmonics: A uniform asymptotic analysis
• Classes of Exact Solutions to Regge-Wheeler and Teukolsky Equations

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• Parameter estimation of gravitational wave echoes from exotic compact objects
• Scalar perturbations around rotating regular black holes and wormholes: quasi-normal modes, ergoregion instability and superradiance
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• Ultra Compact Stars: Reconstructing the Perturbation Potential
• Scalarization of horizonless reflecting stars: neutral scalar fields non-minimally coupled to Maxwell fields
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• Static scalar field condensation in regular asymptotically AdS reflecting star backgrounds
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• Isotropic compact stars in 4D Einstein-Gauss-Bonnet gravity
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• Lower bound on the compactness of isotropic ultra-compact objects
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• On instabilities of stationary scalar field configurations supported by reflecting compact stars