We show that the horizon instability of the extremal Kerr black hole is associated with a singular branch point in the Green function at the superradiant bound frequency. We study generic initial data supported away from the horizon and find an enhanced growth rate due to nonaxisymmetric modes. The growth is controlled by the conformal weight h of each mode. We speculate on connections to near-extremal black holes and holographic duality.

Inspiralling compact binaries are expected to circularize before their gravitational-wave signals reach the sensitive frequency band of ground-based detectors. Current searches for gravitational waves from compact binaries using the LIGO and Virgo detectors therefore use circular templates to construct matched filters. Binary formation models have been proposed which suggest that some systems detectable by the LIGO-Virgo network may have non-negligible eccentricity. We investigate the ability of the restricted 3.5 post-Newtonian order TaylorF2 template bank, used by LIGO and Virgo to search for gravitational waves from compact binaries with masses M ≤ 35M⊙, to detect binaries with non-zero eccentricity. We model the gravitational waves from eccentric binaries using the x-model post-Newtonian formalism proposed by Hinder et al. [I. Hinder, F. Hermann, P. Laguna, and D. Shoemaker, arXiv:0806.1037v1]. We find that small residual eccentricities (e0 0.05 at 40 Hz) do not significantly affect the ability of current LIGO searches to detect gravitational waves from coalescing compact binaries with total mass 2M⊙ < M < 15M⊙. For eccentricities e0 0.1, the loss in matched filter signal-to-noise ratio due to eccentricity can be significant and so templates which include eccentric effects will be required to perform optimal searches for such systems.

We examine Hubeny's scenario according to which a near-extremal Reissner-Nordström black hole can absorb a charged particle and be driven toward an over-extremal state in which the charge exceeds the mass, signaling the destruction of the black hole. Our analysis incorporates the particle's electromagnetic self-force and the energy radiated to infinity in the form of electromagnetic waves. With these essential ingredients, our sampling of the parameter space reveals no instances of an overcharged final state, and we conjecture that the self-force acts as a cosmic censor, preventing the destruction of a near-extremal black hole by the absorption of a charged particle. We argue, on the basis of the third law of black-hole mechanics, that this conclusion is robust and should apply to attempts to overspin a Kerr black hole.

We show that scalar, electromagnetic, and gravitational perturbations of extremal Kerr black holes are asymptotically self-similar under the near-horizon, late-time scaling symmetry of the background metric. This accounts for the Aretakis instability (growth of transverse derivatives) as a critical phenomenon associated with the emergent symmetry. We compute the critical exponent of each mode, which is equivalent to its decay rate. It follows from symmetry arguments that, despite the growth of transverse derivatives, all generally covariant scalar quantities decay to zero. I. INTRODUCTION AND SUMMARYGiven decades of work indicating the basic stability of four-dimensional, asymptotically flat black holes to massless perturbing fields (e.g. [1-5]), Aretakis' 2010 discovery of a horizon instability of extremal black holes [6,7] came as something of a surprise. The instability has a rather unusual character: the growth is polynomial (rather than exponential), occurring only on the horizon, and only for sufficiently high-order transverse derivatives of the perturbing field. Off the horizon, the field and all its derivatives decay to zero [6,8]. On the principle that there are no accidents in physics, one naturally seeks a deeper explanation: What is the origin of this peculiar behavior?The answer, as usual, is symmetry. We will show how the Aretakis instability can be viewed as a critical phenomenon associated with the emergence of a scaling symmetry near the horizon. The relevant scaling limit [9] is well-known for its near-horizon character, but we observe that it also entails late times and is therefore naturally suited to questions of late-time behavior on the horizon. We show that perturbing fields are asymptotically equal to a sum of terms that are self-similar in the limit. The self-similarity accounts for the detailed structure of the instability (transverse derivatives modifying the late-time behavior by one positive power of time), with the numerical values of the exponents completing the description with detailed decay and growth rates.A second question for the Aretakis instability concerns its physical consequences. In previous work with A. Zimmerman [10], we emphasized definite consequences for particular observers or particles, without addressing observer-independent quantities. Very recently, independent work of Hadar and Reall [11] and Burko and Khanna [12] argued, from different angles using different techniques, that general covariance prevents such quantities from becoming large. Burko and Khanna [12] numerically confirmed the rates [10, 13] for scalar (φ ∼ v −1/2 ) and gravitational (ψ 4 ∼ v 3/2 and ψ 0 ∼ v −5/2 ) perturbations of Kerr 1 and noted that the polynomial non-derivative invariants of the Riemann tensor are determined from ψ 0 ψ 4 , which decays like 1/v. They gave further examples of scalar invariants that decay, showing how growing and decaying factors always balance in covariant expressions. Hadar and Reall [11] systematized this type of argument in the context of effective field the...

We analytically study the linear response of a near-extremal Kerr black hole to external scalar, electromagnetic, and gravitational field perturbations. We show that the energy density, electromagnetic field strength, and tidal force experienced by infalling observers exhibit transient growth near the horizon. The growth lasts arbitrarily long in the extremal limit, reproducing the horizon instability of extremal Kerr. We explain these results in terms of near-horizon geometry and discuss potential astrophysical implications.

The gravitational self-force has thus far been formulated in background spacetimes for which the metric is a solution to the Einstein field equations in vacuum. While this formulation is sufficient to describe the motion of a small object around a black hole, other applications require a more general formulation that allows for a nonvacuum background spacetime. We provide a foundation for such extensions, and carry out a concrete formulation of the gravitational self-force in two specific cases. In the first we consider a particle of mass $m$ and scalar charge $q$ moving in a background spacetime that contains a background scalar field. In the second we consider a particle of mass $m$ and electric charge $e$ moving in an electrovac spacetime. The self-force incorporates all couplings between the gravitational perturbations and those of the scalar or electromagnetic fields. It is expressed as a sum of local terms involving tensors defined in the background spacetime and evaluated at the current position of the particle, as well as tail integrals that depend on the past history of the particle. Because such an expression is rarely a useful starting point for an explicit evaluation of the self-force, we also provide covariant expressions for the singular potentials, expressed as local expansions near the world line; these can be involved in the construction of effective extended sources for the regular potentials, or in the computation of regularization parameters when the self-force is computed as a sum over spherical-harmonic modes.Comment: 20 pages, no figure

We show that the emergent near-horizon conformal symmetry of extremal black holes gives rise to universal behavior in perturbing fields, both near and far from the black hole horizon. The scale-invariance of the near-horizon region entails power law timedependence with three universal features: (1) the decay off the horizon is always precisely twice as fast as the decay on the horizon; (2) the special rates of 1/t off the horizon and 1/ √ v on the horizon commonly occur; and (3) sufficiently high-order transverse derivatives grow on the horizon (Aretakis instability). The results are simply understood in terms of nearhorizon (AdS 2 ) holography. We first show how the general features follow from symmetry alone and then go on to present the detailed universal behavior of scalar, electromagnetic, and gravitational perturbations of d-dimensional electrovacuum black holes.

We investigate the stability of highly charged Reissner-Nordström black holes to charged scalar perturbations. We show that the near-horizon region exhibits a transient instability which becomes the Aretakis instability in the extremal limit. The rates we obtain match the enhanced rates for nonaxisymmetric perturbations of the near-extremal and extremal Kerr solutions. The agreement is shown to arise from a shared near-horizon symmetry of the two scenarios.