We introduce a bilinear form for Weyl scalar perturbations of Kerr. The is symmetric and conserved, we show that, when combined with suitable renormalization prescription involving complex r integration contours, quasinormal modes are orthogonal in the different (l, m, n). These properties apparently not evident consequences standard radial angular solutions to decoupled Teukolsky relations rely on Petrov type D character Kerr its t-$\phi$ reflection isometry. that mode excitation...

We examine Hubeny's scenario according to which a near-extremal Reissner-Nordstr\"om black hole can absorb charged particle and be driven toward an over-extremal state in the charge exceeds mass, signaling destruction of hole. Our analysis incorporates particle's electromagnetic self-force energy radiated infinity form waves. With these essential ingredients, our sampling parameter space reveals no instances overcharged final state, we conjecture that acts as cosmic censor, preventing by...

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 using LIGO and Virgo detectors therefore use circular templates construct matched filters. Binary formation models have been proposed which suggest that some systems detectable by LIGO-Virgo network may non-negligible eccentricity. We investigate ability restricted 3.5 post-Newtonian order...

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

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

Inspirals of stellar-mass objects into massive black holes will be important sources for the space-based gravitational-wave detector LISA. Modelling these systems requires calculating metric perturbation due to a point particle orbiting Kerr hole. Currently, linear is obtained with reconstruction procedure that puts it in "no-string" radiation gauge which singular on surface surrounding central Calculating dynamical quantities this involves subtle "gauge completion" as well cancellations...

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

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 background metric. This accounts for Aretakis instability (growth transverse derivatives) as a critical phenomenon associated with emergent symmetry. compute exponent each mode, which is equivalent to its decay rate. It follows from arguments that, despite growth derivatives, all generally covariant scalar...

The gravitational self-force has thus far been formulated in background spacetimes for which the metric is a solution to Einstein field equations vacuum. While this formulation sufficient describe motion of small object around black hole, other applications require more general that allows nonvacuum spacetime. We provide foundation such extensions, and carry out concrete two specific cases. In first we consider particle mass $m$ scalar charge $q$ moving spacetime contains field. second...

Motivated by the theoretical possibility of floating orbits and potential to contribute extra constraints on alternative theories, in this paper we derive self-force equation for a small compact object moving an accelerated world line background spacetime which is solution coupled gravitational scalar field equations scalar-tensor theory. In Einstein frame, governing perturbations sourced particle share same form as scalarvac general relativity, with both falling under class hyperbolic...

We develop a formalism to treat higher order (nonlinear) metric perturbations of the Kerr spacetime in Teukolsky framework. first show that solutions linearized Einstein equation with nonvanishing stress tensor can be decomposed into pure gauge part plus zero mode (infinitesimal perturbation mass and spin) arising from certain scalar ("Debye-Hertz") potential, so-called "corrector tensor." The potential is solution spin $-2$ source. This source, as well tetrad components corrector tensor,...

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 hole horizon. The scale-invariance region entails power law time-dependence with three features: (1) decay off horizon is always precisely twice as fast on horizon; (2) special rates $1/t$ $1/\sqrt{v}$ commonly occur; (3) sufficiently high-order transverse derivatives grow (Aretakis instability). results are simply understood terms...

We develop a complete and systematic analytical approach to field perturbations of extremal Kerr spacetime based on the formalism Mano, Suzuki Takasugi (MST) for Teukolsky equation. Analytical expressions radial solutions frequency-domain Green function in terms infinite series special functions are presented. As an application, we compute, first time, leading late-time behavior due branch point at zero frequency scalar, gravitational, electromagnetic off event horizon. also use MST method...

In this paper we investigate the motion of small compact objects in nonvacuum spacetimes using methods from effective field theory curved spacetime. Although a vacuum formulation is sufficient many astrophysical contexts, there are applications such as role self-force enforcing cosmic censorship context overcharging problem, which necessitate an extension into regime. The defining feature problem coupling between gravitational and nongravitational perturbations. for was recently provided...

We study real-time propagation of a massive scalar field on the extremal BTZ black hole spacetime, focusing Aretakis instability event horizon. obtain simple time-domain expression for $\textrm{AdS}_3$ retarded Green function with Dirichlet boundary conditions and construct corresponding using method images. The decays at different rates off horizon, indicating that transverse derivatives grow time horizon (Aretakis instability). solve null geodesic equation in full generality show is...

We consider force-free plasma waves launched by the motion of conducting material through a magnetic field. develop spacetime-covariant formalism for perturbations uniform field and show how transverse fluid acts as source. that fast-mode are sourced compressibility fluid, with incompressible fluids launching pure-Alfv\'en outflow. Remarkably, this outflow can be written down in closed form an arbitrary time-dependent, nonaxisymmetric flow. The instantaneous flow velocity is imprinted on...

We consider weakly non-linear gravitational perturbations of a near-extremal Kerr black hole governed by the second order vacuum Einstein equation. Using GHZ formalism [Green et al., Class. Quant. Grav. 7(7):075001, 2020], these are parameterized Hertz potential. make an ansatz for potential as series zero-damped quasinormal modes with time-dependent amplitudes, and derive dynamical system them. find that our has time-independent solution within near horizon scaling limit. This equilibrium...

We show that the Aretakis instability of compact extremal horizons persists in planar case interest to holography and discuss its connection with emergence "semi-local quantum criticality" field theory dual. In particular, spatially localized power-law decay this critical phase corresponds growth stress-energy on horizon. For near-extremal black holes these phenomena occur transiently over times order inverse temperature. The boundary is characterized by an emergent temporal conformal...