Horizon instability of extremal Reissner-Nordström black holes to charged perturbations

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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.

Section: Aretakis Instability From Symmetrymentioning

confidence: 99%

“…In defining holographic propagators by limits involving multiplication by x h , we have assumed boundary conditions such that the field goes as x −h at large x in boundary-adapted coordinates and gauge. The scaling self-similarity (14) of the bulk-boundary propagator means that…”

Section: E Scaling Dimensionmentioning

confidence: 99%

Scaling and universality in extremal black hole perturbations

Gralla

Zimmerman

2018

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“…The original result (1.1) held only for initial data that was non-zero on the event horizon, but it soon became clear that the instability persists for data supported arbitrarily far away [8][9][10], although sometimes with different rates [11]. The result was also extended to near-extremal black holes, where the growth occurs transiently (for a time of order the inverse temperature) near the horizon [8,[12][13][14]. Although the precise power laws differ from example to example, this typical behavior of successive derivatives growing one power of v faster has now been seen in a wide variety of perturbation problems involving (near-)extremal black holes, and is known as the Aretakis instability.…”

Section: Introductionmentioning

confidence: 99%

Semi-local quantum criticality and the instability of extremal planar horizons

Gralla

Ravishankar

Zimmerman

2018

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We show that the Aretakis instability of compact extremal horizons persists in the planar case of interest to holography and discuss its connection with the emergence of "semi-local quantum criticality" in the field theory dual. In particular, the spatially localized power-law decay of this critical phase corresponds to spatially localized power-law growth of stress-energy on the horizon. For near-extremal black holes these phenomena occur transiently over times of order the inverse temperature. The boundary critical phase is characterized by an emergent temporal conformal symmetry, and the bulk instability seems to be essential to preserving the symmetry in the presence of interactions. We work primarily in the solvable example of charged scalar perturbations of fivedimensional (near-)extremal planar Reissner-Nordström anti-de Sitter spacetime and argue that the conclusions hold more generally. a

“…The aim of this paper is to study the late time behavior of such black holes analytically using the weakly broken conformal symmetry of their near-horizon region. In particular, gravitational backreaction is accounted for within the Jackiw-Teitelboim model for near-horizon, near-extremal dynamics coupled to bulk matter.types of perturbation fields [14], [15], [16], [17], and in particular in [18] it was shown that a massless scalar displays Aretakis behavior on any extreme BH background. The picture arising from these studies is that the Aretakis behavior is a general feature of extremal BHs, in the following sense: the k-th transverse-to-the-horizon derivative of the perturbation, at late times on the horizon, behaves (no worse than 1 )where ∆ − is a negative k-independent, fixed non-universal constant.…”

mentioning

confidence: 99%

“…types of perturbation fields [14], [15], [16], [17], and in particular in [18] it was shown that a massless scalar displays Aretakis behavior on any extreme BH background. The picture arising from these studies is that the Aretakis behavior is a general feature of extremal BHs, in the following sense: the k-th transverse-to-the-horizon derivative of the perturbation, at late times on the horizon, behaves (no worse than 1 )…”

mentioning

confidence: 99%

Near-extremal black holes at late times, backreacted

Hadar

2019

Black holes display universal behavior near extremality. One such feature is the late-time blowup of derivatives of linearized perturbations across the horizon. For generic initial data, this instability is regulated by backreaction, and the final state is a near-extremal black hole. The aim of this paper is to study the late time behavior of such black holes analytically using the weakly broken conformal symmetry of their near-horizon region. In particular, gravitational backreaction is accounted for within the Jackiw-Teitelboim model for near-horizon, near-extremal dynamics coupled to bulk matter.types of perturbation fields [14], [15], [16], [17], and in particular in [18] it was shown that a massless scalar displays Aretakis behavior on any extreme BH background. The picture arising from these studies is that the Aretakis behavior is a general feature of extremal BHs, in the following sense: the k-th transverse-to-the-horizon derivative of the perturbation, at late times on the horizon, behaves (no worse than 1 )where ∆ − is a negative k-independent, fixed non-universal constant. 2 A convenient way to repackage (1.2) (assuming an expansion in the radial coordinate) is to use the following ansatz for the field (assume a scalar field for simplicity):where F (z) is an arbitrary function which is smooth at z = 0. It is important to note that this type of behavior is consistent with the results of [20], which showed that for generic initial data in extremal RN the decay and blowup rates (1.2) are saturated (again, modulo the skip phenomenon described in footnote 1). Following [21] (see also [3]), plugging (1.3) into the 1+1 dimensional wave equation for each mode and considering the near-horizon, late-time limit reduces it to an ordinary differential equation for F (z), which yields a universal behavior for the field at late times near the horizon. For example, for the spherically symmetric mode (∆ − = −1) of the above discussed neutral massless scalar around extreme RN: 3, (1.4) at late times, where H 0 is interpreted as the ℓ = 0 Aretakis constant.Since the Aretakis analysis concerns linearized perturbations and involves blowup, one must ask whether and how gravitational backreaction becomes important. This was addressed in [22] numerically for spherically symmetric perturbations of a massless, neutral scalar field. The conclusions were that the instability persists under backreaction, and that for generic initial data, the BH approaches a new, non-extremal solution at late times, and this allows perturbations to exponentially decay at times of the order of the inverse temperature. This