Approaching a dynamical extreme black hole horizon

TL;DR

This paper provides an explicit description of the late-time near-horizon behavior of dynamical extreme Reissner-Nordstrom black holes, revealing the persistence of Aretakis instability and the boundary conditions leading to different RN states.

Contribution

It introduces a novel explicit solution framework using JT gravity for the non-linear near-horizon dynamics of DERN black holes with specific boundary conditions.

Findings

Scalar field exhibits Aretakis instability at late times.

Solutions are singularity-free and show outgoing scalar flux.

Boundary conditions place solutions on the threshold between different RN states.

Abstract

We give an explicit closed form description of the late-time near-horizon approach to dynamical extreme Reissner-Nordstrom (DERN) black holes. These are spherically symmetric dynamical solutions of Einstein-Maxwell theory coupled to a neutral scalar that feature: (i) a spacetime metric which tends to that of a static extreme Reissner-Nordstrom (RN), and (ii) a scalar field which exhibits the linear Aretakis instability ad infinitum in the non-linear theory. We employ the two-dimensional Jackiw-Teitelboim (JT) gravity to solve explicitly for the non-linear s-wave dynamics of the four-dimensional theory near an ${\rm AdS}_2\times {\rm S}^2$ throat. For a teleologically defined black hole horizon, we impose boundary conditions on JT's dilaton field (which encodes the gravitational dynamics) and the scalar matter as follows: (i) the JT dilaton decays at late times on the ${\rm AdS}_2$ boundary to a value that corresponds to a static extreme RN in the exterior, and (ii) the scalar obeys boundary conditions characteristic of linear Aretakis behavior on ${\rm AdS}_2$. We ensure our DERN solutions are singularity-free and we note that our approach to DERN is accompanied by a final burst of outgoing scalar matter flux leaking out of the ${\rm AdS}_2$ throat. The boundary conditions we impose on the JT dilaton place its late-time boundary profile on the threshold of black hole formation with sub-extreme and super-extreme RN on either side of our DERNs.