Semi-local Quantum Criticality and the Instability of Extremal Planar Horizons

TL;DR

This paper explores the persistence of the Aretakis instability in planar extremal horizons, linking it to semi-local quantum criticality in the dual field theory, with implications for holography and black hole physics.

Contribution

It demonstrates that the Aretakis instability persists in planar extremal horizons and connects this to semi-local quantum criticality, highlighting the role of bulk instability in symmetry preservation.

Findings

Aretakis instability persists in planar extremal horizons.

Spatially localized power-law decay and growth are linked.

Instability is crucial for maintaining emergent conformal symmetry.

Abstract

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 five-dimensional (near-)extremal planar Reissner-Nordstr\"om anti-de Sitter spacetime and argue that the conclusions hold more generally.