Black hole elasticity and gapped transverse phonons in holography

TL;DR

This paper demonstrates that certain holographic black hole models exhibit solid-like properties, including transverse phonons with a mass gap, linking black hole elasticity to condensed matter phenomena via holography.

Contribution

It identifies transverse phonons as pseudo Goldstone bosons in holographic models with broken translational symmetry, extending effective solid theory to quantum-critical systems.

Findings

Transverse phonons are identified as pseudo Goldstone bosons.

The lowest mode speed relates to the black hole rigidity modulus.

Modes exhibit a mass gap controlled by explicit symmetry breaking.

Abstract

We study the elastic response of planar black hole (BH) solutions in a simple class of holographic models with broken translational invariance. We compute the transverse quasi-normal mode spectrum and the propagation speed of the lowest energy mode. We find that the speed of the lowest mode relates to the BH rigidity modulus as dictated by elasticity theory. This allows to identify these modes as transverse phonons---the pseudo Goldstone bosons of spontaneously broken translational invariance. In addition, we show that these modes have a mass gap controlled by an explicit source of the translational symmetry breaking. These results provide a new confirmation that the BHs in these models do exhibit solid properties that become more manifest at low temperatures. Also, by the AdS/CFT correspondence, this allows to extend the standard results from the effective field theory for solids to quantum-critical materials.