The timbre of Hawking gravitons: an effective description of energy transport from holography

TL;DR

This paper develops an effective field theory for the long-lived phonon mode in holographic black hole models, capturing energy transport and sound attenuation in relativistic fluids via a scalar field with non-trivial spatial momentum dependence.

Contribution

It introduces a novel effective field theory description of the holographic phonon mode, extending the dispersion relation to quartic order and classifying gravitational modes by Markovianity index.

Findings

Reproduces the holographic sound mode dispersion relation to quartic order.

Constructs an effective field theory for attenuated sound dynamics and fluctuations.

Identifies additional zero modes disconnected from the phonon Goldstone mode.

Abstract

Planar black holes in AdS, which are holographically dual to compressible relativistic fluids, have a long-lived phonon mode that captures the physics of attenuated sound propagation and transports energy in the plasma. We describe the open effective field theory of this fluctuating phonon degree of freedom. The dynamics of the phonon is encoded in a single scalar field whose gravitational coupling has non-trivial spatial momentum dependence. This description fits neatly into the paradigm of classifying gravitational modes by their Markovianity index, depending on whether they are long-lived. The sound scalar is a non-Markovian field with index (3-d) for a d-dimensional fluid. We reproduce (and extend) the dispersion relation of the holographic sound mode to quartic order in derivatives, constructing in the process the effective field theory governing its attenuated dynamics and associated stochastic fluctuations. We also remark on the presence of additional spatially homogeneous zero modes in the gravitational problem, which remain disconnected from the phonon Goldstone mode.