Quasinormal modes of a semi-holographic black brane and thermalization

TL;DR

This paper investigates the quasinormal modes and thermalization dynamics of a semi-holographic black brane model, revealing slow thermalization at weak coupling, energy transfer mechanisms, and instabilities related to symmetry breaking and turbulence.

Contribution

It introduces a simplified semi-holographic model with conserved energy, analyzing how mutual coupling affects thermalization, energy transfer, and stability, including the emergence of a Gregory-Laflamme type instability.

Findings

Thermalization can be parametrically slow at weak coupling.

Energy transfer from black brane to perturbative sector is initially dominant.

Existence of a hybrid zero mode that becomes unstable at higher momentum.

Abstract

We study the quasinormal modes and non-linear dynamics of a simplified model of semi-holography, which consistently integrates mutually interacting perturbative and strongly coupled holographic degrees of freedom such that the full system has a total conserved energy. We show that the thermalization of the full system can be parametrically slow when the mutual coupling is weak. For typical homogeneous initial states, we find that initially energy is transferred from the black brane to the perturbative sector, later giving way to complete transfer of energy to the black brane at a slow and constant rate, while the entropy grows monotonically for all time. Larger mutual coupling between the two sectors leads to larger extraction of energy from the black brane by the boundary perturbative system, but also quicker irreversible transfer of energy back to the black brane. The quasinormal modes replicate features of a dissipative system with a softly broken symmetry including the so-called k-gap. Furthermore, when the mutual coupling is below a critical value, there exists a hybrid zero mode with finite momentum which becomes unstable at higher values of momentum, indicating a Gregory-Laflamme type instability. This could imply turbulent equipartitioning of energy between the boundary and the holographic degrees of freedom in the presence of inhomogeneities.