Small Amplitude Forced Fluid Dynamics from Gravity at T = 0

TL;DR

This paper investigates the fluid-gravity duality at zero temperature for a charged fluid under small, low-frequency external forces, by constructing regular gravity dual solutions with a time-dependent boundary dilaton.

Contribution

It develops a modified low frequency expansion to construct regular gravity dual solutions at zero temperature, extending the understanding of fluid-gravity duality in this limit.

Findings

Constructed regular bulk solutions with a time-dependent boundary dilaton.

Established fluid-gravity duality at zero temperature to leading order.

Extended the low frequency expansion method for zero temperature cases.

Abstract

The usual derivative expansion of gravity duals of charged fluid dynamics is known to break down in the zero temperature limit. In this case, the fluid-gravity duality is not understood precisely. We explore this problem for a zero temperature charged fluid driven by a low frequency, small amplitude and spatially homogeneous external force. In the gravity dual, this corresponds to time dependent boundary value of the dilaton. We calculate the bulk solution for the dilaton and the leading backreaction to the metric and the gauge fields using the modified low frequency expansion of [11]. The resulting solutions are regular everywhere, establishing fluid-gravity duality to this order.