Slow Sound in a duct, effective transonic flows and analogue black holes

TL;DR

The paper introduces a novel duct system with compliant walls to simulate analogue gravity effects, demonstrating transonic flows, a Hamiltonian formulation, and a Planckian spectrum emission from sonic horizons.

Contribution

It presents a new experimental setup for studying analogue gravity using compliant-walled ducts and derives the associated Hamiltonian and metric formulations.

Findings

Effective transonic flows achieved at low Mach numbers.

The linear perturbation equation can be expressed in Hamiltonian form.

The emitted spectrum from the sonic horizon is Planckian with a temperature related to surface gravity.

Abstract

We propose a new system suitable for studying analogue gravity effects, consisting of a gas flowing in a duct with a compliant wall. Effective transonic flows are obtained from uniform, low Mach number flows through the reduction of the one-dimensional speed of sound induced by the wall compliance. We show that the modified equation for linear perturbations can be written in a Hamiltonian form. We perform a one-dimensional reduction consistent with the canonical formulation, and deduce the analogue metric along with the first dispersive term. In a weak dispersive regime, the spectrum emitted from a sonic horizon is numerically shown to be Planckian, and with a temperature fixed by the analogue surface gravity.