#pastime

Acoustic Metric in Relativistic Spherical Accretion The acoustic metric is an effective tensor structure derived from linearised relativistic hydrodynamics, governing the propagation of small-amplitude sound perturbations on a stationary background flow in Schwarzschild spacetime. It defines an emergent geometry in which acoustic modes follow null geodesics, enabling analysis of wave scattering, energy flux conservation, and spatial stability without direct reference to the full fluid equations.