Riemannian geometry of gravity waves turbulent black hole analogs

TL;DR

This paper explores the Riemannian geometry of turbulent black hole analogs created by water waves, revealing how curvature acts as a diverging lens and relating curvature to Newtonian gravity in the ergoregion.

Contribution

It extends the gravity water wave black hole analog to turbulent shear flows and computes the Riemannian geometry, providing new insights into curvature effects in such analogs.

Findings

Riemann curvature is constant in turbulent shear flow

Curvature acts as a diverging lens affecting stream lines

Curvature quantities relate to Newtonian gravity in the ergoregion

Abstract

The gravity water wave black (GWBH) hole analog discovered by Schutzhold and Unruh (SU) is extended to allow for the presence of turbulent shear flow. The Riemannian geometry of turbulent black holes (BH) analogs in water waves is computed in the case of laminar tirbulent shear flow. The Riemann curvature is constant and the geodesic deviation equation shows that the curvature acts locally as a diverging lens and the stream lines on opposite sides of the analog black hole flow apart from each other. In this case it is shown that the curvature quantities can be expressed in terms of the Newtonian gravitational constant in the ergoregion. The dispersion relation is obtained for the case of constant flow injection.