Rayleigh and Solberg criteria reversal near black holes: the optical geometry explanation

TL;DR

This paper explains how the Rayleigh and Solberg stability criteria reverse near black holes due to extreme spacetime warping, altering the usual angular momentum distribution requirements for stability.

Contribution

It provides a geometric explanation for the reversal of classical stability criteria near black holes, linking spacetime curvature to fluid stability conditions.

Findings

Rayleigh criterion reverses near black holes

Strong spacetime warping causes inside-out geometry

Stability conditions depend on spacetime curvature

Abstract

The familiar Newtonian version of the Rayleigh criterion demands that for dynamical stability the specific angular momentum should increase with the increasing circumferential radius of circular trajectories of matter. However, sufficiently close to a black hole the Rayleigh criterion reverses: in stable fluids, the angular momentum must decrease with the increasing circumferential radius. The geometrical reason for this reversal is that the space is so very strongly warped that it turns inside-out.