Zermelo Wind: a geometrization of the frame dragging effect

TL;DR

This paper explores Zermelo's navigation problem in spacetime as a way to geometrize the frame dragging effect, connecting it with various physical phenomena like universe expansion and black hole environments.

Contribution

It introduces a novel geometric framework linking Zermelo's navigation problem to frame dragging, providing new insights into gravitational effects in spacetime.

Findings

Zermelo wind corresponds to frame dragging velocity.

Recasting spacetime problems into Zermelo form offers new perspectives.

Application to black hole environments illustrates anti-dragging effects.

Abstract

In this article I discuss Zermelo's navigation problem in spacetime as a geometrization of the frame dragging effect, and recast various examples involving the latter into Zermelo form. I start by describing a stationary spacetime in Zermelo's form and show that the Zermelo wind is the drift velocity under frame dragging effect. Then we discuss various problems in this context, such as Hubble expansion of the universe and accelerated frames in special relativity. Another example I will discuss is the self-gravitating disk around a black hole in post-Newtonian (PN1) approximation to describe the anti-dragging effect in terms of a Zermelo wind.