Zermelo Wind: a geometrization of the frame dragging effect

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.