Centrifugal force in Kerr geometry

TL;DR

This paper derives the correct expression for centrifugal force in Kerr spacetime and applies it to determine the equilibrium shape and maximum ellipticity of a slowly rotating spheroid.

Contribution

It provides a corrected formula for centrifugal force in Kerr geometry and applies it to analyze the equilibrium shape of rotating bodies in this spacetime.

Findings

Derived the correct centrifugal force expression in Kerr geometry.

Determined the ellipticity and maximum radius for a slowly rotating spheroid.

Applied the formula to analyze equilibrium configurations in Kerr spacetime.

Abstract

We have obtained the correct expression for the centrifugal force acting on a particle at the equatorial circumference of a rotating body in the locally non-rotating frame of the Kerr geometry. Using this expression for the equilibrium of an element on the surface of a slowly rotating Maclaurin spheroid, we obtain the expression for the ellipticity (as discussed earlier by Abramowicz and Miller) and determine the radius at which the ellipticity is maximum.