Rigidly rotating ZAMO surfaces in the Kerr spacetime

TL;DR

This paper investigates the properties of rigidly rotating ZAMO surfaces in Kerr spacetime, including inside the black hole, and explores their relevance to physical problems involving stationary observers with zero angular momentum.

Contribution

It introduces the concept of rigidly rotating ZAMO surfaces and analyzes their properties both outside and inside the Kerr black hole.

Findings

ZAMO surfaces are tangent to Killing vectors with constant coefficients.

Properties of ZAMO surfaces are characterized inside and outside the black hole.

Potential applications of ZAMO surfaces to physical problems are discussed.

Abstract

A stationary observer in the Kerr spacetime has zero angular momentum if his/her angular velocity $\omega$ has a particular value, which depends on the position of the observer. Worldlines of such zero angular momentum observers (ZAMOs) with the same value of the angular velocity $\omega$ form a three dimensional surface, which has the property that the Killing vectors generating time translation and rotation are tangent to it. We call such a surface a rigidly rotating ZAMO surface. This definition allows a natural generalization to the surfaces inside the black hole, where ZAMO's trajectories formally become spacelike. A general property of such a surface is that there exist linear combinations of the Killing vectors with constant coefficients which make them orthogonal on it. In this paper we discuss properties of the rigidly rotating ZAMO surfaces both outside and inside the black hole and relevance of these objects to a couple of interesting physical problems.