Forces in Kerr spacetimes with a repulsive cosmological constant

TL;DR

This paper introduces and analyzes forces in Kerr spacetimes with a repulsive cosmological constant using optical reference geometry, focusing on properties of forces on test particles in circular orbits.

Contribution

It extends the framework of optical reference geometry to Kerr spacetimes with a cosmological constant, analyzing force behaviors and classifying spacetimes based on force vanishing points.

Findings

Identification of where gravitational and centrifugal forces vanish and change orientation.

Analysis of the non-vanishing Coriolis force for non-zero velocities.

Classification of spacetimes according to the number of circular orbits with force vanishing.

Abstract

Forces defined in the framework of optical reference geometry are introduced in the case of stationary and axially symmetric Kerr black-hole and naked-singularity spacetimes with a repulsive cosmological constant. Properties of the forces acting on test particles moving along circular orbits in the equatorial plane are discussed, whereas it is shown where the gravitational force vanishes and changes its orientation and where the centrifugal force vanishes and changes its orientation independently of the velocity of test particles related to the optical geometry; the Coriolis force does not vanish for the velocity being non-zero. The spacetimes are classified according to the number of circular orbits where the gravitational and centrifugal forces vanish.