Geodesics for particles with negative energy in Kerr's metric

TL;DR

This paper investigates the behavior of particles with negative energy in Kerr black holes, showing the absence of circular orbits and identifying geodesics that start and end at the singularity.

Contribution

It provides a detailed analysis of negative energy particle geodesics in Kerr spacetime, highlighting the non-existence of certain orbits and conditions for geodesics connecting to the singularity.

Findings

No circular or elliptic orbits for negative energy particles in the ergosphere.

Existence of geodesics starting and ending at the singularity.

Conditions under which geodesics do not connect to the singularity.

Abstract

According to Penrose effect, particles with negative energy can exist in the ergospheres of rotating black holes. We analyze geodesics for such particles and show that there are no circular and elliptic orbits in the ergosphere of a rotating black hole. We also show that there are geodesics which begin and terminate at the singularity and present the conditions under which such geodesics do not begin and terminate at the singularity.