Scalar Resonances in Axially Symmetric Spacetimes

TL;DR

This paper investigates scalar wave resonances in axially symmetric spacetimes, proving the absence of non-axial modes in certain geometries and identifying unstable solutions with closed timelike curves, extending understanding of wave behavior in these backgrounds.

Contribution

It demonstrates the non-existence of non-axial resonant modes in specific axially symmetric spacetimes and finds unstable solutions related to closed timelike curves, advancing the analysis of wave stability.

Findings

Non-axial resonant modes do not exist in studied spacetimes.

Unstable solutions are found in Lanczos dust cylinder and BTZ regions.

Results relate to and extend previous Kerr spacetime studies.

Abstract

We study properties of resonant solutions to the scalar wave equation in several axially symmetric spacetimes. We prove that non-axial resonant modes do not exist neither in the Lanczos dust cylinder, the $(2+1)$ extreme BTZ spacetime nor in a class of simple rotating wormhole solutions. Moreover, we find unstable solutions to the wave equation in the Lanczos dust cylinder and in the $r^2 <0$ region of the extreme $(2+1)$ BTZ spacetime, two solutions that possess closed timelike curves. Similarities with previous results obtained for the Kerr spacetime are explored.