Stationarity and Fredholm Theory in Subextremal Kerr-de Sitter Spacetimes

TL;DR

This paper extends the analysis of wave equations in Kerr-de Sitter spacetimes by demonstrating the flexibility in choosing stationary Killing vectors, which simplifies the ergoregion structure and broadens the applicability of Fredholm theory.

Contribution

It shows multiple valid stationary Killing vector fields can be used in the analysis, including horizon Killing vectors, reducing ergoregions and enhancing the Fredholm framework.

Findings

Multiple stationary Killing vectors are compatible with the analysis.

Using horizon Killing vectors removes ergoregions.

The Fredholm theory applies under these new vector field choices.

Abstract

In a recent paper, we proved that solutions to linear wave equations in a subextremal Kerr-de Sitter spacetime have asymptotic expansions in quasinormal modes up to a decay order given by the normally hyperbolic trapping, extending the results of Vasy (2013). One central ingredient in the argument was a new definition of quasinormal modes, where a non-standard choice of stationary Killing vector field had to be used in order for the Fredholm theory to be applicable. In this paper, we show that there is in fact a variety of allowed choices of stationary Killing vector fields. In particular, the horizon Killing vector fields work for the analysis, in which case one of the corresponding ergoregions is completely removed.