The Strauss conjecture on Kerr black hole backgrounds

TL;DR

This paper proves an analog of the Strauss conjecture for semilinear wave equations on Kerr black hole backgrounds, utilizing weighted Strichartz and localized energy estimates to handle the complex geometry.

Contribution

It extends the Strauss conjecture to Kerr black holes with small angular momentum, introducing new estimates for wave behavior in curved spacetime.

Findings

Weighted Strichartz estimates near infinity

Localized energy estimates on black hole backgrounds

Proof of Strauss conjecture analog in Kerr spacetime

Abstract

We examine solutions to semilinear wave equations on black hole backgrounds and give a proof of an analog of the Strauss conjecture on the Schwarzschild and Kerr, with small angular momentum, black hole backgrounds. The key estimates are a class of weighted Strichartz estimates, which are used near infinity where the metrics can be viewed as small perturbations of the Minkowski metric, and a localized energy estimate on the black hole background, which handles the behavior in the remaining compact set.