Asymptotic Analysis and Stability of Scalar Fields in the Conformally Compactified Kerr Spacetime

Abstract

This work presents a study of the asymptotic behavior of scalar fields in the conformally compactified Kerr spacetime. We derive the leading-order and higher-order terms in the asymptotic expansion of the scalar field near null infinity and analyze the regularity and decay properties of these terms. The stability of the Kerr black hole under scalar field perturbations is examined using energy estimates and Weyl tensor analysis. We find that the scalar field exhibits well-behaved decay properties, ensuring the regularity of the field at null infinity. This analysis is supported by recent developments in the study of scalar field perturbations in Kerr spacetimes