Characterizations of Kerr-de Sitter in arbitrary dimension from null infinity

Area of Science:

• * General Relativity
• * Mathematical Physics

Background:

• * Kerr and Kerr-de Sitter metrics possess unique local geometric properties in four dimensions.
• * Generalizations to higher dimensions lack this local characterization, necessitating alternative analysis methods.
• * Understanding behavior at future null infinity offers a viable approach for characterizing these higher-dimensional metrics.

Purpose of the Study:

• * To generalize the characterization of Kerr-de Sitter metrics to higher dimensions.
• * To explore the asymptotic properties of higher-dimensional spacetimes using established formalisms.
• * To define and characterize the broader Kerr-de Sitter-like class of metrics.

Main Methods:

• * Review of Friedrich's and Fefferman-Graham formalisms for asymptotic initial value problems.
• * Analysis of (anti-)de Sitter-vacuum spacetimes in arbitrary dimensions.
• * Study of geometric identification, conformal equivalence of data, and Killing initial data.
• * Investigation of conformal equivalence of boundary conformal Killing vectors (CKV).

Main Results:

• * Characterization of Kerr-de Sitter metrics via conformal flatness and a canonical TT tensor constructed from CKV at null infinity.
• * Definition of the Kerr-de Sitter-like class, encompassing metrics with arbitrary CKV.
• * Explicit construction of these metrics as limits or analytic extensions of Kerr-de Sitter.
• * Identification of Kerr-Schild property and specific falloff conditions for this class.
• * In five dimensions, correspondence to algebraically special metrics with non-degenerate optical matrices.

Conclusions:

• * The asymptotic data at future null infinity provides a robust method for characterizing higher-dimensional Kerr-de Sitter-like spacetimes.
• * The defined Kerr-de Sitter-like class offers a comprehensive framework for studying these complex metrics.
• * These findings contribute to understanding the interplay of asymptotics, conformal methods, and analysis in general relativity.