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

M Mars1, C Peón-Nieto1,2

  • 1Universidad de Salamanca, Salamanca, Spain.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|January 14, 2024
PubMed
Summary

Researchers characterized higher-dimensional Kerr-de Sitter metrics by analyzing their behavior at future null infinity. This approach defines a larger Kerr-de Sitter-like class with specific asymptotic properties.

Keywords:
Fefferman-GrahamKerr-de Sitterasymptotic initial value problemconformal Killing vectorsgeometric characterization

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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.