Asymptotia of Kerr-de Sitter Black Holes

TL;DR

This paper investigates the asymptotic behavior of black hole spacetimes, identifying conditions under which they approach Kerr--de Sitter geometry, and constrains the geometric data at infinity using conformal geometry and symmetry considerations.

Contribution

It introduces necessary conditions for solutions to asymptotically resemble Kerr--de Sitter black holes using conformal geometry and symmetry analysis.

Findings

Derived conditions for asymptotic approach to Kerr--de Sitter spacetime.

Constrained geometric free data at conformal infinity.

Linked geometric data constraints to stress-energy tensor.

Abstract

Exterior geometries of physical black holes are believed to asymptotically approach the Kerr--de Sitter spacetime at late times. A characteristic feature of that vacuum Einstein solution is the presence of a hidden symmetry generated by a closed conformal Killing--Yano tensor. Using this symmetry and modern conformal geometry technology, we find necessary conditions for generic solutions to asymptotically approach the Kerr--de Sitter metric. Further, we constrain the admissible form of the geometric free data on the conformal infinity giving rise to this family of spacetimes and constrain it in terms of the stress-energy tensor.