Uniqueness of the extremal Schwarzschild de Sitter spacetime

Author:

David Katona, James Lucietti

Keyword:

General Relativity and Quantum Cosmology, General Relativity and Quantum Cosmology (gr-qc), High Energy Physics - Theory (hep-th), Differential Geometry (math.DG)

journal:

date:

2023-09-07 16:00:00

Abstract

We prove that any analytic vacuum spacetime with a positive cosmological constant in four and higher dimensions, that contains a static extremal Killing horizon with a maximally symmetric compact cross-section, must be locally isometric to either the extremal Schwarzschild de Sitter solution or its near-horizon geometry (the Nariai solution). In four-dimensions, this implies these solutions are the only analytic vacuum spacetimes that contain a static extremal horizon with compact cross-sections (up to identifications). We also consider the analogous uniqueness problem for the four-dimensional extremal hyperbolic Schwarzschild anti-de Sitter solution and show that it reduces to an open problem for the spectrum of the laplacian on compact hyperbolic surfaces.

PDF: Uniqueness of the extremal Schwarzschild de Sitter spacetime.pdf