Initial data for rotating cosmologies

Abstract

We revisit the construction of maximal initial data on compact manifolds in vacuum with positive cosmological constant via the conformal method. We discuss, extend and apply recent results of Hebey et al. [19] and Premoselli [31] which yield existence, non-existence, (non-)uniqueness and (linearisation-) stability of solutions of the Lichnerowicz equation, depending on its coefficients. We then focus on so-called $(t,\phi )$-symmetric data as "seed manifolds", and in particular on Bowen-York data on the round hypertorus ${\mathbb{S}}^2\times \mathbb{S}$ (a slice of Nariai) and on Kerr-deSitter. In the former case, we clarify the bifurcation structure of the axially symmetric solutions of the Lichnerowicz equation in terms of the angular momentum as bifurcation parameter, using a combination of analytical and numerical techniques. As to the latter example, we show how dynamical data can be constructed in a natural way via conformal rescalings of Kerr-deSitter data.

22p; corrects typos of version 3, and of published version

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• Overspinning a Kerr black hole: the effect of self-force
• Kerr-de Sitter Universe
• Symmetry and Asymmetry: The Method of Moving Spheres
• A variational analysis of Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds
• The Lichnerowicz equation on compact manifolds with boundary
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Cited by in corpus (3)

• Vacuum initial data on ${\mathbb{S}}^3$ from Killing vectors
• Construction of vacuum initial data by the conformally covariant split system
• Rotating Bowen-York initial data with a positive cosmological constant