Stable cosmological Kaluza-Klein Spacetimes

Abstract

We consider the Einstein flow on a product manifold with one factor being a compact quotient of 3-dimensional hyperbolic space without boundary and the other factor being a flat torus of fixed arbitrary dimension. We consider initial data symmetric with respect to the toroidal directions. We obtain effective Einsteinian field equations coupled to a wave map type and a Maxwell type equation by the Kaluza-Klein reduction. The Milne universe solves those field equations when the additional parts arising from the toroidal dimensions are chosen constant. We prove future stability of the Milne universe within this class of spacetimes, which establishes stability of a large class of cosmological Kaluza-Klein vacua. A crucial part of the proof is the implementation of a new gauge for Maxwell-type equations in the cosmological context, which we refer to as slice-adapted gauge.

References in corpus (7)

• Kaluza-Klein Gravity
• Future Global in time einsteinian spacetimes with U(1) isometry group
• A regime of linear stability for the Einstein-scalar field system with applications to nonlinear Big Bang formation
• The Global Stability of the Minkowski Spacetime Solution to the Einstein-Nonlinear Electromagnetic System in Wave Coordinates
• On the stability of Einstein manifolds
• The Weak Null Condition and Kaluza-Klein Spacetimes
• Global existence of Dirac-wave maps with curvature term on expanding spacetimes

Cited by in corpus (11)

• Probing Massive Scalar Fields from a Pulsar in a Stellar Triple System
• Attractors of the Einstein-Klein Gordon system
• Future stability of the $1+3$ Milne model for Einstein-Klein-Gordon system
• The Stability of Relativistic Fluids in Linearly Expanding Cosmologies
• Stable cosmologies with collisionless charged matter
• Future attractors of Bianchi types II and V cosmologies with massless Vlasov matter
• Global stability of spacetimes with supersymmetric compactifications
• Singularity theorems for warped products and the stability of spatial extra dimensions
• Global well-posedness for a system of quasilinear wave equations on a product space
• On the Global Well-Posedness of the Einstein-Yang-Mills System
• Cosmic Censorship near FLRW spacetimes with negative spatial curvature