On the area of the symmetry orbits of cosmological spacetimes with toroidal or hyperbolic symmetry

Smulevici, Jacques

doi:10.2140/apde.2011.4.191

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1948-206X (online)

ISSN 2157-5045 (print)

Author index

To appear

Other MSP journals

On the area of the symmetry orbits of cosmological spacetimes with toroidal or hyperbolic symmetry

Jacques Smulevici

Vol. 4 (2011), No. 2, 191–245

DOI: 10.2140/apde.2011.4.191

Abstract

We prove several global existence theorems for spacetimes with toroidal or hyperbolic symmetry with respect to a geometrically defined time. More specifically, we prove that generically, the maximal Cauchy development of $T^{2}$ -symmetric initial data with positive cosmological constant $Λ > 0$ , in the vacuum or with Vlasov matter, may be covered by a global areal foliation with the area of the symmetry orbits tending to zero in the contracting direction. We then prove the same result for surface symmetric spacetimes in the hyperbolic case with Vlasov matter and $Λ \geq 0$ . In all cases, there is no restriction on the size of initial data.

Keywords

Einstein equations, singularities, hyperbolic partial differential equations

Mathematical Subject Classification 2000

Primary: 83C05

Milestones

Received: 1 September 2009

Revised: 24 December 2009

Accepted: 31 July 2010

Published: 18 November 2011

Authors

Jacques Smulevici
Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Mühlenberg 1 D-14476 Potsdam-Golm Germany	Laboratoire de Mathématiques Université Paris-Sud 11, bât. 425 91405 Orsay France

Vol. 4, No. 2, 2011