CMC foliations of open spacetimes asymptotic to open Robertson-Walker spacetimes

• Verfasst von: Gerhardt, Claus [VerfasserIn]
• Titel: CMC foliations of open spacetimes asymptotic to open Robertson-Walker spacetimes
• Verf.angabe: Claus Gerhardt
• E-Jahr: 2021
• Jahr: 11 April 2021
• Umfang: 79 S.
• Fussnoten: Gesehen am 04.03.2022
• Titel Quelle: Enthalten in: Pure and applied mathematics quarterly
• Ort Quelle: Henan : University, 2005
• Jahr Quelle: 2021
• Band/Heft Quelle: 17(2021), 1, Seite 269-347
• ISSN Quelle: 1558-8602
• DOI: doi:10.4310/PAMQ.2021.v17.n1.a8
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: ARW spacetimes
• Sach-SW: cosmological spacetime
• Sach-SW: general relativity
• Sach-SW: inverse mean curvature flow
• Sach-SW: Lorentzian manifold
• Sach-SW: mass
• Sach-SW: surfaces
• K10plus-PPN: 1794698019

Abstract

We consider open globally hyperbolic spacetimes N of dimension n + 1, n >= 3, which are spatially asymptotic to a Robertson-Walker spacetime or an open Friedmann universe with spatial curvature (k) over tilde = 0,-1 and prove, under reasonable assumptions, that there exists a unique foliation by spacelike hypersurfaces of constant mean curvature and that the mean curvature function tau is a smooth time function if N is smooth. Moreover, among the Friedmann universes which satisfy the necessary conditions are those that reflect the present assumptions of the development of the universe.