Recollapsing spacetimes with Λ < 0

Author(s)

David Fajman, Maximilian Kraft

Abstract

We show that any homogeneous initial data set with Λ < 0 on a product three-manifold of orthogonal form ( S 1 × F , a 0 2 d z 2 + b 0 2 σ 2 , c 0 d z 2 + d 0 σ ) , where ( F , σ ) is a closed two-surface of constant curvature and a 0 , … , d 0 are suitable constants, recollapses under the Einstein-flow with a negative cosmological constant and forms crushing singularities at the big bang and the big crunch, respectively. Towards certain singularities among those the Kretschmann scalar remains bounded. We then show that the presence of a massless scalar field causes the Kretschmann scalar to blow-up towards both ends of spacetime for all solutions in the corresponding class. By standard arguments this recollapsing behaviour extends to an open neighbourhood in the set of initial data sets and is in this sense generic close to the homogeneous regime.

Organisation(s)

Gravitational Physics

Journal

Classical and Quantum Gravity

Volume

40

No. of pages

34

ISSN

0264-9381

DOI

https://doi.org/10.48550/arXiv.2211.04059

Publication date

07-2023

Peer reviewed

Yes

Austrian Fields of Science 2012

103028 Theory of relativity

Keywords

ASJC Scopus subject areas

Physics and Astronomy (miscellaneous)

Portal url

https://ucrisportal.univie.ac.at/en/publications/recollapsing-spacetimes-with---0(0455b30a-1477-43dd-96f3-b1bb21760e7c).html