On the existence of smooth Cauchy steep time functions

2016/01/22 by E. Minguzzi, E Minguzzi
Mathematics · Physics and Astronomy · #Cauchy distribution #Cosmology and Gravitation Theories #Differentiable function #Geometric Analysis and Curvature Flows #Initial value problem #Minkowski space #Noncommutative and Quantum Gravity Theories #Order (exchange) #Simple (philosophy) #Space time #Spacetime #gr-qc #math-ph #math.MP

paper · pdf · doi:10.1088/0264-9381/33/11/115001

published as Classical and Quantum Gravity 33 (2016) 115001 · Latex2e, 4 pages

arxiv created 2016/01/22 · openalex publication_date 2016/04/27 · arxiv updated 2016/04/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

A simple proof (based on results in Chruściel et al 2015 Ann. Henri Poincaré arXiv:1301.2909) is given that every globally hyperbolic spacetime admits a smooth Cauchy steep time function. This result is useful in order to show that globally hyperbolic spacetimes can be isometrically embedded in Minkowski spacetimes and that they split as a product. The proof is based on a recent result on the differentiability of Geroch's volume functions.

Citations

• On differentiability of volume time functions
• Domain of Dependence
• The Large Scale Structure of Space-Time
• On smooth Cauchy hypersurfaces and Geroch's splitting theorem