Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes

被引：210
|
作者：
Bernal, AN [1 ]
Sánchez, M [1 ]
机构：
[1] Univ Granada, Fac Ciencias, Dpto Geometria & Topol, E-18071 Granada, Spain
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2005年 / 257卷 / 01期
关键词：
Neural Network; Statistical Physic; Complex System; Nonlinear Dynamics; Quantum Computing;
D O I：
10.1007/s00220-005-1346-1
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
The folk questions in Lorentzian Geometry which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: ( a) any globally hyperbolic spacetime ( M, g) admits a smooth time function T whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting M = R x S, g = - beta( T, x) dT(2) + (g) over bar T, ( b) if a spacetime M admits a ( continuous) time function t then it admits a smooth ( time) function T with timelike gradient del T on all M.
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页码：43 / 50
页数：8
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