We are concerned with the existence of smooth time functions on connected time-oriented Lorentzian manifolds. The problem is tackled in a more general abstract setting, namely in a manifold M where is just defined a field of tangent convex cones (C-x)(x is an element of M) enjoying mild continuity properties. Under some conditions on its integral curves, we will construct a time function. Our approach is based on the definition of an intrinsic length for curves indicating how a curve is far from being an integral trajectory of C-x. We find connections with topics pertaining to Hamilton-Jacobi equations, and make use of tools and results issued from weak KAM theory.
On smooth time functions / Albert, Fathi; Siconolfi, Antonio. - In: MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY. - ISSN 0305-0041. - STAMPA. - 152:2(2012), pp. 303-339. [10.1017/s0305004111000661]
On smooth time functions
SICONOLFI, Antonio
2012
Abstract
We are concerned with the existence of smooth time functions on connected time-oriented Lorentzian manifolds. The problem is tackled in a more general abstract setting, namely in a manifold M where is just defined a field of tangent convex cones (C-x)(x is an element of M) enjoying mild continuity properties. Under some conditions on its integral curves, we will construct a time function. Our approach is based on the definition of an intrinsic length for curves indicating how a curve is far from being an integral trajectory of C-x. We find connections with topics pertaining to Hamilton-Jacobi equations, and make use of tools and results issued from weak KAM theory.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.