Trajectories connecting two submanifolds on a non-complete Lorentzian manifold
Date
2004-01-14
Authors
Bartolo, Rossella
Germinario, Anna
Sanchez, Miguel
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
This article presents existence and multiplicity results for orthogonal trajectories joining two submanifolds Σ1 and Σ2 of a static space-time manifold M under the action of gravitational and electromagnetic vector potential. The main technical difficulties are because M may not be complete and Σ1, Σ2 may not be compact. Hence, a suitable convexity assumption and hypotheses at infinity are needed. These assumptions are widely discussed in terms of the electric and magnetic vector fields naturally associated. Then, these vector fields become relevant from both their physical interpretation and the mathematical gauge invariance of the equation of the trajectories.
Description
Keywords
Lorentzian manifolds, Gravitational and electromagnetic fields, Convex boundary, Critical point theory
Citation
Bartolo, R., Germinario, A., & Sanchez, M. (2004). Trajectories connecting two submanifolds on a non-complete Lorentzian manifold. <i>Electronic Journal of Differential Equations, 2004</i>(10), pp. 1-20.
Rights
Attribution 4.0 International