Completeness of first and second order ODE flows and of Euler–Lagrange equations

Minguzzi, E.

doi:10.1016/j.geomphys.2015.06.010

Cited by 2 publications

(2 citation statements)

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“…These models are also interesting from a purely mathematical point of view, since they are examples of geometries of low regularity, which has attracted growing attention recently, see e.g. [CG12, KSSV15,Min15,Säm16,Sbi15]. Our main result here is that all impulsive geometries in the full class of pp-waves are geodesically complete irrespective of the spatial asymptotics of the profile function.…”

Section: Introductionmentioning

confidence: 91%

“…More substantial results on non-autonomous NPWs have been given in [CRS12] based on recent results on the completeness of trajectories of equations like (25) and (27) in [CRS13] (for more general and somewhat sharper results see [Min15]). Since we will also use these statements in our discussion of the general case (1) we recall in the following the key notions and theorems.…”

Section: Geodesic Completenessmentioning

confidence: 99%

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Completeness of general pp -wave spacetimes and their impulsive limit

Sämann¹,

Steinbauer²,

Švarc³

2016

Class. Quantum Grav.

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We investigate geodesic completeness in the full family of pp-wave or Brinkmann spacetimes in their extended as well as in their impulsive form. This class of geometries contains the recently studied gyratonic pp-waves, modelling the exterior field of a spinning beam of null particles, as well as NPWs, which generalise classical pp-waves by allowing for a general wave surface. The problem of geodesic completeness reduces to the question of completeness of trajectories on a Riemannian manifold under an external force field. Building upon respective recent results we derive completeness criteria in terms of the spatial asymptotics of the profile function in the extended case. In the impulsive case we use a fixed point argument to show that irrespective of the behaviour of the profile function all geometries in the class are complete.

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Section: Introductionmentioning

confidence: 91%