Synchronous Lagrangian variational principles in General Relativity

Lagrangian Formulation of General Relativity

Variational principles for Lagrangian-averaged fluid dynamics

Abstract The Lagrangian average (LA) of the ideal fluid equations preserves their fundamental transport structure. This transport structure is responsible for the Kelvin circulation theorem of the LA flow and, hence, for its potential vorticity convection and helicity conservation. We show that Lagrangian averaging also preserves the Euler–Poincaré variational framework that implies the exact i...

Canonical Lagrangian Dynamics and General Relativity

Building towards a more covariant approach to canonical classical and quantum gravity we outline an approach to constrained dynamics that de-emphasizes the role of the Hamiltonian phase space and highlights the role of the Lagrangian phase space. We identify a “Lagrangian one-form” to replace the standard symplectic one-form, which we use to construct the canonical constraints and an associated...

Metric-Aft'me Variational Principles in General Relativity II. Relaxation of the Riemannian Constraint

We continue our investigation of a variational principle for general relativity in which the metric tensor and the (asymmetric) linear connection are varied independently. As in Part I, the matter Lagrangian is minimally coupled to the connection and the gravitational Lagrangian is taken to be the curvature scalar, but we now relax the Riemannian constraint as far as possible-that is, as far as...

A Variational Approach to Homogeneous Scalar Fields in General Relativity

A result of existence of homogeneous scalar field solutions between prescribed configurations is given, using a modified version [8] of Euler–Maupertuis least action variational principle. Solutions are obtained as limit of approximating variational problems, solved using techniques introduced by Rabinowitz in [20].