Dynamics of a self gravitating light-like matter shell: a gauge-invariant Lagrangian and Hamiltonian description

Abstract

A complete Lagrangian and Hamiltonian description of the theory of self-gravitating light-like matter shells is given in terms of gauge-independent geometric quantities. For this purpose the notion of an extrinsic curvature for a null-like hypersurface is discussed and the corresponding Gauss-Codazzi equations are proved. These equations imply Bianchi identities for spacetimes with null-like, singular curvature. Energy-momentum tensor-density of a light-like matter shell is unambiguously defined in terms of an invariant matter Lagrangian density. Noether identity and Belinfante-Rosenfeld theorem for such a tensor-density are proved. Finally, the Hamiltonian dynamics of the interacting system: ``gravity + matter'' is derived from the total Lagrangian, the latter being an invariant scalar density.

20 pages, RevTeX4, no figures

References in corpus (6)

• Isolated Horizons: Hamiltonian Evolution and the First Law
• Generic Isolated Horizons and their Applications
• Geometry of General Hypersurfaces in Spacetime: Junction Conditions
• Embedding variables in the canonical theory of gravitating shells
• Unitary dynamics of spherical null gravitating shells
• Intrinsic Geometry of a Null Hypersurface

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