Large Deformations of Relativistic Membranes: A Generalization of the Raychaudhuri Equations

Details Large Deformations of Relativistic Membranes: A Generalization of the Raychaudhuri Equations Large Deformations of Relativistic Membranes: A Generalization of the Raychaudhuri Equations

1994-11-23

arxiv.org/abs/gr-qc/9411061v2

Phys.Rev. D52 (1995) 1072-1081

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, Plain Tex, sign errors corrected, new references added. To appear in Physical Review D

Scientific paper

10.1103/PhysRevD.52.1072

A coupled system of non-linear partial differential equations is presented which describes non-perturbatively the evolution of deformations of a relativistic membrane of arbitrary dimension, $D$, in an arbitrary background spacetime. These equations can be considered from a formal point of view as higher dimensional analogs of the Raychaudhuri equations for point particles to which they are shown to reduce when $D=1$. For $D=1$ or $D=2$ (a string), there are no constraints on the initial data. If $D>2$, however, there will be constraints with a corresponding complication of the evolution problem. The consistent evolution of the constraints is guaranteed by an integrability condition which is satisfied when the equations of motion are satisfied. Explicit calculations are performed for membranes described by the Nambu action.

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