Defining perturbations on submanifolds

Karim A. Malik, María Rodríguez-Martínez, and David Langlois
Phys. Rev. D 68, 123517 – Published 17 December 2003
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Abstract

We study the definition of perturbations in the presence of a submanifold, such as, e.g., a brane. In the standard theory of cosmological perturbations, one compares quantities at the same coordinate points in the nonperturbed and the perturbed manifolds, identified via a (nonunique) mapping between the two manifolds. In the presence of a physical submanifold one needs to modify this definition in order to evaluate perturbations of quantities at the submanifold location. As an application, we compute the perturbed metric and the extrinsic curvature tensors at the brane position in a general gauge.

  • Received 12 May 2003

DOI:https://doi.org/10.1103/PhysRevD.68.123517

©2003 American Physical Society

Authors & Affiliations

Karim A. Malik, María Rodríguez-Martínez, and David Langlois

  • GRECO, Institut d’Astrophysique de Paris, CNRS, 98bis Boulevard Arago, 75014 Paris, France

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Issue

Vol. 68, Iss. 12 — 15 December 2003

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