Defining perturbations on submanifolds

Details Defining perturbations on submanifolds Defining perturbations on submanifolds

2003-05-09

arxiv.org/abs/gr-qc/0305036v1

Phys.Rev. D68 (2003) 123517

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, 2 figures, Revtex4

Scientific paper

10.1103/PhysRevD.68.123517

We study the definition of perturbations in the presence of a submanifold, like e.g. a brane. In the standard theory of cosmological perturbations, one compares quantities at the same coordinate points in the non-perturbed and the perturbed manifolds, identified via a (non-unique) 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.

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