Multi-step Fermi normal coordinates

We generalize the concept of Fermi normal coordinates adapted to a geodesic to the case where the tangent space to the manifold at the base point is decomposed into a direct product of an arbitrary number of subspaces, so that we follow several geodesics in turn to find the point with given coordina...

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Bibliographic Details
Published inClassical and quantum gravity Vol. 30; no. 17; pp. 175018 - 14
Main Authors Kontou, Eleni-Alexandra, Olum, Ken D
Format Journal Article
LanguageEnglish
Published IOP Publishing 07.09.2013
Subjects
coordinates
Fermi
Inflation
Joints
Mathematical analysis
Mathematical models
Quantum gravity
Subspaces
Tangents
Tensors
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Summary:We generalize the concept of Fermi normal coordinates adapted to a geodesic to the case where the tangent space to the manifold at the base point is decomposed into a direct product of an arbitrary number of subspaces, so that we follow several geodesics in turn to find the point with given coordinates. We compute the connection and the metric as integrals of the Riemann tensor. We calculate explicitly an example of a five-dimensional brane inflation spacetime. In the case of one subspace (Riemann normal coordinates) or two subspaces, we recover some results previously found by Nesterov, using somewhat different techniques.
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ISSN:0264-9381
1361-6382
DOI:10.1088/0264-9381/30/17/175018