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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| Published in | Classical and quantum gravity Vol. 30; no. 17; pp. 175018 - 14 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
IOP Publishing
07.09.2013
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| Subjects | |
| Online Access | Get full text |
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| Abstract | 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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| AbstractList | 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. |
| Author | Olum, Ken D Kontou, Eleni-Alexandra |
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| Cites_doi | 10.7208/chicago/9780226870373.001.0001 10.1088/0264-9381/16/2/011 10.1103/PhysRevD.71.063506 10.1103/PhysRevD.87.064009 10.1063/1.1724316 10.1017/CBO9780511524646 10.1098/rspa.1971.0085 10.1103/PhysRevD.74.064019 10.1007/s00023-011-0080-9 |
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| References | 1 Misner C W (2) 1973 3 4 6 7 8 9 Nesterov A I (5) 1999; 16 10 |
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| SubjectTerms | coordinates Fermi Inflation Joints Mathematical analysis Mathematical models Quantum gravity Subspaces Tangents Tensors |
| Title | Multi-step Fermi normal coordinates |
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