### Abstract

Original language | English |
---|---|

Article number | 022502 |

Number of pages | 13 |

Journal | Journal of Mathematical Physics |

Volume | 49 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 |

### Fingerprint

### Keywords

- Particle-theory and field-theory models of the early Universe
- Spacetime topology
- causal structure
- spinor structure
- Geometry
- differential geometry
- topology

### Cite this

*Journal of Mathematical Physics*,

*49*(2), [022502]. https://doi.org/10.1063/1.2837431

**The Principle of Equivalence and Cosmological Metrics.** / Hall, Graham Stanley; Lonie, D. P.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 49, no. 2, 022502. https://doi.org/10.1063/1.2837431

}

TY - JOUR

T1 - The Principle of Equivalence and Cosmological Metrics

AU - Hall, Graham Stanley

AU - Lonie, D. P.

PY - 2008

Y1 - 2008

N2 - This paper is concerned with the extent to which the geodesics of space-time (that is, the experimental consequences of the principle of equivalence) determine the metric in general relativity theory and, in particular, in Friedmann-Robertson-Walker-Lemaitre (FRWL) space-times. Thus it discusses projective structure in these space-times. The approach will be from a geometrical point of view and it is shown that if two space-time metrics share the same (unparametrized) geodesics and one is a (generic) FRWL metric then so is the other and that each is a member of a well defined family of projectively related (FRWL) metrics. Similar techniques are then applied to study the existence and properties of symmetries of the Weyl projective tensor and projective symmetries in FRWL space-times.

AB - This paper is concerned with the extent to which the geodesics of space-time (that is, the experimental consequences of the principle of equivalence) determine the metric in general relativity theory and, in particular, in Friedmann-Robertson-Walker-Lemaitre (FRWL) space-times. Thus it discusses projective structure in these space-times. The approach will be from a geometrical point of view and it is shown that if two space-time metrics share the same (unparametrized) geodesics and one is a (generic) FRWL metric then so is the other and that each is a member of a well defined family of projectively related (FRWL) metrics. Similar techniques are then applied to study the existence and properties of symmetries of the Weyl projective tensor and projective symmetries in FRWL space-times.

KW - Particle-theory and field-theory models of the early Universe

KW - Spacetime topology

KW - causal structure

KW - spinor structure

KW - Geometry

KW - differential geometry

KW - topology

U2 - 10.1063/1.2837431

DO - 10.1063/1.2837431

M3 - Article

VL - 49

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 2

M1 - 022502

ER -