### Abstract

This paper considers four-dimensional manifolds upon which there is a Lorentz metric It and a symmetric connection Gamma which are originally assumed unrelated. It then derives sufficient conditions on h and Gamma (expressed through the curvature tensor of Gamma) for Gamma to be the Levi-Civita connection of some (local) Lorentz metric g and calculates the relationship between g and h. Some examples are provided which help to assess the strength of the sufficient conditions derived.

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

Pages (from-to) | 2995-3010 |

Number of pages | 15 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 39 |

DOIs | |

Publication status | Published - 2006 |

### Keywords

- GENERAL-RELATIVITY
- CURVATURE COLLINEATIONS
- EINSTEIN SPACES
- HOLONOMY GROUPS
- TERMS
- GIJ

### Cite this

*Journal of Physics A: Mathematical and General*,

*39*, 2995-3010. https://doi.org/10.1088/0305-4470/39/12/009

**On the Compatibility of Lorentz Metrics with Linear Connections on 4-dimensional Manifolds.** / Hall, Graham Stanley; Lonie, D. P.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 39, pp. 2995-3010. https://doi.org/10.1088/0305-4470/39/12/009

}

TY - JOUR

T1 - On the Compatibility of Lorentz Metrics with Linear Connections on 4-dimensional Manifolds

AU - Hall, Graham Stanley

AU - Lonie, D. P.

PY - 2006

Y1 - 2006

N2 - This paper considers four-dimensional manifolds upon which there is a Lorentz metric It and a symmetric connection Gamma which are originally assumed unrelated. It then derives sufficient conditions on h and Gamma (expressed through the curvature tensor of Gamma) for Gamma to be the Levi-Civita connection of some (local) Lorentz metric g and calculates the relationship between g and h. Some examples are provided which help to assess the strength of the sufficient conditions derived.

AB - This paper considers four-dimensional manifolds upon which there is a Lorentz metric It and a symmetric connection Gamma which are originally assumed unrelated. It then derives sufficient conditions on h and Gamma (expressed through the curvature tensor of Gamma) for Gamma to be the Levi-Civita connection of some (local) Lorentz metric g and calculates the relationship between g and h. Some examples are provided which help to assess the strength of the sufficient conditions derived.

KW - GENERAL-RELATIVITY

KW - CURVATURE COLLINEATIONS

KW - EINSTEIN SPACES

KW - HOLONOMY GROUPS

KW - TERMS

KW - GIJ

U2 - 10.1088/0305-4470/39/12/009

DO - 10.1088/0305-4470/39/12/009

M3 - Article

VL - 39

SP - 2995

EP - 3010

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

ER -