### Abstract

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

Article number | 032501 |

Number of pages | 14 |

Journal | Journal of Mathematical Physics |

Volume | 55 |

Issue number | 3 |

Early online date | 10 Mar 2014 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- general relativity
- conformal geometry
- MacDowell-Mansouri gravity

### Cite this

*Journal of Mathematical Physics*,

*55*(3), [032501]. https://doi.org/10.1063/1.4867337

**Conformal holonomy in MacDowell-Mansouri gravity.** / Reid, James A.; Wang, Charles H.-T.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 55, no. 3, 032501. https://doi.org/10.1063/1.4867337

}

TY - JOUR

T1 - Conformal holonomy in MacDowell-Mansouri gravity

AU - Reid, James A.

AU - Wang, Charles H.-T.

PY - 2014

Y1 - 2014

N2 - The MacDowell-Mansouri formulation of general relativity is based on a gauge theory whose gauge algebra depends on the sign of the cosmological constant. In this article, we show that the gauge algebra is uniquely determined by the conformal structure of spacetime itself. Specifically, we show that in vacuum: the spacetime conformal holonomy algebra coincides with the MacDowell-Mansouri gauge algebra for both signs of the cosmological constant, in both Lorentzian and Euclidean metric signatures.

AB - The MacDowell-Mansouri formulation of general relativity is based on a gauge theory whose gauge algebra depends on the sign of the cosmological constant. In this article, we show that the gauge algebra is uniquely determined by the conformal structure of spacetime itself. Specifically, we show that in vacuum: the spacetime conformal holonomy algebra coincides with the MacDowell-Mansouri gauge algebra for both signs of the cosmological constant, in both Lorentzian and Euclidean metric signatures.

KW - general relativity

KW - conformal geometry

KW - MacDowell-Mansouri gravity

U2 - 10.1063/1.4867337

DO - 10.1063/1.4867337

M3 - Article

VL - 55

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 3

M1 - 032501

ER -