Conformal holonomy in MacDowell-Mansouri gravity

Journal Article · Sat Mar 15 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4867337· OSTI ID:22251117

Reid, James A., E-mail: [e-mail] ^[1]; Wang, Charles H.-T., E-mail: [e-mail] ^[1]; STFC Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX ^[2]

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1. SUPA Department of Physics, University of Aberdeen, Aberdeen, AB24 3UE (United Kingdom)
2. (United Kingdom)

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.

• OSTI ID: 22251117
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
COSMOLOGICAL CONSTANT
EUCLIDEAN SPACE
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
GRAVITATION
SPACE-TIME