https://doi.org/10.1140/epjc/s10052-022-10550-3
Regular Article - Theoretical Physics
Dualized gravity beyond linear approximation
1
Canadian Quantum Research Center (CQRC), 204-3002, 32 Ave, V1T 2L7, Vernon, BC, Canada
2
School of Physics, Damghan University, P.O. Box 3671641167, Damghan, Iran
3
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, OX2 6GG, Oxford, UK
4
Irving K. Barber School of Arts and Sciences, University of British Columbia-Okanagan, V1V 1V7, Kelowna, BC, Canada
5
Department of Physics and Astronomy, University of Lethbridge, T1K 3M4, Lethbridge, AB, Canada
Received:
17
November
2021
Accepted:
25
June
2022
Published online:
27
August
2022
We will construct a loop space formalism for general relativity, and construct the Polyakov variables as connections for such a loop space. We will use these Polyakov variables to construct a dual theory of gravity beyond linear approximation. It will be demonstrated that this loop space duality reduces to the Hodge duality for linearized gravity. Furthermore, a loop space curvature will be constructed from this Polyakov variable. It will be shown that this loop space curvature vanishes in the absence of topological defects, and so it can be used to investigate gravitational monopoles. We will also construct the suitable monopole charge for such gravitational monopoles.
© The Author(s) 2022
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