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Pure Lorentz spin connection theories and uniqueness of general relativity

Krasnov, Kirill; Mitsou, Ermis

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Professor of Mathematical Sciences

Ermis Mitsou


General relativity (GR) can be reformulated as a diffeomorphism invariant gauge theory of the Lorentz group, with Lagrangian of the type f(F ? F), where F is the curvature two-form of the spin connection. A theory from this class with a generic f is known to propagate eight degrees of freedom: a massless graviton, a massive graviton and a scalar. GR in this formalism avoids extra degrees of freedom because the function f is special and leads to the appearance of six extra primary constraints on the phase space variables. Our main new result is that there are other theories of the type f(F ? F) that lead to six extra primary constraints. However, only in the case of GR the dynamics is such that these six primary constraints get supplemented by six secondary constraints, which gives the end result of two propagating degrees of freedom. This is how uniqueness of GR manifests itself in this 'pure spin connection' formalism. The other theories we discover are shown to give examples of irregular dynamical systems. At the linear level around (anti-)de Sitter space they have two degrees of freedom, as GR, with the extra ones manifesting themselves only non-linearly.


Krasnov, K., & Mitsou, E. (2021). Pure Lorentz spin connection theories and uniqueness of general relativity. Classical and Quantum Gravity, 38(20), Article 205009.

Journal Article Type Article
Acceptance Date Sep 10, 2021
Online Publication Date Sep 29, 2021
Publication Date Oct 21, 2021
Deposit Date Oct 4, 2021
Publicly Available Date Sep 30, 2022
Journal Classical and Quantum Gravity
Print ISSN 0264-9381
Electronic ISSN 1361-6382
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 38
Issue 20
Article Number 205009
Keywords Physics and Astronomy (miscellaneous)
Public URL
Publisher URL
Additional Information This is the Accepted Manuscript version of an article accepted for publication in Classical and Quantum Gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at


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