2009/12/10 by Marc Henneaux, Axel Kleinschmidt, Gustavo Lucena Gómez · 151 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Class (philosophy) #Classical mechanics #Cosmology and Gravitation Theories #Diffeomorphism #Epistemology #Gauge theory #Gravitation #Hamiltonian (control theory) #Hamiltonian constraint #Loop quantum gravity #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Philosophy #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Theoretical physics #hep-th
paper · pdf · doi:10.1103/physrevd.81.064002
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 81(6) (American Physical Society) · 28 pages, 2 references added
arxiv created 2009/12/10 · openalex publication_date 2010/03/03 · arxiv updated 2010/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The dynamical consistency of the nonprojectable version of Ho\ifmmode \checkr\else \vr\fiava gravity is investigated by focusing on the asymptotically flat case. It is argued that for generic solutions of the constraint equations the lapse must vanish asymptotically. We then consider particular values of the coupling constants for which the equations are tractable and in that case we prove that the lapse must vanish everywhere---and not only at infinity. Put differently, the Hamiltonian constraints are generically all second-class. We then argue that the same feature holds for generic values of the couplings, thus revealing a physical inconsistency of the theory. In order to cure this pathology, one might want to introduce further constraints but the resulting theory would then lose much of the appeal of the original proposal by Ho\ifmmode \checkr\else \vr\fiava. We also show that there is no contradiction with the time-reparametrization invariance of the action, as this invariance is shown to be a so-called ``trivial gauge symmetry'' in Ho\ifmmode \checkr\else \vr\fiava gravity, hence with no associated first-class constraints.