Classification of primary constraints for new general relativity in the premetric approach

Abstract

We introduce a novel procedure for studying the Hamiltonian formalism of new general relativity (NGR) based on the mathematical properties encoded in the constitutive tensor defined by the premetric approach. We derive the canonical momenta conjugate to the tetrad field and study the eigenvalues of the Hessian tensor, which is mapped to a Hessian matrix with the help of indexation formulas. The properties of the Hessian matrix heavily rely on the possible values of the free coefficients $c_i,i=1,2,3$ appearing in the NGR Lagrangian. We find four null eigenvalues associated with trivial primary constraints in the temporal part of the momenta. The remaining eigenvalues are grouped in four sets, which have multiplicity 3, 1, 5 and 3, and can be set to zero depending on different choices of the coefficients $c_i$. There are nine possible different cases when one, two, or three sets of eigenvalues are imposed to vanish simultaneously. All cases lead to a different number of primary constraints, which are consistent with previous work on the Hamiltonian analysis of NGR by Blixt et al. (2018).

13 pages, 2 tables, no figures, comments welcome; title changed, discussion added

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Cited by in corpus (10)

• Spherically symmetric vacuum solutions in 1-Parameter New General Relativity and their phenomenology
• Lorentz symmetries and primary constraints in covariant teleparallel gravity
• Geometry and covariance of symmetric teleparallel theories of gravity
• Revisiting Stability in New General Relativity
• Static spherically symmetric solutions in New General Relativity
• Gravitational Waves in New General Relativity
• Conformal Transformations and Cosmological Perturbations in New General Relativity
• Noether's second theorem in teleparallel gravity
• The Hamiltonian constraint in the symmetric teleparallel equivalent of general relativity
• Weak Gravity Limit in Newer General Relativity