Hamiltonian formulation of unimodular gravity in the teleparallel geometry

Abstract

In the context of the teleparallel equivalent of general relativity we establish the Hamiltonian formulation of the unimodular theory of gravity. Here we do not carry out the usual $3+1$ decomposition of the field quantities in terms of the lapse and shift functions, as in the ADM formalism. The corresponding Lagrange multiplier is the timelike component of the tetrad field. The dynamics is determined by the Hamiltonian constraint ${\mathcal{H}}_0^{\prime }$ and a set of primary constraints. The constraints are first class and satisfy an algebra that is similar to the algebra of the Poincaré group.

21 pages, no figures

References in corpus (2)

• Unimodular cosmology and the weight of energy
• The angular momentum of the gravitational field and the Poincare group

Cited by in corpus (1)

• Degrees of freedom of $f(T)$ gravity