Hamiltonian formulation of unimodular gravity in the teleparallel geometry

TL;DR

This paper develops a Hamiltonian formulation of unimodular gravity within teleparallel geometry, avoiding the traditional 3+1 decomposition and revealing a Poincaré-like algebra of constraints.

Contribution

It introduces a novel Hamiltonian approach to unimodular gravity in teleparallel geometry without using the ADM 3+1 split.

Findings

Constraints are first class and form a Poincaré-like algebra.

The Hamiltonian is determined by a single constraint ${\ m\cal H}_0'$.

The formulation provides a new perspective on the dynamics of unimodular gravity.

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 ${\cal H}'_0$ and a set of primary constraints. The constraints are first class and satisfy an algebra that is similar to the algebra of the Poincar\'e group.