Review of the Hamiltonian analysis in teleparallel gravity

TL;DR

This paper reviews and compares various Hamiltonian analysis approaches in teleparallel gravity theories, clarifying differences and unifying understanding of primary constraints in $f( ext{T})$ models.

Contribution

It provides a comprehensive comparison of Hamiltonian analyses in teleparallel gravity, introducing primary constraints for $f( ext{T}_{ ext{NGR}})$ theories for the first time.

Findings

Clarified relations between different Hamiltonian approaches

Presented primary constraints for $f( ext{T}_{ ext{NGR}})$ theories

Unified analysis of $f( ext{T})$ and new general relativity

Abstract

We review different approaches to the Hamiltonian analysis of teleparallel theories of gravity. In particular the Hamiltonian analysis for $f(\mathbb{T})$ theories led to disputed results in the literature. The aim of this review is to relate the different notations and assumptions in the different approaches in a comprehensive way, so that they can be compared more easily. To do this we present the primary constraints of the $f({\mathbb{T}_{\textrm{NGR}}})$ gravity class of theories for the first time. The particular cases studied in the literature, $f(\mathbb{T})$ gravity and new general relativity, are contained in this parent theory. We compare their Hamiltonian analyses done by different authors in the literature among each other by relating them to our analysis of $f({\mathbb{T}_{\textrm{NGR}}})$ in detail.