Review of the Hamiltonian analysis in teleparallel gravity

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 $f({\mathbb{T}}_{\text{NGR}})$ 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 $f({\mathbb{T}}_{\text{NGR}})$ in detail.

arXiv comment36 pages, 2 tables, 1 figure; matches the published version

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Cited by in corpus (14)

• Teleparallel Gravity: From Theory to Cosmology
• Perturbations in Non-Flat Cosmology for $f(T)$ gravity
• Static spherically symmetric black holes in weak f(T)-gravity
• Issues of Lorentz-invariance in f(T) gravity and calculations for spherically symmetric solutions
• The $3+1$ Formalism in the Geometric Trinity of Gravity
• Lorentz symmetries and primary constraints in covariant teleparallel gravity
• Scale-invariant cosmology in de Sitter gauge theory
• Hamilton's equations in the covariant teleparallel equivalent of general relativity
• The issue of Branched Hamiltonian in F(T) Teleparallel Gravity
• The generalization of the ADM gravitational energy-momentum
• Noether's second theorem in teleparallel gravity
• Conservation laws in gauge gravity theory
• Global portraits of nonminimal teleparallel inflation
• Hamiltonian surface charges in General Parallel Relativity