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Hamiltonian formulation of general relativity in the teleparallel geometry

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J. W. Maluf, J. F. da Rocha-Neto

General Relativity and Quantum Cosmology · Submitted 16 Feb 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We establish the Hamiltonian formulation of the teleparallel equivalent of general relativity, without fixing the time gauge condition, by rigorously performing the Legendre transform.

how it is stated · asserted 1.00 read the record →

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arXiv IDgr-qc/0002059 (version 2)
Pith IDZG72SD26, Pith's permanent record of this paper and its review
CitationJ. F. da Rocha-Neto, J. W. Maluf. "Hamiltonian formulation of general relativity in the teleparallel geometry." arXiv:gr-qc/0002059 (2000). https://pith.science/paper/ZG72SD26
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,864 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We establish the Hamiltonian formulation of the teleparallel equivalent of general relativity, without fixing the time gauge condition, by rigorously performing the Legendre transform. The time gauge condition, previously considered, restricts the teleparallel geometry to the three-dimensional spacelike hypersurface. Geometrically, the teleparallel geometry is now extended to the four-dimensional space-time. The resulting Hamiltonian formulation is different from the standard ADM formulation in many aspects, the main one being that the dynamics is now governed by the Hamiltonian constraint H_0 and a set of primary constraints. The vector constraint H_i is derived from the Hamiltonian constraint. The vanishing of the latter implies the vanishing of the vector constraint.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We establish the Hamiltonian formulation of the teleparallel equivalent of general relativity, without fixing the time gauge condition, by rigorously performing the Legendre transform. contribution 0.99 0.96 0.69 asserted 1.00
s1 The time gauge condition, previously considered, restricts the teleparallel geometry to the three-dimensional spacelike hypersurface. background 0.98 0.08 0.06 asserted 1.00
s2 Geometrically, the teleparallel geometry is now extended to the four-dimensional space-time. interpretation 0.60 0.65 0.14 asserted 1.00
s3 The resulting Hamiltonian formulation is different from the standard ADM formulation in many aspects, the main one being that the dynamics is now governed by the Hamiltonian constraint H_0 and a set of primary constraints. result 0.98 0.90 0.59 asserted 1.00
s4 The vector constraint H_i is derived from the Hamiltonian constraint. result 0.98 0.88 0.10 asserted 1.00
s5 The vanishing of the latter implies the vanishing of the vector constraint. result 0.78 0.78 0.10 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • references and citing sentences
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  • T body sentences
  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We establish the Hamiltonian formulation of the teleparallel equivalent of general relativity, without fixing the time gauge condition, by rigorously performing the Legendre transform. The time gauge condition, previously considered, restricts the teleparallel geometry to the three-dimensional spacelike hypersurface. Geometrically, the teleparallel geometry is now extended to the four-dimensional space-time. The resulting Hamiltonian formulation is different from the standard ADM formulation in many aspects, the main one being that the dynamics is now governed by the Hamiltonian constraint H_0 and a set of primary constraints. The vector constraint H_i is derived from the Hamiltonian constraint. The vanishing of the latter implies the vanishing of the vector constraint.

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References
How the literature uses it

18 arXiv papers cite this in 24 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 17 sentences without a confident label

Uses its method or tool 1 paper
Cites it as support 1 paper
  • The possibility (iii) corresponds to TEGR, while (i) is the generic case for $f(T)$ gravity, as confirmed by the detailed work of Miao Li et al. [ref] , which was based on the Hamiltonian analysis of [ref] .

    Remnant Symmetry, Propagation and Evolution in f(T) Gravity · Comments on Propagation and Evolution in $f(T)$ Gravity · 0.96

Cites it as background 5 papers

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