Hamiltonian formulation of general relativity in the teleparallel geometry

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.

22 pages, Latex file, no figures. The title has been changed. The complete constraint algebra is presented. The derivation of the vector constraint from the Hamiltonian constraint is presented with further details. Version to appear in the PRD

References in corpus (3)

• Gravitational Lorentz Force and the Description of the Gravitational Interaction
• Hamiltonian structure of the teleparallel formulation of GR
• General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry

Cited by in corpus (73)

• The teleparallel equivalent of general relativity
• Teleparallel Gravity: From Theory to Cosmology
• Non trivial frames for f(T) theories of gravity and beyond
• Spherically symmetric static spacetimes in vacuum f(T) gravity
• Energy and angular momentum of the gravitational field in the teleparallel geometry
• Problems with Propagation and Time Evolution in f(T) Gravity
• Hamiltonian formalism for f(T) gravity
• On reference frames in spacetime and gravitational energy in freely falling frames
• Primordial Fluctuations within Teleparallelism
• Kerr-Newman Solution and Energy in Teleparallel Equivalent of Einstein Theory
• The gravitational energy-momentum tensor and the gravitational pressure
• Hamiltonian and primary constraints of new general relativity
• Regularized expression for the gravitational energy-momentum in teleparallel gravity and the principle of equivalence
• Quest for the extra degree of freedom in f(T) gravity
• Charged Dilaton, Energy, Momentum and Angular-Momentum in Teleparallel Theory Equivalent to General Relativity
• Stationary Axisymmetric Solutions and their Energy Contents in Teleparallel Equivalent of Einstein Theory
• Review of the Hamiltonian analysis in teleparallel gravity
• Charged Axially Symmetric Solution and Energy in Teleparallel Theory Equivalent to General Relativity
• Brane World black holes in Teleparallel Theory Equivalent to General Relativity and their Killing vectors, Energy, Momentum and Angular-Momentum
• Hamiltonian formulation of teleparallel gravity
• The angular momentum of the gravitational field and the Poincare group
• Charged Axially Symmetric Solution, Energy and Angular Momentum in Tetrad Theory of Gravitation
• Cosmological frames for theories with absolute parallelism
• ADM formulation and Hamiltonian analysis of $f(Q)$ gravity
• Remnant Symmetry, Propagation and Evolution in f(T) Gravity
• Dirac spinor fields in the teleparallel gravity: comment on "Metric-affine approach to teleparallel gravity"
• The gravitational energy-momentum flux
• Dirac-Bergmann analysis and Degrees of Freedom of Coincident $f(Q)$-gravity
• Hamiltonian formulation of unimodular gravity in the teleparallel geometry
• Pseudoinvariance and the extra degree of freedom in f(T) gravity
• Modelling the Accelerating Universe with $f(Q)$ Gravity: Observational Consistency
• Counting Components in the Lagrange Multiplier Formulation of Teleparallel Theories
• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry
• The energy-momentum of plane-fronted gravitational waves in the teleparallel equivalent of GR
• Kinematic quantum states for the Teleparallel Equivalent of General Relativity
• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry: derivation of constraint algebra
• Energy and Angular Momentum Densities in a Godel-Type Universe in the Teleparallel Geometry
• Energy Contents of Some Well-Known Solutions in Teleparallel Gravity
• Weak field reduction in teleparallel coframe gravity. Vacuum case
• On the gravitational angular momentum of rotating sources
• Hamiltonian formulation of a simple theory of the teleparallel geometry
• Gravitational Energy of Kerr and Kerr Anti-de Sitter Space-times in the Teleparallel Geometry
• The Teleparallel Equivalent of General Relativity and the Gravitational Centre of Mass
• Classification of primary constraints for new general relativity in the premetric approach
• Energy Contents of Gravitational Waves in Teleparallel Gravity
• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• Variables suitable for constructing quantum states for the Teleparallel Equivalent of General Relativity II
• Energy of general 4-dimensional stationary axisymmetric spacetime in the teleparallel geometry
• Neutron Stars in Teleparallel Gravity
• Variables suitable for constructing quantum states for the Teleparallel Equivalent of General Relativity I
• Gravitomagnetic effect and spin-torsion coupling
• The angular momentum of plane-fronted gravitational waves in the teleparallel equivalent of general relativity
• Gravitational energy, gravitational pressure, and the thermodynamics of a charged black hole in teleparallel gravity
• The generalization of the ADM gravitational energy-momentum
• Hamiltonian Analysis In New General Relativity
• On the gravitational energy problem and the energy of photons
• Energy Contents of a Class of Regular Black Hole Solutions in Teleparallel Gravity
• Reconstructing modified and alternative theories of gravity
• Dark matter effects in modified teleparallel gravity
• The Hamiltonian constraint in the symmetric teleparallel equivalent of general relativity
• First-order hyperbolic formulation of the pure tetrad teleparallel gravity theory
• Gravitational energy of a magnetized Schwarzschild black hole - a teleparallel approach
• Gravitational Pressure, apparent horizon and thermodynamics of FLRW universe in the teleparallel gravity
• Degrees of Freedom of New General Relativity I: Type 2, Type 3, Type 5, and Type 8
• On Special Re-quantization of a Black Hole
• On Non-commutative Corrections of Gravitational Energy in Teleparallel Gravity
• Constraints of the Teleparallel Equivalent of General Relativity in a gauge
• Gravitational radiation of accelerated sources
• Generators of Local Lorentz Transformation in ADM-Vielbein Formalism of Gravitational Relativity
• Degrees of freedom of a quadratic scalar-nonmetricity theory
• Gravitational radiation fields in teleparallel equivalent of general relativity and their energies
• Flat spin connections in the Teleparallel equivalent of General Relativity
• Gravitational energy in pp-wave spacetimes