Hamiltonian and primary constraints of new general relativity

Abstract

We derive the kinematic Hamiltonian for the so-called "new general relativity" class of teleparallel gravity theories, which is the most general class of theories whose Lagrangian is quadratic in the torsion tensor and does not contain parity violating terms. Our approach makes use of an explicit expression for the flat, in general, nonvanishing spin connection, which avoids the use of Lagrange multipliers, while keeping the theory invariant under local Lorentz transformations. We clarify the relation between the dynamics of the spin connection degrees of freedom and the tetrads. The terms constituting the Hamiltonian of the theory can be decomposed into irreducible parts under the rotation group. Using this, we demonstrate that there are nine different classes of theories, which are distinguished by the occurrence or non-occurrence of certain primary constraints. We visualize these different classes and show that the decomposition into irreducible parts allows us to write the Hamiltonian in a common form for all nine classes, which reproduces the specific Hamiltonians of more restricted classes in which particular primary constraints appear.

arXiv comment13 pages, 1 figure, journal version

References in corpus (21)

• f(T) teleparallel gravity and cosmology
• Coincident General Relativity
• The covariant formulation of f(T) gravity
• Degrees of freedom of $f(T)$ gravity
• On the covariance of teleparallel gravity theories
• New classes of modified teleparallel gravity models
• Hamiltonian formulation of general relativity in the teleparallel geometry
• Propagation of gravitational waves in symmetric teleparallel gravity theories
• Hamiltonian formalism for f(T) gravity
• Hamiltonian structure of the teleparallel formulation of GR
• Teleparallel theories of gravity as analogue of non-linear electrodynamics
• Propagation of gravitational waves in teleparallel gravity theories
• Hamiltonian formulation of teleparallel gravity
• Ghost and tachyon free Poincaré gauge theories: a systematic approach
• Remnant Symmetry, Propagation and Evolution in f(T) Gravity
• Premetric equivalent of general relativity: Teleparallelism
• Counting Components in the Lagrange Multiplier Formulation of Teleparallel Theories
• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry
• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry: derivation of constraint algebra
• Hamiltonian formulation of a simple theory of the teleparallel geometry
• Hamiltonian structure and gauge symmetries of Poincare gauge theory

Cited by in corpus (42)

• Cosmology in $f(Q)$ geometry
• Teleparallel Gravity: From Theory to Cosmology
• Comparing Equivalent Gravities: common features and differences
• Modified teleparallel theories of gravity in symmetric spacetimes
• Cosmological viable models in $f(T,B)$ gravity as solutions to the $H_0$ tension
• Isotropization of locally rotationally symmetric Bianchi-I universe in $f(Q)$-gravity
• Constraining Teleparallel Gravity through Gaussian Processes
• Review of the Hamiltonian analysis in teleparallel gravity
• Post-Newtonian limit of Teleparallel Horndeski gravity
• On the gauge fixing in the Hamiltonian analysis of general teleparallel theories
• Non-Linear Obstructions for Consistent New General Relativity
• Cosmological perturbations in modified teleparallel gravity models: Boundary term extension
• Parameterized post-Newtonian limit of general teleparallel gravity theories
• Reflections on the covariance of modified teleparallel theories of gravity
• The $3+1$ Formalism in the Geometric Trinity of Gravity
• Testing the violation of the equivalence principle in the electromagnetic sector and its consequences in $f(T)$ gravity
• Spherically symmetric vacuum solutions in 1-Parameter New General Relativity and their phenomenology
• Dynamical complexity of the Teleparallel gravity cosmology
• Pseudoinvariance and the extra degree of freedom in f(T) gravity
• Lorentz gauge-invariant variables in torsion-based theories of gravity
• Lorentz symmetries and primary constraints in covariant teleparallel gravity
• Disformal transformations in modified teleparallel gravity
• Classification of primary constraints for new general relativity in the premetric approach
• Einstein-Proca theory from the Einstein-Cartan formulation
• (3+1)-Formulation for Gravity with Torsion and Non-Metricity: The Stress-Energy-Momentum Equation
• Geodesic Congruences and a Collapsing Stellar Distribution in f (T ) Theories
• Hamilton's equations in the covariant teleparallel equivalent of general relativity
• Revisiting Stability in New General Relativity
• Generalised Proca Theories in Teleparallel Gravity
• Static spherically symmetric solutions in New General Relativity
• Gravitational Waves in New General Relativity
• (3+1)-Formulation for Gravity with Torsion and Non-Metricity II: The Hypermomentum Equation
• Teleparallel bigravity
• Hamiltonian Analysis In New General Relativity
• Hamiltonian of new general relativity using differential forms
• Conformal Transformations and Cosmological Perturbations in New General Relativity
• Noether's second theorem in teleparallel gravity
• A unified-description of curvature, torsion, and non-metricity of the metric-affine geometry with the Möbius representation
• The Hamiltonian constraint in the symmetric teleparallel equivalent of general relativity
• Degrees of Freedom of New General Relativity I: Type 2, Type 3, Type 5, and Type 8
• Weak Gravity Limit in Newer General Relativity
• Precision Cosmology in Modified and Extended Theories of Gravity: an insightful test