Energy and angular momentum of the gravitational field in the teleparallel geometry

Abstract

The Hamiltonian formulation of the teleparallel equivalent of general relativity is considered. Definitions of energy, momentum and angular momentum of the gravitational field arise from the integral form of the constraint equations of the theory. In particular, the gravitational energy-momentum is given by the integral of scalar densities over a three-dimensional spacelike hypersurface. The definition for the gravitational energy is investigated in the context of the Kerr black hole. In the evaluation of the energy contained within the external event horizon of the Kerr black hole we obtain a value strikingly close to the irreducible mass of the latter. The gravitational angular momentum is evaluated for the gravitational field of a thin, slowly rotating mass shell.

33 pages, Latex file, 1 figure, to appear in the Phys. Rev. D

References in corpus (1)

• Quasilocal Thermodynamics of Kerr and Kerr-anti-de Sitter Spacetimes and the AdS/CFT Correspondence

Cited by in corpus (75)

• f(T) teleparallel gravity and cosmology
• The teleparallel equivalent of general relativity
• Teleparallel Palatini theories
• On reference frames in spacetime and gravitational energy in freely falling frames
• Rotating AdS black holes in Maxwell-$f(T)$ gravity
• A Built-in Inflation in the $f(T)$-Cosmology
• Stability of motion and thermodynamics in charged black holes in $f(T)$ gravity
• The gravitational energy-momentum tensor and the gravitational pressure
• Kerr-Newman Solution and Energy in Teleparallel Equivalent of Einstein Theory
• Reissner Nordstr$\ddot{o}$m solutions and Energy in teleparallel theory
• Exact Teleparallel Gravity of Binary Black Holes
• Regularized expression for the gravitational energy-momentum in teleparallel gravity and the principle of equivalence
• Reissner-Nordström Spacetime in the Tetrad Theory of Gravitation
• 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
• $D$-dimensional charged Anti-de-Sitter black holes in $f(T)$ gravity
• Brane World black holes in Teleparallel Theory Equivalent to General Relativity and their Killing vectors, Energy, Momentum and Angular-Momentum
• Charged Axially Symmetric Solution and Energy in Teleparallel Theory Equivalent to General Relativity
• The angular momentum of the gravitational field and the Poincare group
• Charged Axially Symmetric Solution, Energy and Angular Momentum in Tetrad Theory of Gravitation
• Kerr geometry in f(T) gravity
• Reconstruction of $f(T)$-gravity in the absence of matter
• Analytic rotating black hole solutions in $N$-dimensional $f(T)$ gravity
• On the energy of homogeneous cosmologies
• Dirac spinor fields in the teleparallel gravity: comment on "Metric-affine approach to teleparallel gravity"
• The gravitational energy-momentum flux
• Noether charge and black hole entropy in teleparallel gravity
• Can $f(T)$ models play a bridge between early and late time Universe?
• Teleparallel Versions of Friedmann and Lewis-Papapetrou Spacetimes
• Hamiltonian formulation of unimodular gravity in the teleparallel geometry
• Influence of GUP corrected Casimir energy on zero tidal force wormholes in modified teleparallel gravity with matter coupling
• Constraining extended teleparallel gravity via cosmography: A model-independent approach
• Energy Distribution in f(R) Gravity
• The energy-momentum of plane-fronted gravitational waves in the teleparallel equivalent of GR
• Gravitational pressure on event horizons and thermodynamics in the teleparallel framework
• Revisiting diagonal tetrads: New Black Hole solutions in $f(T)$ gravity
• Space-time defects and teleparallelism
• Energy and Angular Momentum Densities in a Godel-Type Universe in the Teleparallel Geometry
• A Complete Cosmological Scenario in Teleparallel Gravity
• Weak field reduction in teleparallel coframe gravity. Vacuum case
• Energy Contents of Some Well-Known Solutions in Teleparallel Gravity
• The Hidden Flat Like Universe II: Quasi inverse power law inflation by $f(T)$ gravity
• Gravitational Energy of Kerr and Kerr Anti-de Sitter Space-times in the Teleparallel Geometry
• Charged Anti-de Sitter BTZ black holes in Maxwell-$f(T)$ gravity
• Energy Contents of Gravitational Waves in Teleparallel Gravity
• On Teleparallel Quantum Gravity in Schwarzschild Space-Time
• Gravitational Corrections to the Energy-Levels of a Hydrogen Atom
• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• Energy of general 4-dimensional stationary axisymmetric spacetime in the teleparallel geometry
• Energy-Momentum of the Friedmann Models in General Relativity and Teleparallel Theory of Gravity
• Gravitomagnetic effect and spin-torsion coupling
• The angular momentum of plane-fronted gravitational waves in the teleparallel equivalent of general relativity
• Energy and angular momentum of general 4-dimensional stationary axi-symmetric spacetime in teleparallel geometry
• On the Quantization of the Charge-Mass Ratio
• Gravitational energy, gravitational pressure, and the thermodynamics of a charged black hole in teleparallel gravity
• Local Lorentz transformation and exact spherically symmetric vacuum solutions in f(T) gravity theories
• On Gravitational Entropy of de Sitter Universe
• The generalization of the ADM gravitational energy-momentum
• Bondi-Sachs energy-momentum and the energy of gravitational radiation
• On the gravitational energy problem and the energy of photons
• Neutral compact spherically symmetric stars in teleparallel gravity
• Perturbations of the Gravitational Energy in the TEGR: Quasinormal Modes of the Schwarzschild Black Hole
• Energy Contents of a Class of Regular Black Hole Solutions in Teleparallel Gravity
• Conventionalism, cosmology and teleparallel gravity
• Spherically symmetric charged black hole in conformal teleparallel equivalent of general relativity
• Gravitational waves and the breaking of parallelograms in space-time
• Gravitational energy of a magnetized Schwarzschild black hole - a teleparallel approach
• Gravitational Pressure and the Accelerating Universe
• On the Black Hole Acceleration in the C-metric Space-time
• Mass and angular momentum for the Kerr black hole in TEGR and STEGR
• On Non-commutative Corrections of Gravitational Energy in Teleparallel Gravity
• Kerr-Schild metrics in teleparallel gravity
• Gravitational energy in pp-wave spacetimes
• Black holes solutions in power-law Maxwell-$f(T)$ gravity in diverse dimensions
• Gravitational radiation fields in teleparallel equivalent of general relativity and their energies