On reference frames in spacetime and gravitational energy in freely falling frames

Abstract

We consider the interpretation of tetrad fields as reference frames in spacetime. Reference frames may be characterized by an antisymmetric acceleration tensor, whose components are identified as the inertial accelerations of the frame (the translational acceleration and the frequency of rotation of the frame). This tensor is closely related to gravitoelectromagnetic field quantities. We construct the set of tetrad fields adapted to observers that are in free fall in the Schwarzschild spacetime, and show that the gravitational energy-momentum constructed out of this set of tetrad fields, in the framework of the teleparallel equivalent of general relatrivity, vanishes. This result is in agreement with the principle of equivalence, and may be taken as a condition for a viable definition of gravitational energy.

19 pages, no figures, accepted by Classical and Quantum Gravity

References in corpus (11)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• Gravitational Lorentz Force and the Description of the Gravitational Interaction
• Metric-affine approach to teleparallel gravity
• Energy and angular momentum of the gravitational field in the teleparallel geometry
• Hamiltonian formulation of general relativity in the teleparallel geometry
• Length measurement in accelerated systems
• Covariance properties and regularization of conserved currents in tetrad gravity
• The gravitational energy-momentum tensor and the gravitational pressure
• The angular momentum of the gravitational field and the Poincare group
• Vacuum Electrodynamics of Accelerated Systems: Nonlocal Maxwell's Equations
• The gravitational energy-momentum flux

Cited by in corpus (49)

• The teleparallel equivalent of general relativity
• Regularizing role of teleparallelism
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• Charged Black Holes in Generalized Teleparallel Gravity
• Is Teleparallel Gravity really equivalent to General Relativity?
• Planar Symmetry in f(T) gravity
• Influence of GUP corrected Casimir energy on zero tidal force wormholes in modified teleparallel gravity with matter coupling
• On Conserved Quantities for the Schwarzschild Black Hole in Teleparallel Gravity
• On the energy of charged black holes in generalized dilaton-axion gravity
• The energy-momentum of plane-fronted gravitational waves in the teleparallel equivalent of GR
• Flat connection for rotating vacuum spacetimes in extended teleparallel gravity theories
• On the energy of Hořava-Lifshitz black holes
• Difficulties of Teleparallel Theories of Gravity with Local Lorentz Symmetry
• On the construction of Fermi-Walker transported frames
• On the gravitational angular momentum of rotating sources
• The Teleparallel Equivalent of General Relativity and the Gravitational Centre of Mass
• Energy of spherically symmetric spacetimes on regularizing teleparallelism
• On FRW Model in Conformal Teleparallel Gravity
• On Dark Energy and Accelerated Reference Frames
• On Teleparallel Quantum Gravity in Schwarzschild Space-Time
• Pound-Rebka experiment and torsion in the Schwarzschild spacetime
• A solution of the non-uniqueness problem of the Dirac Hamiltonian and energy operators
• Repulsive gravity near naked singularities and point massive particles
• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• Neutron Stars in Teleparallel Gravity
• A simpler solution of the non-uniqueness problem of the covariant Dirac theory
• The Work-Energy Relation for Particles on Geodesics in the pp-Wave Spacetimes
• The angular momentum of plane-fronted gravitational waves in the teleparallel equivalent of general relativity
• On Gravitational Entropy of de Sitter Universe
• Electrodynamics in accelerated frames revisited
• 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
• Magnetic black holes in Weitzenböck geometry
• Gravitational energy and radiation of a charged black hole
• Should there be a spin-rotation coupling for a Dirac particle?
• The equivalence principle for a plane gravitational wave in torsion based and non-metricity based teleparallel equivalents of general relativity
• Energy distribution of a regular black hole solution in Einstein-nonlinear electrodynamics
• Perturbations of the Gravitational Energy in the TEGR: Quasinormal Modes of the Schwarzschild Black Hole
• Energy Distribution for Non-commutative Radiating Schwarzschild Black Holes
• Gravitational energy of a magnetized Schwarzschild black hole - a teleparallel approach
• Role of the remnant symmetries in gravitational theories based on absolute parallelism: a 2D standpoint
• Gravitational waves and the breaking of parallelograms in space-time
• On the Black Hole Acceleration in the C-metric Space-time
• On the total energy conservation of the Alcubierre spacetime
• Mass and angular momentum for the Kerr black hole in TEGR and STEGR
• Gravitational Energy Creation in the Sandwich pp-Waves Collision
• Matrix theory of gravitation