Localization of Energy in General Relativity

Abstract

In the framework of the teleparallel equivalent of general relativity the energy density of asymptoticaly flat gravitational fields can be naturally and unambiguously defined. Upon integration of the energy density over the whole three dimensional space we obtain the ADM energy. We use this energy density to calculate the energy inside a Schwarzschild black hole.

12 pages, LaTex file, no figures

Cited by in corpus (43)

• f(T) teleparallel gravity and cosmology
• The teleparallel equivalent of general relativity
• Torsion Gravity: a Reappraisal
• Gravitational Energy-Momentum Density in Teleparallel Gravity
• Observational constraints on cosmological solutions of $f(Q)$ theories
• Energy and angular momentum of the gravitational field in the teleparallel geometry
• Hamiltonian formulation of general relativity in the teleparallel geometry
• Primordial Fluctuations within Teleparallelism
• Covariance properties and regularization of conserved currents in tetrad gravity
• Hamiltonian structure of the teleparallel formulation of GR
• Rotating AdS black holes in Maxwell-$f(T)$ gravity
• The gravitational energy-momentum tensor and the gravitational pressure
• Gravitoelectromagnetism, Solar System Test and Weak-Field Solutions in $f(T,B)$ Gravity with Observational Constraints
• $D$-dimensional charged Anti-de-Sitter black holes in $f(T)$ gravity
• General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry
• Analytic rotating black hole solutions in $N$-dimensional $f(T)$ gravity
• The quadratic spinor Lagrangian is equivalent to the teleparallel theory
• On the energy of homogeneous cosmologies
• Teleparallel Energy-Momentum Distribution of Lewis-Papapetrou Spacetimes
• The gravitational energy-momentum flux
• Gravitational energy of rotating black holes
• Conservation laws in the teleparallel theory of gravity
• On the energy of charged black holes in generalized dilaton-axion gravity
• On the energy of Hořava-Lifshitz black holes
• On the distribution of gravitational energy in the de Sitter space
• Space-time defects and teleparallelism
• Static Bondi Energy in the Teleparallel Equivalent of General Relativity
• Gravitational Energy of Kerr and Kerr Anti-de Sitter Space-times in the Teleparallel Geometry
• Gravitational energy of conical defects
• On Teleparallel Quantum Gravity in Schwarzschild Space-Time
• Sparling two-forms, the conformal factor and the gravitational energy density of the teleparallel equivalent of general relativity
• Energy of general 4-dimensional stationary axisymmetric spacetime in the teleparallel geometry
• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• Horizon Mass Theorem
• Conservation laws in the teleparallel theory with a positive cosmological constant
• Weighing the Black Hole via Quasi-local Energy
• Gravitational energy of a magnetized Schwarzschild black hole - a teleparallel approach
• Weighing The Black Holes Of GW150914
• On the correspondence between energy conservation and energy-momentum tensor conservation in cosmology
• On Special Re-quantization of a Black Hole
• Rotating cosmological cylindrical wormholes in GR and TEGR sourced by anisotropic fluids
• Can torsion play a role in angular momentum conservation law?
• Gravitational Energy Creation in the Sandwich pp-Waves Collision