On the gravitational angular momentum of rotating sources

Abstract

The gravitational energy-momentum and angular momentum satisfy the algebra of the Poincare group in the full phase space of the teleparallel equivalent of general relativity. The expression for the gravitational energy-momentum may be written as a surface integral in the three-dimensional spacelike hypersurface, whereas the definition for the angular momentum is given by a volume integral. It turns out that in practical calculations of the angular momentum of the gravitational field generated by localized sources like rotating neutron stars, the volume integral reduces to a surface integral, and the calculations can be easily carried out. Similar to previous investigations in the literature, we show that the total angular momentum is finite provided a certain asymptotic behaviour is verified. We discuss the dependence of the gravitational angular momentum on the frame, and argue that it is a measure of the dragging of inertial frames.

19 pages, accepted by General Relativity and Gravitation

References in corpus (6)

• Hamiltonian formulation of general relativity in the teleparallel geometry
• On reference frames in spacetime and gravitational energy in freely falling frames
• The gravitational energy-momentum tensor and the gravitational pressure
• Regularized expression for the gravitational energy-momentum in teleparallel gravity and the principle of equivalence
• The angular momentum of the gravitational field and the Poincare group
• On the roots of the Poincare structure of asymptotically flat spacetimes

Cited by in corpus (9)

• The teleparallel equivalent of general relativity
• Anisotropic fluid for a set of non-diagonal tetrads in f(T) gravity
• Charged Black Holes in Generalized Teleparallel Gravity
• Planar Symmetry in f(T) gravity
• Rotating charged AdS solutions in quadratic $f(T)$ gravity
• On Teleparallel Quantum Gravity in Schwarzschild Space-Time
• Neutron Stars in Teleparallel Gravity
• The angular momentum of plane-fronted gravitational waves in the teleparallel equivalent of general relativity
• Gravitational energy of a magnetized Schwarzschild black hole - a teleparallel approach