Gravitational energy

Abstract

Observers at rest in a stationary spacetime flat at infinity can measure small amounts of rest-mass+internal energies+kinetic energies+pressure energy in a small volume of fluid attached to a local inertial frame. The sum of these small amounts is the total "matter energy" for those observers. The total mass-energy minus the matter energy is the binding gravitational energy. Misner, Thorne and Wheeler evaluated the gravitational energy of a spherically symmetric static spacetime. Here we show how to calculate gravitational energy in any static and stationary spacetime for isolated sources with a set of observers at rest. The result of MTW is recovered and we find that electromagnetic and gravitational 3-covariant energy densities in conformastatic spacetimes are of opposite signs. Various examples suggest that gravitational energy is negative in spacetimes with special symmetries or when the energy-momentum tensor satisfies usual energy conditions.

12 pages. Accepted for publication in Class. Quantum Grav

References in corpus (3)

• Relativistic conservation laws and integral constraints for large cosmological perturbations
• On the mass of a Kerr-anti-de Sitter spacetime in D dimensions
• On the uniqueness of harmonic coordinates

Cited by in corpus (6)

• Cosmic clocks, cosmic variance and cosmic averages
• Gauge-Invariant Localization of Infinitely Many Gravitational Energies from All Possible Auxiliary Structures
• Energetics in Condensate Star and Wormholes
• Energy and angular momentum densities of stationary gravity fields
• Gravitational energy in stationary spacetimes
• Energy nonconservation and relativistic trajectories: Unimodular gravity and beyond