Covariant energy-momentum and an uncertainty principle for general relativity

Understand

We introduce a naturally-defined totally invariant spacetime energy expression for general relativity incorporating the contribution from gravity.

• The extension links seamlessly to the action integral for the gravitational field.
• The demand that the general expression for arbitrary systems reduces to the Tolman integral in the case of stationary bounded distributions, leads to the matter-localized Ricci integral for energy-momentum in support of the energy localization hypothesis.
• The role of the observer is addressed and as an extension of the special relativistic case, the field of observers comoving with the matter is seen to compute the intrinsic global energy of a system.