Energy in gravitational theories. Definition, positivity theorems, and stability.
Abstract
The physical meaning of energy in generally covariant gravitational models is analyzed and shown to lead to a simple invariant formal definition. The derivation of the recent positive energy and stability theorems for Einstein and supergravities with arbitrary cosmological constant are derived. Other models, such as tensorscalar and higher derivative gravity, are briefly considered, as are semiclassical stability and KaluzaKlein theory. It is concluded that energy is unique, welldefined, and has all the desirable stability properties for physically relevant solutions in most gravitational models with or without cosmological constant. It is positivedefinite for all classical solutions of Einstein's equations asymptotic to the appropriate vacuumMinkowski or de Sitter spaces. Energy positivity also holds, at least formally, in all supergravities with arbitrary N.
 Publication:

Annals of the New York Academy of Sciences
 Pub Date:
 1984
 DOI:
 10.1111/j.17496632.1984.tb23339.x
 Bibcode:
 1984NYASA.422...45D
 Keywords:

 Cosmology;
 Energy Distribution;
 Gravitation Theory;
 Relativity;
 Systems Stability;
 Unified Field Theory;
 Asymptotic Properties;
 Einstein Equations;
 Quantum Theory;
 SpaceTime Functions;
 Tensor Analysis;
 Uniqueness Theorem;
 Astrophysics;
 Gravitation Theory