Energy conditions and classical scalar fields Original Research Article

Attention has been recently called upon the fact that the weak and null energy conditions are violated in wormhole solutions of Einsteinʹs theory with classical, nonminimally coupled, scalar fields as material source. It is shown that the discussion is only meaningful when ambiguities in the definitions of stress-energy tensor and energy density of a nonminimally coupled scalar are resolved. The three possible approaches are discussed with emphasis on the positivity of the respective energy densities and covariant conservation laws. The root of the ambiguities is traced to the energy localization problem for the gravitational field.