Energy conditions and classical scalar fields

TL;DR

This paper examines the violations of energy conditions in wormhole solutions with classical scalar fields, emphasizing the importance of resolving ambiguities in defining energy density and stress-energy tensor.

Contribution

It clarifies the ambiguities in energy definitions for nonminimally coupled scalar fields and discusses their implications for energy conditions in wormhole physics.

Findings

Identifies three approaches to define energy density for scalar fields.

Highlights the role of energy localization issues in gravitational fields.

Discusses conditions under which energy violations occur in wormhole solutions.

Abstract

Attention has been recently called upon the fact that the weak and null energy conditions and the second law of thermodynamics are violated in wormhole solutions of Einstein's 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.