For the singularity theorems of Hawking and Penrose to hold, the stress-energy tensor of matter must satisfy certain restrictions. A model is developed representing the interior of a collapsing, spherically symmetric cloud of matter, which is everywhere free of singularities, due to a relaxation of the so-called "weak energy condition." The regions of the model in which the condition must be violated, and the properties of matter and energy which result, are determined. The indications are that, at least in spherically symmetric cases involving very large masses, the energy condition must be violated in a region where the density is no larger than normal matter densities, which seems physically implausible. Hence suspending the energy conditions may not be a reasonable approach to the avoidance of singularities.

• Received 29 November 1982

DOI:https://doi.org/10.1103/PhysRevD.28.1265