Abstract. This paper develops a theory of thin shells within the context of the Einstein-Cartan theory by extending the known formalism of general relativity. In order to perform such an extension, we require the general non-symmetric stress-energy tensor to be conserved leading, as Cartan pointed out himself, to a strong constraint relating the curvature and the torsion of spacetime. When we restrict ourselves to the class of spacetimes satisfying this constraint, we are able to properly describe thin shells and derive the general expression of the surface stress-energy tensor both in its four-dimensional and in its three-dimensional intrinsic form. We finally derive a general family of static solutions of the Einstein-Cartan theory exhibiting a natural family of null hypersurfaces and use it to apply our formalism to the construction of a null shell of matter.

PACS numbers: 0450, 0420J, 0430N

Print publication: Issue 13 (7 July 2000)
Received 4 February 2000