On the extension of the concept of Thin Shells to The Einstein-Cartan Theory

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 curvature and torsion of spacetime. When we restrict ourselves to the class of space-times satisfying this constraint, we are able to properly describe thin shells and derive the general expression of 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.

Latex, 21 pages, 1 combined Latex/Postscript figure; Accepted for publication in Classical and Quantum Gravity

References in corpus (4)

• Singular Hypersurfaces in Scalar-Tensor Theories of Gravity
• Some Physical Consequences of Abrupt Changes in the Multipole Moments of a Gravitating Body
• Implications of Spontaneous Glitches in the Mass and Angular Momentum in Kerr Space-Time
• Peeling properties of lightlike signals in General Relativity

Cited by in corpus (7)

• Area-law versus Rényi and Tsallis black hole entropies
• On the junction conditions in $f(R)$-gravity with torsion
• Spin polarised magnetized cylinder in torsioned spacetime
• On the stress-energy tensor of a null shell in Einstein-Cartan gravity
• Revisiting the Israel junction conditions in Einstein-Cartan gravity
• Galactic dynamo seeds from non-superconducting spin-polarised strings
• Generalized regularly discontinuous solutions of the Einstein equations