Static compact objects in Einstein-Cartan theory

Abstract

We generalize the Tolman-Oppenheimer-Volkoff equations for space-times endowed with a Weyssenhoff like torsion field in the Einstein-Cartan theory. The new set of structure equations clearly show how the presence of torsion affects the geometry of the space-time. We obtain new exact solutions for compact objects with non-null spin surrounded by vacuum, explore their properties and discuss how these solutions should be smoothly matched to an exterior space-time. We study how spin changes the Buchdahl limit for the maximum compactness of stars. Moreover, under rather generic conditions, we prove that in the context of a Weyssenhoff like torsion, no static, spherically symmetric compact objects supported only by the spin can exist. We also provide some algorithms to generate new solutions.

arXiv comment23 pages, 9 figures

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• Relativistic cosmology and intrinsic spin of matter: Results and theorems in Einstein-Cartan theory
• Junction conditions in gravity theories with extra scalar degrees of freedom
• Toward Singularity Theorems with Torsion
• Consistent solution of Einstein-Cartan equations with torsion outside matter
• Junction conditions for LRS spacetimes in the $1+1+2$ covariant formalism
• Some exact relativistic star solutions in $f(R)$ gravity
• Locally Rotationally Symmetric Spacetimes in Einstein-Cartan Theory and Their Classification
• Kinematic reconstruction of torsion as dark energy in Friedmann cosmology