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.
Highlights
Compact objects, in particular neutron stars, represent one of richest environments to probe fundamental physics due their extreme gravitational fields, densities and the state of the matter that composes them, especially, at the core
The recent detection of gravitational waves due to the coalescing of two orbiting neutron stars [1] opened a new window to study their tidal deformations, allowing the study of the properties of the matter fields that compose this kind of objects
The usage of neutron stars as a physics laboratory is only possible if we have a deep knowledge of their properties
Summary
In particular neutron stars, represent one of richest environments to probe fundamental physics due their extreme gravitational fields, densities and the state of the matter that composes them, especially, at the core. A way around this problem is to endow the space-time with additional geometrical structure, providing extra degrees of freedom to model spin and its relation with the gravitational field This is the fundamental idea behind the so-called Einstein-Cartan-Sciama-Kible (ECSK) theory of gravity. In this theory the connection is not imposed be symmetric so that, the anti-symmetric part of the connection defines an extra tensor field: torsion In this way, it is possible to impose a local Poincaré gauge symmetry on the tangent space of each point of the manifold such that the matter intrinsic spin can be related with the torsion tensor field.
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