# Static compact objects in Einstein-Cartan theory

## TL;DR

This paper extends the equations describing compact objects in Einstein-Cartan theory with torsion, finds new solutions, and analyzes how spin influences their properties and limits, including the maximum compactness of stars.

## Contribution

It introduces generalized structure equations for torsion-affected space-times, derives new solutions, and proves the non-existence of spin-supported static compact objects under certain conditions.

## Key findings

- Torsion modifies the geometry of space-time in compact objects.
- New exact solutions for spin-supported objects are obtained.
- Spin affects the Buchdahl limit for star compactness.

## 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.