Compact stars in $f(T) = T +\xi T^\beta$ gravity

The Teleparallel Theory is equivalent to General Relativity, but whereas inthe latter gravity has to do with curvature, in the former gravity is describedby torsion. As is well known, there is in the literature a host of alternativetheories of gravity, among them the so called extended theories, in whichadditional terms are added to the action, such as for example in the $f(R)$ and$f(T)$ gravities, where $R$ is the Ricci scalar and $T$ is the scalar torsion,respectively. One of the ways to probe alternative gravity is via compactobjects. In fact, there is in the literature a series of papers on compactobjects in $f(R)$ and $f(T)$ gravity. In particular, there are several papersthat consider $f(T) = T + \xi T^2$, where $\xi$ is a real constant. In thispaper, we generalise such extension considering compact stars in $f (T ) = T +\xi T^\beta$ gravity, where $\xi$ and $\beta$ are real constants and lookingout for the implications in their maximum masses and compactness in comparisonto the General Relativity. Also, we are led to constrain the $\beta$ parameterto positive integers which is a restriction not imposed by cosmology.