Absence of Relativistic Stars in f(T) Gravity

TL;DR

This paper demonstrates that in f(T) gravity, realistic neutron star solutions only exist when the function is linear in T, effectively reducing to the Teleparallel Equivalent of General Relativity, unlike in f(R) models.

Contribution

It shows that non-linear f(T) functions cannot support relativistic neutron stars, highlighting a fundamental limitation of f(T) gravity models.

Findings

Neutron star solutions in f(T) gravity require f(T) to be linear in T.

Non-linear f(T) models do not admit relativistic neutron star solutions.

f(T) gravity constraints are stricter than in f(R) models.

Abstract

In this work we investigate the structure of neutron stars in modified f(T) gravity models. We find that, unlike the f(R) models, the equations of motion put a rather strict constraint on the possible f(T) functions. Specifically, after analyzing the problem in two different choice of coordinates with spherical symmetry, we conclude that the relativistic neutron star solution in f(T) gravity models is possible only if f(T) is a linear function of the torsion scalar T, that is in the case of Teleparallel Equivalent of General Relativity.