Disformal transformations in modified teleparallel gravity

TL;DR

This paper investigates disformal transformations within teleparallel gravity, deriving explicit formulas for geometric objects and analyzing their effects on $f(T)$ gravity, highlighting limitations and potential applications.

Contribution

It provides explicit component formulas for disformal transformations in teleparallel gravity and examines their impact on local Lorentz invariance in $f(T)$ models.

Findings

Disformal transformations cannot remove Lorentz-breaking terms in $f(T)$ gravity.

Explicit formulas for torsion-related geometric objects under disformal transformations.

Disformal transformations have potential applications in scalar-torsion gravity models.

Abstract

In this work, we explore disformal transformations in the context of the teleparallel equivalent of general relativity and modified teleparallel gravity. We present explicit formulas in components for disformal transformations of the main geometric objects in these theories such as torsion tensor, torsion vector and contortion. Most importantly, we consider the boundary term which distinguishes the torsion scalar from the Ricci scalar. With that we show for $f(T)$ gravity that disformal transformations from the Jordan frame representation are unable to straightforwardly remove local Lorentz breaking terms that characterize it. However, we have shown that disformal transformations have interesting properties, which can be useful for future applications in scalar-torsion gravity models, among others.