Disformal transformations in modified teleparallel gravity

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.

12 pages, no figures; prepared for proceedings of the 10th Mathematical Physics Meeting: School and Conference on Modern Mathematical Physics, 9 - 14 September 2019, Belgrade, Serbia, in which one of us (AG) participated; matches the published version

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Cited by in corpus (11)

• Teleparallel Gravity: From Theory to Cosmology
• Foundational issues in f(T) gravity theory
• Minkowski space in $f(T)$ gravity
• Bianchi identities in f(T) gravity: paving the way to confrontation with astrophysics
• Testing the violation of the equivalence principle in the electromagnetic sector and its consequences in $f(T)$ gravity
• Pseudoinvariance and the extra degree of freedom in f(T) gravity
• Disforming to Conformal Symmetry
• Teleparallel bigravity
• Conformal Transformations and Cosmological Perturbations in New General Relativity
• Field transformations and invariant quantities in scalar-teleparallel theories of gravity
• Contemplating the fate of modified gravity