Teleparallel theories of gravity as analogue of non-linear electrodynamics

Understand

The teleparallel formulation of gravity theories reveals close structural analogies to electrodynamics, which are more hidden in their usual formulation in terms of the curvature of spacetime.

• We show how every locally Lorentz invariant teleparallel theory of gravity with second order field equations can be understood as built from a gravitational field strength and excitation tensor which are related to each other by a constitutive relation, analogous to the axiomatic construction of theories of electrodynamics.
• We demonstrate how the previously studied models of $f(\mathbb{T})$ and $f(T_\text{ax},T_\text{ten},T_\text{vec})$ gravity as well as teleparallel dark energy can be formulated in this language.
• The advantage of this approach to gravity is that the field equations for different models all take the same compact form and general results can be obtained.