Is Teleparallel Gravity really equivalent to General Relativity?

Abstract

An axiomatization of the so-called Teleparallel Equivalent to General Relativity is presented. A set of formal and semantic postulates are elaborated from where the physical meaning of various key concepts of the theory are clarified. These concepts include those of inertia, Lorentz and diffeomorphism invariance, and reference frame. It is shown that Teleparallel Gravity admits a wider representation of space-time than General Relativity, allowing to define properties of the gravitational field such as energy and momentum that are usually considered problematic. In this sense, although the dynamical equations of both theories are equivalent, their inequivalence from a physical point of view is demonstrated. Finally, the axiomatic formulation is used to compare Teleparallel Gravity with other theories of gravity based on absolute parallelism such as non-local and f(T) gravity.

21 pages, accepted for publication in Annalen der Physik

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Cited by in corpus (23)

• Teleparallel Gravity: From Theory to Cosmology
• $f(Q,T)$ gravity
• Teleparallel Palatini theories
• Weyl type $f(Q,T)$ gravity, and its cosmological implications
• Weak Field Limit and Gravitational Waves in $f(T,B)$ Teleparallel Gravity
• The gravitational energy-momentum pseudotensor: the cases of $f(R)$ and $f(T)$ gravity
• Minimal coupling in presence of non-metricity and torsion
• Noether charge and black hole entropy in teleparallel gravity
• Gravitational Waves in Higher Order Teleparallel Gravity
• Difficulties of Teleparallel Theories of Gravity with Local Lorentz Symmetry
• The energy-momentum tensor of gravitational waves, Wyman spacetime and freely falling observers
• Conformally invariant proper time with general non-metricity
• $f(T)$ Cosmology with Nonzero Curvature
• 100 years of mathematical cosmology: Models, theories, and problems
• $f(T,B)$ gravity in a Friedmann-Lema\^ıtre-Robertson-Walker universe with nonzero spatial curvature
• Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity
• The generalization of the ADM gravitational energy-momentum
• Gravitational energy and radiation of a charged black hole
• On the gravitational energy problem and the energy of photons
• Observational constraints on viscous cosmology in $f(T,L_m)$ gravity
• Dynamical system analysis in multiscalar-torsion cosmology
• Kantowski-Sachs cosmology in scalar-torsion theory
• Chiral Gravitational Wave Background from Audible Axion via Nieh-Yan Term