Generalizations of teleparallel gravity and local Lorentz symmetry

By T. Sotiriou, Baojiu Li, John D. Barrow. 2010

261 citations recorded by the source corpus.

We analyze the relation between teleparallelism and local Lorentz invariance. We show that generic modifications of the teleparallel equivalent to general relativity will not respect local Lorentz symmetry. We clarify the reasons for this and explain why the situation is different in general relativity. We give a prescription for constructing teleparallel equivalents for known theories. We also explicitly consider a recently proposed class of generalized teleparallel theories, called f(T) theories of gravity, and show why restoring local Lorentz symmetry in such theories cannot lead to sensible dynamics, even if one gives up teleparallelism. A key feature of general relativity is observer independence, expressed through general covariance. This makes it possible to formulate the theory in terms of spacetime tensors, without making any reference to the tangent space of each point of the spacetime manifold (even though this is where vectors and tensors are naturally defined). Also, in general relativity, the spacetime geometry can be fully described by the metric alone, because the connection that defines parallel transport is assumed to be the Levi-Civita connection of the metric. The effects of the gravitational interaction are described in terms of the curvature of spacetime, which responds to the distribution and motion of mass-energy. The avoidance of any reference to the tangent space in general relativity is not mandatory. It is straightforward to introduce an orthonormal basis for the tangent space at each point, the vierbein or tetrad fields, ha (x µ ), project along this basis and formulate the theory in terms of the projected quantities. This is generally referred to as the tetrad or vierbein formalism. Such an approach has advantages, especially when working with fermions. In the tangent-space picture of general relativity, distances are measured with the flat metric, but there still exists a non-vanishing connection with non-vanishing curvature.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ac065f1f6ea6dc397ac7e4e6374a8d1c1b504cc1

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Citations in the corpus

Teleparallel theories of gravity: illuminating a fully invariant approach (2018, background): “The issue that has caused a lot of attention and raised some doubts about the consistency of f (T) gravity and other modified teleparallel gravity models is the question of local Lorentz invariance [9, 12].”
Observational constraints on teleparallel dark energy (2011, background): “An interesting and necessary investigation would be to go beyond the background analysis, and examine observables that arise at the perturbation level, such are the growth of matter overdensities and the gravitational-wave spectrum, since these could also clarify possible Lorentz-violation problems ”
Solar system constraints on f(T) gravity (2012, background): “…in the generalf (T) gravity this is not the case anymore, and in general one has a more complicated relation connecting the vierbein tetrad with the metric, with the formerb ing non-diagonal even for a diagonal metric (Sotiriou et al. (2011)), as it arises from Lorentz transformations of (7).”