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Einstein's vierbein formulation of general relativity based on the notion of distant parallelism (teleparallelism) naturally introduces a covariant surface term in addition to the Einstein-Hilbert action. We investigate the action principle in teleparallelism with the existence of spacetime boundaries and find that the covariant surface term exactly eliminates all the unwanted surface terms that reside in the metric formulation of general relativity, in the role of a Gibbons-Hawking-York (GHY) term. The identity of such a covariant GHY term is further confirmed by the recovery of the correct black hole entropy from the free energy due to the spacetime boundary. These results indicate that the vierbein formulation of gravity generally exhibits a well-posed action principle and readily admits the path-integral approach to quantization.

We show that in theories of generalised teleparallel gravity, whose Lagrangians are algebraic functions of the usual teleparallel Lagrangian, the action and the field equations are not invariant under local Lorentz transformations. We also argue that these theories appear to have extra degrees of freedom with respect to general relativity. The usual teleparallel Lagrangian, which has been extensively studied and leads to a theory dynamically equivalent to general relativity, is an exception. Both of these facts appear to have been overlooked in the recent literature on f(T) gravity, but are crucial for assessing the viability of these theories as alternative explanations for the acceleration of the universe., Comment: 4 pages, no figure; v2: Added discussion about modifying the theory in order to make it manifestly Lorentz covariant and one reference; v3: minor changes to match published version

Recently, generalizations of the Ashtekar constraints are derived via the Nieh-Yan topological term. To be fair, such canonical transformations have been applied before in a gauge framework of gravity. Moreover, in the case of the teleparallelism equivalent of Einstein's theory, one can go further and show that the Chern-Simons solutions of the Gauss-type constraints wind around torsional instantons, thus establishing an analogue to the $\ensuremath{\theta}$ vacua of Yang-Mills theory.

Born-Infeld strategy to smooth theories having divergent solutions is applied to teleparallel equivalent of General Relativity. Differing from other theories of modified gravity, modified teleparallelism leads to second order equations, since teleparallel Lagrangian only contains first derivatives of the vierbein. We show that Born-Infeld-modified teleparallelism solves the particle horizon problem in a spatially flat FRW universe by providing an initial exponential expansion without resorting to an inflaton field., Comment: 4 pages, 2 figures. Version to be published in Physical Review D

Contrary to the claim in a recent publication [Phys. Rev. D 67, 044016 (2003)], I explicitly demonstrate the consistency of the coupling of Dirac fields to the teleparallelism equivalent of general relativity. Moreover, it is pointed out that, in a metric-affine framework, a $\mathrm{SL}(4,R)$-covariant generalization of the Dirac equation needs to be considered.

In reply to the criticism made by Mielke in the pereceding Comment [Phys. Rev. D69 (2004) 128501] on our recent paper, we once again explicitly demonstrate the inconsistency of the coupling of a Dirac field to gravitation in the teleparallel equivalent of general relativity. Moreover, we stress that the mentioned inconsistency is generic for {\it all} sources with spin and is by no means restricted to the Dirac field. In this sense the $SL(4,R)$-covariant generalization of the spinor fields in the teleparallel gravity theory is irrelevant to the inconsistency problem., Comment: Revtex, 4 pages, no figures

The teleparallel gravity theory, treated physically as a gauge theory of translations, naturally represents a particular case of the most general gauge-theoretic model based on the general affine group of spacetime. On the other hand, geometrically, the Weitzenboeck spacetime of distant parallelism is a particular case of the general metric-affine spacetime manifold. These physical and geometrical facts offer a new approach to the teleparallelism. We present a systematic treatment of the teleparallel gravity within the framework of the metric-affine theory. The symmetries, conservation laws and the field equations are consistently derived, and the physical consequences are discussed in detail. We demonstrate that the so-called teleparallel GR-equivalent model has a number of attractive features which distinguishes it among the general teleparallel theories, although it has a consistency problem when dealing with spinning matter sources., Comment: Revtex4, 22 pages, no figures. Accepted for publication in Phys. Rev. D

The teleparallelism theory of gravity is presented as a constrained Poincar\'e gauge theory. Arguments are given in favor of a two-parameter family of field Lagrangians quadratic in torsion. The inclusion of a "parity violating" term in the field Lagrangian avoids difficulties with the initial-data problem, recently discussed in the literature. Several new exact solutions of the corresponding teleparallelism theory give considerable insight into its physical consequences. The resulting general field equations are analyzed in the weak-field approximation excluding ghosts and tachyons. The physical meaning of the six additional components of the tetrad field (as compared with the metric) appears naturally from our theory and is made clear.