Equivalent teleparallel theories in diagonalizable spacetimes: Comment on "Metric-affine approach to teleparallel gravity"

Dirac spinor fields in the teleparallel gravity: comment on "Metric-affine approach to teleparallel gravity"

We show that the coupling of a Dirac spinor field with the gravitational field in the teleparallel equivalent of general relativity is consistent. For an arbitrary SO(3,1) connection there are two possibilities for the coupling of the spinor field with the gravitational field. The problems of consistency raised by Y. N. Obukhov and J. G. Pereira in the paper {\it Metric-affine approach to teleparallel gravity} [gr-qc/0212080] take place only in the framework of one particular coupling. By adopting an alternative coupling the consistency problem disappears.

Comment on "Self-dual teleparallel formulation of general relativity and the positive energy theorem" G. Y. Chee

We give a correct tensor proof of the positive energy problem for the case including momentum on basis of conditions of existence of the two-to-one correspondence between the Sen-Witten spinor field and the Sen-Witten orthonormal frame. These conditions were obtained in our previous publications, but true significance of our works was not estimated properly by G.Y.Chee, and these were not correct quoted in his publication. On other hand, the main result of our work is key argument in favour of geometrical nature of the Sen-Witten spinor field.

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Comment on `The Classical Limit of Teleparallel Gravity'

本文针对arXiv:2406.17594中纯标架表述下TEGR牛顿极限的主张展开批判，重点驳斥了“存在正则牛顿极限时极限联络挠率必为零”的核心结论。

Generators of Internal Lorentz Transformations and of General Affine Coordinate Transformations in Teleparallel Theory of (2+1)-Dimensional Gravity --- Cases with Static Circularly Symmetric Space-Times---

In a teleparallel theory of (2+1)-dimensional gravity developed in a previous paper, we examine generators of internal Lorentz transformations and of general affine coordinate transformations for static circularly symmetric exact solutions of gravitational field equation. The \lq \lq spin" angular momentum, the energy-momentum and the \lq \lq extended orbital angular momentum" are explicitly given for each solution. Also, we give a critical comment on Deser's claim that neither momentum nor boosts are definable for finite energy solutions of three-dimensional Einstein gravity.

Teleparallel theory as a gauge theory of translations: comments and issues

The Teleparallel Equivalent to General Relativity (TEGR) is often presented as a gauge theory of translations, i.e., that uses \emph{only} the translation group $T_4 = (\setR^4, +)$ as its gauge group. In a previous work we argued against this \emph{translation-only} formalism on the basis of its mathematical shortcomings. We then provided an alternative proposal using a Cartan connection. Recently, a reply by some of the authors defending TEGR as a \emph{translation-only} gauge theory discussed our objections. Here, we first clarify our arguments, and give new proofs of some statements, to an…

Gravitational energy, gravitational pressure, and the thermodynamics of a charged black hole in teleparallel gravity

We investigate, in the case of a Reissner-Nordström black hole, the definitions of gravitational energy and gravitational pressure that naturally arise in the framework of the Teleparallel Equivalent of General Relativity. In particular, we calculate the gravitational energy enclosed by the event horizon of the black hole, E, and the radial pressure over it, p. With these quantities we then analyse the thermodynamic relation dE + pdV (as p turns out to be a density, dV is actually given by dV = dr dθdϕ, in spherically-type coordinates). We compare the latter with the standard first law of blac…