Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFlat spin connections in the Teleparallel equivalent of General Relativity
103
0
0.0
(
0
)
Authors
A. Zubiaga
Ask ChatGPT about the research
No Arabic abstract
This work generalizes the treatment of flat spin connections in the teleparallel equivalent of general relativity. It is shown that a general flat spin connection form a subspace in the affine space of spin connections which is dynamically decoupled from the tetrad and the matter fields. A translation in the affine subspace introduces a torsion term without changing the tetrad. Instead, the change in the torsion is related to the introduction of a global acceleration field term that introduces Lorentz inertial effects in the reference frame. The dynamics of the gravitationally coupled matter fields remains however equivalent regardless of the flat spin connection chosen. The implications of the break of this invariance by a general $f(T)$ and $f(R)$ is discussed.
rate research
Read More
Spaniol and Andrade introduced grvitoelectromagnetism in TEGR by considering superpotentials, times the determinant of tetrads, as the gravitoelectromagnetic fields. However, since this defined gravitoelectromagnetic field strength does not give rise to a complete set of Maxwell-like equations, we propose an alternative definition of the gravitoelectromagnetic field strength: instead of superpotentials, torsions are taken as the gravitoelectromagnetic field strengths. Based on this new proposal we are able to derive a complete set of Maxwell-like equations. We then apply them to obtain explicit expressions of the gravitoelectromagnetic fields both in Schwarzchilds spacetime and for gravitational waves.
It has been shown recently that within the framework of the teleparallel equivalent of general relativity (TEGR) it is possible to define the energy density of the gravitational field. The TEGR amounts to an alternative formulation of Einsteins general relativity, not to an alternative gravity theory. The localizability of the gravitational energy has been investigated in a number of space-times with distinct topologies, and the outcome of these analises agree with previously known results regarding the exact expression of the gravitational energy, and/or with the specific properties of the space-time manifold. In this article we establish a relationship between the expression for the gravitational energy density of the TEGR and the Sparling two-forms, which are known to be closely connected with the gravitational energy. We also show that our expression of energy yields the correct value of gravitational mass contained in the conformal factor of the metric field.
In cite{Bahamonde:2019zea}, a spherically symmetric black hole (BH) was derived from the quadratic form of $f(T)$. Here we derive the associated energy, invariants of curvature, and torsion of this BH and demonstrate that the higher-order contribution of torsion renders the singularity weaker compared with the Schwarzschild BH of general relativity (GR). Moreover, we calculate the thermodynamic quantities and reveal the effect of the higher--order contribution on these quantities. Therefore, we derive a new spherically symmetric BH from the cubic form of $f(T)=T+epsilonBig[frac{1}{2}alpha T^2+frac{1}{3}beta T^3Big]$, where $epsilon<<1$, $alpha$, and $beta$ are constants. The new BH is characterized by the two constants $alpha$ and $beta$ in addition to $epsilon$. At $epsilon=0$ we return to GR. We study the physics of these new BH solutions via the same procedure that was applied for the quadratic BH. Moreover, we demonstrate that the contribution of the higher-order torsion, $frac{1}{2}alpha T^2+frac{1}{3}beta T^3$, may afford an interesting physics.
The junction conditions for General Relativity in the presence of domain walls with intrinsic spin are derived in three and higher dimensions. A stress tensor and a spin current can be defined just by requiring the existence of a well defined volume element instead of an induced metric, so as to allow for generic torsion sources. In general, when the torsion is localized on the domain wall, it is necessary to relax the continuity of the tangential components of the vielbein. In fact it is found that the spin current is proportional to the jump in the vielbein and the stress-energy tensor is proportional to the jump in the spin connection. The consistency of the junction conditions implies a constraint between the direction of flow of energy and the orientation of the spin. As an application, we derive the circularly symmetric solutions for both the rotating string with tension and the spinning dust string in three dimensions. The rotating string with tension generates a rotating truncated cone outside and a flat space-time with inevitable frame dragging inside. In the case of a string made of spinning dust, in opposition to the previous case no frame dragging is present inside, so that in this sense, the dragging effect can be shielded by considering spinning instead of rotating sources. Both solutions are consistently lifted as cylinders in the four-dimensional case.
The restoration of spin connection clarifies the long known local Lorentz invariance problem in telelparallel gravities. It is considered now that any tetrad together with the associated spin connection can be equally utilized. Among the tetrads there is a particular one, namely proper tetrad, in which all the spurious inertial effects are removed and the spin connection vanishes. A specific tetrad was proposed in the literature for spherically symmetric cases, which has been used in regularizing the action, as well as in searching solutions in various scenarios. We show in this paper that the this tetrad is not the unique choice for the proper tetrad. We construct a new tetrad that can be considered as the proper one, and it will lead to different behaviors of the field equation and results in different solutions. With this proper tetrad, it is possible to find solutions to teleparallel gravities in the strong field regime, which may have physical applications. In the flat spacetime limit, the new tetrad coincides with the aforementioned one.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
