Tetrad Field Research Articles

Comparing Hamiltonians of a spinning test particle for different tetrad fields

This work is concerned with suitable choices of tetrad fields and coordinate systems for the Hamiltonian formalism of a spinning particle derived in [E. Barausse, E. Racine, and A. Buonanno, Phys. Rev. D 80, 104025 (2009)]. After demonstrating that with the originally proposed tetrad field the components of the total angular momentum are not preserved in the Schwarzschild limit, we analyze other hitherto proposed tetrad choices. Then, we introduce and thoroughly test two new tetrad fields in the horizon penetrating Kerr-Schild coordinates. Moreover, we show that for the Schwarzschild spacetime background the linearized in spin Hamiltonian corresponds to an integrable system, while for the Kerr spacetime we find chaos which suggests a nonintegrable system.

On selfdual spin-connections and asymptotic safety

We explore Euclidean quantum gravity using the tetrad field together with a selfdual or anti-selfdual spin-connection as the basic field variables. Setting up a functional renormalization group (RG) equation of a new type which is particularly suitable for the corresponding theory space we determine the non-perturbative RG flow within a two-parameter truncation suggested by the Holst action. We find that the (anti-)selfdual theory is likely to be asymptotically safe. The existing evidence for its non-perturbative renormalizability is comparable to that of Einstein–Cartan gravity without the selfduality condition.

First-order minisuperspace model for the Faddeev formulation of gravity

Faddeev formulation of general relativity (GR) is considered where the metric is composed of ten vector fields or a ten-dimensional tetrad. Upon partial use of the field equations, this theory results in the usual GR. Earlier we have proposed some minisuperspace model for the Faddeev formulation where the tetrad fields are piecewise constant on the polytopes like 4-simplices or, say, cuboids into which [Formula: see text] can be decomposed. Now we study some representation of this (discrete) theory, an analogue of the Cartan–Weyl connection-type form of the Hilbert–Einstein action in the usual continuum GR.

Strange stars in f ( T ) $f(T)$ gravity with MIT bag model

This paper deals with existence of strange stars in $f\left(T\right) $ modified gravity. For this purpose, we have taken the diagonal tetrad field of static spacetime with charged anisotropic fluid and MIT bag model, which provide the linear relation between radial pressure and density of the matter. Further, the analysis of the resulting equations have been done by assuming the parametric form of the metric functions in term of the radial profiles with some unknown constant (introduced by Krori and Barua). By the matching of two metrices, unknown constant of the metric functions appear in terms of mass, radius and charge of the stars, the observed values of these quantities have been used for the detail analysis of the the derived model. We have discuss the regularity, anisotropy, energy conditions, stability and surface redshift of the model.

Kerr-dS/AdS null tetrads in modified teleparallel gravity theories and thermodynamics

We apply a diagonal axially symmetric tetrad to the field equations of the lowest order of \(f(T)\), “where \(T\) is the teleparallel torsion scalar”, and get an exact vacuum solution which describes Kerr-dS/AdS spacetime. We rewrite the tetrad field of the derived solution in a null tetrad form and multiply it by a boost local Lorentz transformation, which contains unknown function of generalized coordinates, and get a new tetrad field. An exact vacuum solutions, which represents Kerr-dS/AdS spacetime, are derived under the following constraints: (i) The scalar torsion, \(T ={T^{\alpha}}_{\mu \nu}{S_{\alpha}}^{\mu \nu}=T_{0}\), where \(T_{0}\) is constant. (ii) The total derivative term is constant. (iii) The combination of the scalar torsion and the total derivative term is constant. We show that all the derived solutions coincide with general relativity solution when the constants of the torsion scalar, the total derivative term and the combination of the torsion scalar and total derivative term are vanishing. When the rotation parameter vanishing, the solution in the lower order of \(f(T)\) approaches asymptotically de Sitter spacetime, and show the existence of the Nariai spacetime as a background solution. The scalar torsion of Nariai spacetime is vanishing naturally without any constraint. Considering the perturbation around the Nariai spacetime up to the first order, we show the behavior of black hole horizon. We investigate that the anti-evaporation does not exist on the classical level. Finally, we used the total derivative term and the Euclidean continuation method to calculate the energy of Kerr-dS/AdS, entropy and temperature. The mass of a Kerr-dS/AdS black hole is interpreted, in terms of thermodynamic potentials, as being the enthalpy, with the pressure given by the cosmological constant.

Kerr-NUT black hole thermodynamics in f(T) gravity theories

An axially symmetric tetrad field is applied to the field equation of f(T) gravity theory, where T is the scalar torsion tensor. A solution, with three constants of integration, for the linear case, $ f(T)=T$ , is derived. Then, we substitute this solution in the tetrad field and change the angle $ \phi$ to $ \Phi$ , such that $ \Phi$ is a function of r , $ \theta$ and $ \phi$ , i.e. $ \Phi=N(r,\theta,\phi)$ . We calculate the scalar torsion and its derivatives, then, a constraint on the scalar torsion is assumed to be constant. From this assumption the value of $ N(r,\theta,\phi)$ is derived. We show that the value of $ N(r,\theta,\phi)$ is a solution to the f(T) gravitational theories provided some restrictions on the form of f(T) and its first derivatives. The associated metric of the derived solution is shown to represent the Kerr-NUT spacetime. The energy of the derived solution is calculated using the Euclidean continuation method and we show that the NUT parameter may be related to the electromagnetic field which is a consistent value with what was obtained before from other definitions. Finally, we calculate the thermodynamical quantities of the Kerr-NUT space times and investigate the first law of thermodynamics and quantum statistical relation.

Conserved charges of Schwarzschild-NUT-AdS space–time using the method of regularization through relocalization

A tetrad field, which gives Schwarzschild-NUT-AdS metric, is provided. We calculate the total conserved charges of this tetrad. This is done by using “regularization through relocalization” for the first time. This method gives the correct value of the total charge of Schwarzschild-NUT-AdS space–time, which depends on the gravitational mass of the system. We show that the NUT parameter has no physical meaning on the conserved quantities of the Schwarzschild-NUT-AdS space–time.

Kerr–Newman-NUT Black Hole in f(T) Gravity Theory and Its Thermodynamical Quantities

We show by explicit calculations that any general relativity solution remains a solution in f(T) gravitational theories provided some constraints on f(T) and its first derivatives are satisfied. This is done by applying an axially-symmetric tetrad field to the charged field equation of f(T), where \(T = T^{\mu }_{\nu \lambda }S_{\mu }^{\nu \lambda }\) is the scalar torsion tensor, gravity theory. In the linear case, f(T) = T which corresponds to general relativity theory, we derive solution with four constants of integration. For the non-linear case, we substitute the derived solution in the tetrad field and change the azimuthal coordinate to be a function of r, θ and ϕ, i.e., \(\Phi = L(r,\theta ,\phi )\). We calculate the scalar torsion and its derivatives then, a condition one the scalar torsion to be constant is assumed. We derive the value of \(L(r,\theta ,\phi )\) which satisfies this condition. The associated metric of the derived solution is shown to be a charged Kerr-NUT space time. The energy of this solution is calculated using the Euclidean continuation method and a consistent value is derived. We also calculate the thermodynamical quantities of charged Kerr-NUT space time and investigate the first law of thermodynamics and quantum statistical relation.

Remnant group of local Lorentz transformations inf(T)theories

It is shown that the extended teleparallel gravitational theories, known as $f(T)$ theories, inherit some on shell local Lorentz invariance associated with the tetrad field defining the spacetime structure. We discuss some enlightening examples, such as Minkowski spacetime and cosmological (Friedmann-Robertson-Walker and Bianchi type I) manifolds. In the first case, we show that the absence of gravity reveals itself as an incapability in the selection of a preferred parallelization at a local level, due to the fact that the infinitesimal local Lorentz subgroup acts as a symmetry group of the frame characterizing Minkowski spacetime. Finite transformations are also discussed in these examples and, contrary to the common lore on the subject, we conclude that the set of tetrads responsible for the parallelization of these manifolds is quite vast and that the remnant group of local Lorentz transformations includes one- and two-dimensional Abelian subgroups of the Lorentz group.

Axially Symmetric-dS Solution in Teleparallelf(T)Gravity Theories

We apply a tetrad field with six unknown functions to Einstein field equations. Exact vacuum solution, which represents axially symmetric-dS spacetime, is derived. We multiply the tetrad field of the derived solution by a local Lorentz transformation which involves a generalization of the angleϕand get a new tetrad field. Using this tetrad, we get a differential equation from the scalar torsionT=TαμνSαμν. Solving this differential equation we obtain a solution to thef(T)gravity theories under certain conditions on the form off(T)and its first derivatives. Finally, we calculate the scalars of Riemann Christoffel tensor, Ricci tensor, Ricci scalar, torsion tensor, and its contraction to explain the singularities associated with this solution.

Regularization off(T)Gravity Theories and Local Lorentz Transformation

We regularized the field equations off(T)gravity theories such that the effect of local Lorentz transformation (LLT), in the case of spherical symmetry, is removed. A “general tetrad field,” with an arbitrary function of radial coordinate preserving spherical symmetry, is provided. We split that tetrad field into two matrices; the first represents a LLT, which contains an arbitrary function, and the second matrix represents a proper tetrad field which is a solution to the field equations off(T)gravitational theory (which are not invariant under LLT). This “general tetrad field” is then applied to the regularized field equations off(T). We show that the effect of the arbitrary function which is involved in the LLT invariably disappears.

Kerr–Newman solution in modified teleparallel theory of gravity

A nondiagonal tetrad field having six unknown functions plus an angle Φ, which is a function of the radial coordinate r, azimuthal angle θ and the polar angle ϕ, is applied to the charged field equations of modified teleparallel theory of gravity. A special nonvacuum solution is derived with three constants of integration. The tetrad field of this solution is axially symmetric and its scalar torsion is constant. The associated metric of the derived solution gives Kerr–Newman spacetime. We have shown that the derived solution can be described by a local Lorentz transformations plus a diagonal tetrad field that is the square root of the Kerr–Newman metric. We show that any solution of general relativity (GR) can be a solution in f(T) under certain conditions.

A special Kerr-solution in f(T) gravitational theories

A tetrad field with six unknown functions is applied to the field equation of teleparallel equivalent of general relativity and analytic solution is derived. The coordinate \(\phi \) to \(N(r,\theta ,\phi )\) is generalized and the new anstaz to the field equation of \(f(T)\) gravitational theories is applied. A special solution, with scalar torsion \(T={T^\alpha }_{\mu \nu } {S_\alpha }^{\mu \nu }=\hbox {constant}\), is derived with two constants of integration. The tetrad field of this solution is axially symmetric and its associated metric gives Kerr space-time.

Chiral viscoelastic response in Weyl semimetals

We investigate the viscoelastic response of the electronic degrees of freedom in three-dimensional Weyl semimetals and obtain the effective action for this response. This action is derived by adapting Fujikawa's method on chiral anomaly in curved space for the most general Hamiltonian of Weyl semimetals. We clarify that the Weyl semimetal phase will give rise to the nontrivial chiral viscoelastic effect due to the perturbations of the tetrad field in the elastic media, which indicates that the crystal dislocations in Weyl semimetals will generate the energy-momentum current along the direction of dislocations which is analogous to the chiral magnetic effect predicted in electromagnetic response. And this nontrivial viscoelastic response can also be used to detect the properties of Weyl semimetals in the future.

Exact homogenous anisotropic solution in f(T) gravity theory

A diagonal, homogenous anisotropic, tetrad field involving two unknown functions of temporal coordinate is applied to the equations of motion of f(T) gravity theory. An exact solution with three constants of integration is obtained. The scalar torsion of this solution is constant. The parameters of cosmology are computed and some cosmological problems are analyzed. We show that our model is accelerated.

Charged axially-symmetric solution in f(T) gravity theory

In present article, an axially symmetric tetrad field has been applied to the charged field equations of f(T) gravity theory. Some constraints have been imposed to solve the resulting non-linear partial differential equations. An exact non-vacuum charged solution with three constants of integration is derived. The solution does not have non-trivial scalar torsion, $${\mathcal {T}}={T^i}_{jk}{S_i}^{jk}$$ . Total conserved charges, using Poincare gauge version, are calculated to understand the physical meaning of the three constants of integration. It has been shown that these constants are gravitational mass, angular momentum of the rotating source and charge parameter.

Schwarzschild-dS Solution in Modified Teleparallel Gravity Theories

A tetrad field, having one unknown function of radial coordinate r and an angle Φ which is a function of the azimuthal angle ϕ, is applied to the field equation of modified teleparallel theory of gravity with cosmological constant. Exact vacuum solution is derived whose scalar torsion, \(T = T_{\mu \nu }^{\alpha }S_{\alpha }^{\mu \nu }\), (where \(T_{\mu \nu }^{\alpha }\) is the torsion tensor and \(S_{\alpha }^{\mu \nu }\) is a tensor defined in terms of the contortion and torsion tensors), is vanishing. When the angle Φ coincides with the polar angle (−ϕ), another solution is derived whose scalar torsion is constant. The space-time of the derived solutions is rewritten as a multiplication of two matrices: The first matrix is a special case of Euler’s angle “so(3)” while the second matrix represents the square root of the spherically-symmetric-dS metric.

On the uniqueness of the Dirac theory in curved and flat spacetime

In this work a number of examples are used to illustrate uniqueness of physical prediction of the Dirac theory in a curved and a flat spacetime. Dirac Hamiltonians in arbitrary, including time‐dependent, gravitational fields uniquely determine physical characteristics of quantum‐mechanical systems irrespective of the choice of the tetrad fields. Direct spin‐rotation coupling that occurs with a certain choice of tetrads does not manifest itself in final physical characteristics of the systems and therefore does not represent a physically relevant effect.

Should There Be a Spin-Rotation Coupling for a Dirac Particle?

It was argued by Mashhoon that a spin-rotation coupling term should add to the Hamiltonian operator in a rotating frame, as compared with the one in an inertial frame. For a Dirac particle, the Hamiltonian and energy operators H and E were recently proved to depend on the tetrad field. We argue that this non-uniqueness of H and E really is a physical problem. We compute the energy operator in the inertial and the rotating frame, using three tetrad fields: one for each of two frameworks proposed to select the tetrad field so as to solve this non-uniqueness problem, and one proposed by Ryder. We find that Mashhoon's term is there if the tetrad rotates as does the reference frame --- but then it is also there in the energy operator for the inertial frame. In fact, the Dirac Hamiltonian operators in two reference frames in relative rotation, but corresponding to the same tetrad field, differ only by the angular momentum term. If the Mashhoon effect is to exist for a Dirac particle, the tetrad field must be selected in a specific way for each reference frame.

Schwarzschild-NUT solution in modified teleparallel gravity theory

Spherically symmetric tetrad field is applied to the field equation of modified teleparallel gravity theory. Some constraints are assumed on the resulting non-linear partial differential equations. Exact vacuum solution is derived with two constants of integration. The derived solution has a vanishing scalar torsion, i.e., T=T μ νλ S μ νλ =0 and its space-time is axially symmetric. It is shown that this solution can be rewritten as a product of three matrices, two local Lorentz transformations and one diagonal tetrad field. The local Lorentz transformations represent “so(3)” and a boost transformation and the diagonal tetrad reproduce the same metric field of the original tetrad.