Regularized expression for the gravitational energy-momentum in teleparallel gravity and the principle of equivalence

The expression of the gravitational energy-momentum defined in the context of the teleparallel equivalent of general relativity is extended to an arbitrary set of real-valued tetrad fields, by adding a suitable reference space subtraction term. The characterization of tetrad fields as reference frames is addressed in the context of the Kerr space–time. It is also pointed out that Einstein’s version of the principle of equivalence does not preclude the existence of a definition for the gravitational energy-momentum density.     

Gravitational leptogenesis in teleparallel and symmetric teleparallel gravities

In this study, we investigate the possibilities of generating baryon number asymmetry under thermal equilibrium within the frameworks of teleparallel and symmetric teleparallel gravities. Through the derivative couplings of the torsion scalar and the non-metricity scalar to baryons, baryon number asymmetry is produced in the radiation dominated epoch. For gravitational baryogenesis mechanisms in these two frameworks, the produced baryon-to-entropy ratio is too small to be consistent with observations. However, the gravitational leptogenesis models within both frameworks have the potential to explain the observed baryon-antibaryon asymmetry.     

Gravitational pressure,apparent horizon and thermodynamics of FLRW universe in the teleparallel gravity

In the context of the teleparallel equivalent of general relativity the concept of gravitational pressure and gravitational energy-momentum arisen in a natural way. In the case of a Friedmann–Lemaitre–Robertson–Walker space FLRW we obtain the total energy contained inside the apparent horizon and the radial pressure over the apparent horizon area. We use these definitions to written a thermodynamics relation \(T_{A}dS_{A} = dE_{A}+P_{A}dV_{A}\) at the apparent horizon, where \(E_{A}\) is the total energy inside the apparent horizon, \(V_{A}\) is the areal volume of the apparent horizon, \(P_{A}\) is the radial pressure over the apparent horizon area, \(S_{A}\) is the entropy which can be assumed as one quarter of the apparent horizon area only for a non stationary apparent horizon. We identify \(T_{A}\) as the temperature at the surface of the apparent horizon. We shown that for all expanding accelerated FLRW model of universe the radial pressure is positive.     

Holographic renormalization in teleparallel gravity

We consider the problem of IR divergences of the action in the covariant formulation of teleparallel gravity in asymptotically Minkowski spacetimes. We show that divergences are caused by inertial effects and can be removed by adding an appropriate surface term, leading to the renormalized action. This process can be viewed as a teleparallel analog of holographic renormalization. Moreover, we explore the variational problem in teleparallel gravity and explain how the variation with respect to the spin connection should be performed.     

Matter stability in modified teleparallel gravity

We study the matter stability in modified teleparallel gravity or f(T)$f(T)$ theories. We show that there is no Dolgov–Kawasaki instability in these types of modified teleparallel gravity theories. This gives for the f(T)$f(T)$ theories a great advantage over their f(R)$f(R)$ counterparts because from the stability point of view there isn?t any limit on the form of functions that can be chosen.     

Gravitational energy-momentum densities of arbitrary weight

Various familiar expressions for the gravitational energy-momentum complex are derived from a generalised superpotential for arbitrary weight.     

Gravitational energy-momentum: The Einstein pseudotensor reexamined

By using a suitable two-point scalar field, a covariant formulation of the Einstein pseudotensor is given. A unique choice of scalar field is made possible by examining the role of linear and angular momentum in their correct geometric context. It is shown that, contrary to many text-book statements, linear momentum is not generated by infinitesimal coordinate transformations on space-time. Use is made of the nonintersecting lifted geodesies on the tangent bundle,T M, to space-time, to define a globally regular three-dimensional Lagrangian submanifold ofT M, relative to an observer at some pointz in space-time. By integrating over this submanifold rather than a necessarily singular spacelike hypersurface, gravitational linear and angular momentum, relative toz, are defined, and shown to have sensible physical properties.This essay received an honorable mention from the Gravity Research Foundation for the year 1979-Ed.     

Energy conditions in generalized teleparallel gravity models

In this paper, we investigate the energy conditions (including null, weak, strong, dominant) in generalized teleparallel gravities including pure $F(T)$ , teleparallel gravity with non-minimally coupled scalar field and $F(T)$ with non-minimally coupled scalar field models. In particular, we apply them to Friedmann–Robertson–Walker cosmology and obtain some corresponding results. Using two specific phenomenological forms of $F(T)$ , we show that some of the energy conditions are violated.     

Gravastar in the framework of symmetric teleparallel gravity

We present a novel gravastar model based on the Mazur-Mottola (2004) method with an isotropic matter distribution in \begin{document}$ f(Q) $\end{document} gravity. The gravastar, which is a hypothesized substitute for a black hole, is built using the Mazur-Mottola mechanism. This approach allows us to define the gravastar as having three stages. The first one is an inner region with negative pressure; the next region is a thin shell that is made up of ultrarelativistic stiff fluid, and we studied the proper length, energy, entropy, and surface energy density for this region. Additionally, we demonstrated the possible stability of our suggested thin shell gravastar model through the graphical study of the surface redshift. The exterior Schwarzschild geometry describes the outer region of the gravastar. In the context of \begin{document}$ f(Q) $\end{document} gravity, we discovered analytical solutions for the interior of gravastars that are free of any type of singularity and the event horizon.     

Dark energy cosmology with tachyon field in teleparallel gravity

We construct a tachyon teleparallel dark energy model for a homogeneous and isotropic flat universe in which a tachyon as a non-canonical scalar field is non-minimally coupled to gravity in the framework of teleparallel gravity. The explicit form of potential and coupling functions are obtained under the assumption that the Lagrangian admits the Noether symmetry approach. The dynamical behavior of the basic cosmological observables is compared to recent observational data, which implies that the tachyon field may serve as a candidate for dark energy.     

ADM-like Hamiltonian formulation of gravity in the teleparallel geometry

We present a new Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) meant to serve as the departure point for canonical quantization of the theory. TEGR is considered here as a theory of a cotetrad field on a spacetime. The Hamiltonian formulation is derived by means of an ADM-like $3+1$ decomposition of the field and without any gauge fixing. A complete set of constraints on the phase space and their algebra are presented. The formulation is described in terms of differential forms.     

Gravitational radiation in quantum gravity

The effective field theory of quantum gravity generically predicts non-locality to be present in the effective action, which results from the low-energy propagation of gravitons and massless matter. Working to second order in gravitational curvature, we reconsider the effects of quantum gravity on the gravitational radiation emitted from a binary system. In particular, we calculate for the first time the leading order quantum gravitational correction to the classical quadrupole radiation formula which appears at second order in Newton’s constant.     

Nonlinear electrodynamics coupled to teleparallel theory of gravity

Using nonlinear electrodynamics coupled to teleparallel theory of gravity, regular charged spherically symmetric solutions are obtained. The nonlinear theory is reduced to the Maxwell one in the weak limit and the solutions correspond to charged spacetimes. One of the obtained solutions contains an arbitrary function which we call general solution since we can generate from it the other solutions. The metric associated with these spacetimes is the same, i.e., regular charged static spherically symmetric black hole. In calculating the energy content of the general solution using the gravitational energy--momentum within the framework of the teleparallel geometry, we find that the resulting form depends on the arbitrary function. Using the regularized expression of the gravitational energy--momentum we obtain the value of energy.     

Dynamical instability of shear-free collapsing star in extended teleparallel gravity

We study the spherically symmetric collapsing star in terms of dynamical instability. We take the framework of extended teleparallel gravity with a non-diagonal tetrad, a power-law form of the model presenting torsion and a matter distribution as a non-dissipative anisotropic fluid. The vanishing shear scalar condition is adopted to gain insight in a collapsing star. We apply a first order linear perturbation scheme to the metric, the matter, and f(T) functions. The dynamical equations are formulated under this perturbation scheme to develop collapsing equation for finding dynamical instability limits in two regimes, such as the Newtonian and the post-Newtonian regime. We obtain a constraint-free solution of a perturbed time dependent part with the help of a vanishing shear scalar. The adiabatic index exhibits the instability ranges through the second dynamical equation which depend on physical quantities such as the density, the pressure components, the perturbed parts of the symmetry of the star, etc. We also develop some constraints on the positivity of these quantities and obtain instability ranges to satisfy the dynamical instability condition.     

Gravitational radiation fields in teleparallel equivalent of general relativity and their energies

We derive two new retarded solutions in the teleparallel theory equivalent to general relativity (TEGR).One of these solutions gives a divergent energy.Therefore,we use the regularized expression of the gravitational energymomentum tensor,which is a coordinate dependent.A detailed analysis of the loss of the mass of Bondi space-time is carried out using the flux of the gravitational energy-momentum.     

Dynamics of charged anisotropic spherical collapse in energy-momentum squared gravity

This paper investigates the dynamics of charged spherical collapse with anisotropic matter configuration in the context of energy-momentum squared gravity. This newly developed proposal resolves the big-bang singularity and yields the physically viable cosmological results in the early time universe. We establish dynamical equations through Misner-Sharp technique and analyze the effects of charge, anisotropy, effective matter variables and dark source terms on the collapse rate. A relation between Weyl scalar, fluid parameters and dark source terms is also established. The spacetime is not conformally flat due to the presence of anisotropic pressure, multivariate functions and their derivatives. In order to obtain conformally flat spacetime, we consider a specific model of this gravity, neglect the impact of charge and assume the isotropic matter distribution which yields homogeneity of the energy density and conformally flat spacetime. We conclude that positive dark source terms, anisotropy and charge yield the action of a repulsive force which enhances the stability of the system and hence diminishes the collapse rate.     

Gravitational energy of a magnetized Schwarzschild black hole: a teleparallel approach

We investigate the distribution of gravitational energy in the spacetime of a Schwarzschild black hole immersed in a cosmic magnetic field. This is done in the context of the teleparallel equivalent of general relativity, which is an alternative geometrical formulation of general relativity, where gravity is described by a spacetime endowed with torsion rather than curvature, whose fundamental field variables are tetrad fields. We calculate the energy enclosed by a two-surface of constant radius—in particular, the energy enclosed by the event horizon of the black hole. In this case we find that the magnetic field has the effect of increasing the gravitational energy as compared to the vacuum Schwarzschild case. We also compute the energy (i) in the weak magnetic field limit, (ii) in the limit of vanishing magnetic field, and (iii) in the absence of the black hole. In all cases our results are consistent with what should be expected on physical grounds.     

Gravitational collapse with standard and dark energy in the teleparallel equivalent of general relativity

A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity(TEGR).A spacetime which is not asymptotically flat is derived.The energy conditions of this spacetime are studied.It is shown that after some time the strong energy condition is not enough to satisfy showing a transition from standard matter to dark energy.The singularities of this solution are discussed.