The gravitational energy

We present the expression $t_{\mu\nu}$ of the energy-momentum tensor of the gravitational field in the framework of the recent proposal of the Geometric Scalar theory of gravity (GSG). From the conservation of $t_{\mu\nu}$ it follows the dynamics of the gravitational field. As an example of this expression for $t_{\mu\nu}$ we calculate the gravitational energy of a compact object.Comment: 8 page

Dragged Metrics

We show that the path of any accelerated body in an arbitrary space-time geometry $g_{\mu\nu}$ can be described as geodesics in a dragged metric $\hat{q}_{\mu\nu}$ that depends only on the background metric and on the motion of the body. Such procedure allows the interpretation of all kind of non-gravitational forces as modifications of the metric of space-time. This method of effective elimination of the forces by a change of the metric of the substratum can be understood as a generalization of the d'Alembert principle applied to all relativistic processes

The gravitational mechanism to generate mass II

With the eminent confirmation or disproof of the existence of Higgs boson by experiments on the LHC it is time to analyze in a non-dogmatic way the suggestions to understand the origin of the mass. Here we analyze the recent proposal according to which gravity is what is really responsible for the generation of mass of all bodies. The great novelty of such mechanism is that the gravitational field acts merely as a catalyst, once the final expression of the mass does not depend either on the intensity or on the particular characteristics of the gravitational field.Comment: This is the further development of previous article (The gravitational mechanism to generate mass, arXiv:1008.2371) which appeared in Classical and Quantum Gravity 28 (2011) 03500

What is the origin of the mass of the Higgs boson?

The purpose of this paper is to present a unified description of mass generation mechanisms that have been investigated so far and that are called the Mach and Higgs proposals. In our mechanism, gravity acts merely as a catalyst and the final expression of the mass depends neither on the intensity nor on the particular properties of the gravitational field. We shall see that these two strategies to provide mass for all bodies that operate independently and competitively can be combined into a single unified theoretical framework. As a consequence of this new formulation we are able to present an answer to the question: what is the origin of the mass of the Higgs boson?Comment: 7 pages. arXiv admin note: substantial text overlap with arXiv:1111.4228, arXiv:1008.237

Friedmann-like solutions with a non-vanishing Weyl tensor

We have solved the Einstein equations of general relativity for a class of metrics with constant spatial curvature and found a non-vanishing Weyl tensor in the presence of an energy-momentum tensor with an anisotropic pressure component. The time evolution of the spacetime is guided by the usual Friedmann equations and the constraints on the hypersurface comprise a separated system of equations that can be independently solved. Contrary to the apparent behavior induced by some choices of coordinates, the metric we have obtained is completely regular everywhere and is free of singularities (except the well-known Friedmann singularity at $t=0$). The physical features of this solution are elucidated by using the Quasi-Maxwellian equations (a set of third order differential equations describing the dynamics of the gravitational field in terms of the Weyl tensor). The motion of test particles is also analyzed in order to confirm the maximal extension of the manifold under consideration. These results indicate that the anisotropic pressure could mimic dark matter effects on certain geodesic congruences keeping the cosmic flow unchanged.Comment: We did a proof-reading of the previous version and now we include a more detailed discussion of our result

The Quasi-Maxwellian Equations of General Relativity: Applications to the Perturbation Theory

A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is made. Our main interest concerns its applications to the analysis of the perturbation of standard cosmology in the Friedman-Lema\^itre-Robertson-Walker framework. The major achievement of the QM scheme is its use of completely gauge independent quantities. We shall see that in the QM-scheme we deal directly with observable quantities. This reveals its advantage over the old method introduced by Lifshitz et al that deals with perturbation in the standard Einstein framework. For completeness, we compare the QM-scheme to the gauge-independent method of Bardeen, a procedure consisting on particular choices of the perturbed variables as a combination of gauge dependent quantities.Comment: The main goal of this review is to make a little more popular the use of the JEK frame in the realm of perturbation theory of Friedman universes. Indeed, the Lifshitz-Bardeen method and the JEK frame give the same results for the perturbations in the linear regime. The main interest on JEK rests on its unambiguous way to deal with perturbation within the cosmological FLRW scenari

Dynamical Wormhole Definitions Confronted

Crude comparison between four alternative proposals for the very definition of a wormhole is provided, all of which were intended to apply to the dynamical cases. An interesting dynamical solution, based upon large scale magnetic fields, is used for the comparisons. Such solution goes beyond the perfect fluid approximation due to an anisotropic pressure component, bringing to the fore some unsuspected features of those definitions. Certain notions as reversible traversability are claimed as a way to select among those definitions the best suited one to represent our intuition of what a wormhole solution is expected to be.Comment: 14 pages, 21 figure

Lattice-layer entanglement in Bernal-stacked bilayer graphene

The complete lattice-layer entanglement structure of Bernal stacked bilayer graphene is obtained for the quantum system described by a tight-binding Hamiltonian which includes mass and bias voltage terms. Through a suitable correspondence with the parity-spin $SU(2)\otimes SU(2)$ structure of a Dirac Hamiltonian, when it brings up tensor and pseudovector external field interactions, the lattice-layer degrees of freedom can be mapped into such a parity-spin two-qubit basis which supports the interpretation of the bilayer graphene eigenstates as entangled ones in a lattice-layer basis. The Dirac Hamiltonian mapping structure simply provides the tools for the manipulation of the corresponding eigenstates and eigenenergies of the Bernal-stacked graphene quantum system. The quantum correlational content is then quantified by means of quantum concurrence, in order to have the influence of mass and bias voltage terms quantified, and in order to identify the role of the trigonal warping of energy in the intrinsic entanglement. Our results show that while the mass term actively suppresses the intrinsic quantum entanglement of bilayer eigenstates, the bias voltage term spreads the entanglement in the Brillouin zone around the Dirac points. In addition, the interlayer coupling modifies the symmetry of the lattice-layer quantum concurrence around a given Dirac point. It produces some distortion on the quantum entanglement profile which follows the same pattern of the isoenergy line distortion in the Bernal-stacked bilayer graphene.Comment: 24 pages, 8 figure

The Cν\nuB energy density through the quantum measurement theory

We apply concepts from the quantum measurement theory to obtain some cosmological neutrino background (C$\nu$B) properties and discuss their relevance in defining theoretical bounds on cosmological neutrino energy density. Describing three neutrino generations as a composite quantum system through the generalized theory of quantum measurement provides us with the probabilistic correlation between observable energies and neutrino flavor eigenstates. By observing that flavor-averaged and flavor-weighted energies are the quantum observables respectively generated by selective and non-selective quantum measurement schemes, it is possible to identify the constraints on the effective mass value expression that determines the neutrino contribution to the energy density of the cosmic inventory. Our results agree with the quantum mechanics viewpoint that asserts that the cosmological neutrino energy density is obtained from a coherent sum of mass eigenstate energies, for normal and inverted mass hierarchies.Comment: 19 pages, 5 figures, for completeness, in the Appendix, we have added the contents related to Quantum Measurement schemes reproduced from arXiv:1104.3120 of one of the authors of this manuscript (Alex E. Bernardini). The credits/quotations are consistent and accurately given to arXiv:1104.3120. The authors suggest the reading of arXiv:1104.3120 as a background for the present manuscrip

Entanglement of Dirac bi-spinor states driven by Poincar\'e classes of \mbox{SU}(2) \otimes \mbox{SU}(2) coupling potentials

A generalized description of entanglement and quantum correlation properties constraining internal degrees of freedom of Dirac(-like) structures driven by arbitrary Poincar\'e classes of external field potentials is proposed. The role of (pseudo)scalar, (pseudo)vector and tensor interactions in producing/destroying intrinsic quantum correlations for \mbox{SU}(2) \otimes \mbox{SU}(2) bi-spinor structures is discussed in terms of generic coupling constants. By using a suitable ansatz to obtain the Dirac Hamiltonian eigenspinor structure of time-independent solutions of the associated Liouville equation, the quantum entanglement, via concurrence, and quantum correlations, via geometric discord, are computed for several combinations of well-defined Poincar\'e classes of Dirac potentials. Besides its inherent formal structure, our results setup a framework which can be enlarged as to include localization effects and to map quantum correlation effects into Dirac-like systems which describe low-energy excitations of graphene and trapped ions.Comment: 29 pages, 8 figure