Energy and Momentum densities of cosmological models, with equation of state ρ=μ\rho=\mu, in general relativity and teleparallel gravity

We calculated the energy and momentum densities of stiff fluid solutions, using Einstein, Bergmann-Thomson and Landau-Lifshitz energy-momentum complexes, in both general relativity and teleparallel gravity. In our analysis we get different results comparing the aforementioned complexes with each other when calculated in the same gravitational theory, either this is in general relativity and teleparallel gravity. However, interestingly enough, each complex's value is the same either in general relativity or teleparallel gravity. Our results sustain that (i) general relativity or teleparallel gravity are equivalent theories (ii) different energy-momentum complexes do not provide the same energy and momentum densities neither in general relativity nor in teleparallel gravity. In the context of the theory of teleparallel gravity, the vector and axial-vector parts of the torsion are obtained. We show that the axial-vector torsion vanishes for the space-time under study.Comment: 15 pages, no figures, Minor typos corrected; version to appear in International Journal of Theoretical Physic

Nonlinear Gravitational Waves: Their Form and Effects

A gravitational wave must be nonlinear to be able to transport its own source, that is, energy and momentum. A physical gravitational wave, therefore, cannot be represented by a solution to a linear wave equation. Relying on this property, the second-order solution describing such physical waves is obtained. The effects they produce on free particles are found to consist of nonlinear oscillations along the direction of propagation.Comment: 15 pages, no figures. v2: presentation changes aiming at clarifying the text; matches published versio

Energy and Momentum Distributions of Kantowski and Sachs Space-time

We use the Einstein, Bergmann-Thomson, Landau-Lifshitz and Papapetrou energy-momentum complexes to calculate the energy and momentum distributions of Kantowski and Sachs space-time. We show that the Einstein and Bergmann-Thomson definitions furnish a consistent result for the energy distribution, but the definition of Landau-Lifshitz do not agree with them. We show that a signature switch should affect about everything including energy distribution in the case of Einstein and Papapetrou prescriptions but not in Bergmann-Thomson and Landau-Lifshitz prescriptions.Comment: 12 page

A General Relativistic Model for Magnetic Monopole-Infused Compact Objects

Emergent concepts from astroparticle physics are incorporated into a classical solution of the Einstein-Maxwell equations for a binary magnetohydrodynamic fluid, in order to describe the final equilibrium state of compact objects infused with magnetic monopoles produced by proton-proton collisions within the intense dipolar magnetic fields generated by these objects during their collapse. It is found that the effective mass of such an object's acquired monopolar magnetic field is three times greater than the mass of its native fluid and monopoles combined, necessitating that the interior matter undergo a transition to a state of negative pressure in order to attain equilibrium. Assuming full symmetry between the electric and magnetic Maxwell equations yields expressions for the monopole charge density and magnetic field by direct analogy with their electrostatic equivalents; inserting these into the Einstein equations then leads to an interior metric which is well-behaved from the origin to the surface, where it matches smoothly to an exterior magnetic Reissner-Nordstr\"om metric free of any coordinate pathologies. The source fields comprising the model are all described by simple, well-behaved polynomial functions of the radial coordinate, and are combined with straightforward regularity conditions to yield expressions delimiting several fundamental physical parameters pertaining to this hypothetical astrophysical object.Comment: Accepted for publication in "Astrophysics and Space Science.

General Relativistic Singularity-Free Cosmological Model

We "explain", using a Classical approach, how the Universe was created out of "nothing", i.e., with no input of initial energy nor mass. The inflationary phase, with exponential expansion, is accounted for, automatically, by our equation of state for the very early Universe. This is a Universe with no-initial infinite singularity of energy density.Comment: Astrophysics and Space Science, 321,157 (2009

The Pioneer Anomaly and a Machian Universe

We discuss astronomical and astrophysical evidence, which we relate to the principle of zero-total energy of the Universe, that imply several relations among the mass M, the radius R and the angular momentum L of a "large" sphere representing a Machian Universe. By calculating the angular speed, we find a peculiar centripetal acceleration for the Universe. This is an ubiquituous property that relates one observer to any observable. It turns out that this is exactly the anomalous acceleration observed on the Pioneers spaceships. We have thus, shown that this anomaly is to be considered a property of the Machian Universe. We discuss several possible arguments against our proposal.Comment: 6 pages including front page. Publishe

The gravitational interaction of light: from weak to strong fields

An explanation is proposed for the fact that pp-waves superpose linearly when they propagate parallely, while they interact nonlinearly, scatter and form singularities or Cauchy horizons if they are antiparallel. Parallel pp-waves do interact, but a generalized gravitoelectric force is exactly cancelled by a gravitomagnetic force. In an analogy, the interaction of light beams in linearized general relativity is also revisited and clarified, a new result is obtained for photon to photon attraction, and a conjecture is proved. Given equal energy density in the beams, the light-to-light attraction is twice the matter-to-light attraction and four times the matter-to-matter attraction.Comment: 17 pages, LaTeX, no figures. To appear in General Relativity and Gravitatio

Energy and Momentum Densities Associated with Solutions Exhibiting Directional Type Singularities

We obtain the energy and momentum densities of a general static axially symmetric vacuum space-time described by the Weyl metric, using Landau-Lifshitz and Bergmann-Thomson energy-momentum complexes. These two definitions of the energy-momentum complex do not provide the same energy density for the space-time under consideration, while give the same momentum density. We show that, in the case of Curzon metric which is a particular case of the Weyl metric, these two definitions give the same energy only when $R \to \infty$. Furthermore, we compare these results with those obtained using Einstein, Papapetrou and M{\o}ller energy momentum complexes.Comment: 10 pages, references added, minor corrections [Admin note: substantial overlap with gr-qc/0403097 , gr-qc/0403039

Gravitational Collapse of Null Radiation and a String fluid

We consider the end state of collapsing null radiation with a string fluid. It is shown that, if diffusive transport is assumed for the string, that a naked singularity can form (at least locally). The model has the advantage of not being asymptotically flat. We also analyse the case of a radiation-string two-fluid and show that a locally naked singularity can result in the collapse of such matter. We contrast this model with that of strange quark matter.Comment: RevTeX 4.0 (8 pages - no figures). submitted to Phys Rev D. Some changes to abstract, introduction and conclusion - references update

The averaged tensors of the relative energy-momentum and angular momentum in general relativity and some their applications

There exist at least a few different kind of averaging of the differences of the energy-momentum and angular momentum in normal coordinates {\bf NC(P)} which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [1-8] giving the {\it canonical superenergy and angular supermomentum tensors}. In this paper we present another averaging of the differences of the energy-momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy-momentum and angular momentum densities. But these averaged relative energy-momentum and angular momentum tensors, closely related to the canonical superenergy and angular supermomentum tensors, {\it depend on some fundamental length $L>0$}. The averaged relative energy-momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to {\it coordinate independent} analysis (local and in special cases also global) of this field. We have applied the averaged relative energy-momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general) universes. The obtained results are very interesting, e.g., the averaged relative energy density is {\it positive definite} for the all Friedman universes.Comment: 30 pages, minor changes referring to Kasner universe