arXiv subjects

J. W. Maluf

Publications and source records attributed to J. W. Maluf.

At least 19 recordsLinked to original sources

arXiv2026

The Role of Gravitational Energy Flux in Cosmic Acceleration

The article deals with the role of gravitational radiation energy in the large-scale dynamics of the universe. Motivated by the observed accelerated expansion, we investigate whether gravitational energy, treated as a well-defined physical quantity within the teleparallel equivalent of general relativity, contributes to cosmological acceleration through its associated energy flux. Using radiative space-times described by the Bondi--Sachs framework, we analyze the total gravitational energy and the corresponding energy flux evaluated in asymptotic regions. Particular emphasis is placed on the cumulative character of gravitational radiation over long time scales and on the fact that gravitational energy in this formulation is not positively definite. The present analysis provides a consistent theoretical basis for assessing the relevance of gravitational radiation energy and its flux in cosmological contexts.

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arXiv2026

Blueshift of light rays induced by gravitational wave memory effect

The article deals with photon propagation in pp-wave spacetimes in the strong gravitational-wave regime and its consequences for redshift measurements. We show that null geodesics crossing a localized pp-wave pulse exhibit an energy memory effect, producing a finite asymptotic shift in the photon frequency measured by static observers. This path-dependent contribution acts directly on the redshift observable and may help account for divergent interpretations of supernova redshift data in the presence of intervening gravitational radiation.

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arXiv2024

Energy of Gravitational Radiation and the Background Energy of the Space-Time

We address the issue of gravitational radiation in the context of the Bondi-Sachs space-time, and consider the expression for the gravitational energy of the radiation obtained in the realm of the teleparallel equivalent of general relativity (TEGR). This expression is independent of the radial distance (i.e., of powers of $1/r$) and depends exclusively on the functions $c(u,θ,ϕ)$ and $d(u,θ,ϕ)$, which yield the news functions ($u$ is the retarded time, $u=t-r$). We investigate the mathematical and physical features of this energy expression in the simpler framework of axial symmetry. Once a burst of gravitational radiation takes place in a self gravitating system, that leads to a loss of the Bondi mass, gravitational radiation is emitted throughout the whole space-time. The existence and presence of this radiation in the background structure of the space-time is consistent with the analysis developed by Papapetrou, and Hallidy and Janis, who found no proof that a gravitational system that emits a burst of gravitational radiation is preceded and followed by two stationary gravitational field configurations, namely, it seems that it is impossible for a gravitational system, which is initially stationary, to return to a stationary state after emitting a burst of axially symmetric gravitational radiation, in which case the space-time is not even asymptotically stationary. Therefore, it is plausible that the gravitational energy of radiation is present in the background structure of the space-time, and this is the energy predicted in the TEGR. This analysis lead us to conjecture that the noise detected in the large terrestrial gravitational wave observatories is intrinsically related to the background gravitational radiation.

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arXiv2024

The irreducible mass of a regular rotating black hole

This article presents an analysis of regular rotating black hole solutions within the framework of Teleparallel Equivalent to General Relativity (TEGR). The study evaluates the total energy and derives an analytical expression for the irreducible mass of a regular black hole. The results reveal the significance of these regular black holes as approximations of real astrophysical objects. The investigation explores the behavior of the total energy for different surfaces and its value at spatial infinity. Additionally, the article addresses the instability of the inner horizon and examines the inertial acceleration of an observer inside the inner horizon.

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arXiv2023

Tetrad Fields, Reference Frames, and the Gravitational Energy-Momentum in the Teleparallel Equivalent of General Relativity

We review the concept and definitions of the energy-momentum and angular momentum of the gravitational field in the teleparallel equivalent of general relativity (TEGR). The importance of these definitions is justified by three major reasons. First, the TEGR is a well established and widely accepted formulation of the gravitational field, whose basic field strength is the torsion tensor of the Weitzenböck connection. Second, in the phase space of the TEGR there exists an algebra of the Poincaré group. Not only the definitions of the gravitational energy-momentum and 4-angular momentum satisfy this algebra, but also the first class constraints related to these definitions satisfy the algebra. And third, numerous applications of these definitions lead to physically consistent results. These definitions follow from a well established Hamiltonian formulation, and rely on the idea of localization of the gravitational energy. In this review we revisit the concept of localizability of the gravitational energy, in light of results obtained in recent years. We have studied the behaviour of free particles in the space-time of plane fronted gravitational waves (pp-waves). Free particles are here understood as particles that are not subject to external forces other than the gravitational acceleration due to pp-waves. Since these particles acquire or loose kinetic energy locally, the transfer of energy from or to the gravitational field must also be localized. We consider this theoretical result an important and definite argument in favour of the localization of the gravitational energy-momentum, and by extension, of the gravitational 4-angular momentum.

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arXiv2023

On the Thermodynamics of Gravitational Radiation

This article deals with the thermodynamics of gravitational radiation arising from the Bondi-Sachs space-time. The equation of state found allows us to conclude that the dependence of the energy density on the temperature is a quadratic power of the latter. Such a conclusion is possible once the consequences of the first law of thermodynamics are analyzed. Then, in analogy to electromagnetic radiation, the same approach as used by Planck to obtain the quantum of energy of the gravitational radiation is proposed. An energy for the graviton proportional to the cubic frequency is found. The graviton is here understood as the quantum of gravitational energy.

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arXiv2023

Kerr-Schild Tetrads and the Nijenhuis Tensor

We write the Kerr-Schild tetrads in terms of the flat space-time tetrads and of a (1,1) tensor $S^λ_μ$. This tensor can be considered as a projection operator, since it transforms (i) flat space-time tetrads into non-flat tetrads, and vice-versa, and (ii) the Minkowski space-time metric tensor into a non-flat metric tensor, and vice-versa. The $S^λ_μ$ tensor and its inverse are constructed in terms of the standard null vector field $l_μ$ that defines the Kerr-Schild form of the metric tensor in general relativity, and that yields black holes and non-linear gravitational waves as solutions of the vacuum Einstein's field equations. We show that the condition for the vanishing of the Ricci tensor obtained by Kerr and Schild, in empty space-time, is also a condition for the vanishing of the Nijenhuis tensor constructed out of $S^λ_μ$. Thus, a theory based on the Nijenhuis tensor yields an important class of solutions of the Einstein's field equations, namely, black holes and non-linear gravitational waves. We also show that the present mathematical framework can easily admit modifications of the Newtonian potential that may explain the long range gravitational effects related to galaxy rotation curves.

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arXiv2022

On the Black Hole Acceleration in the C-metric Space-time

We consider the C-metric as a gravitational field configuration that describes an accelerating black hole in the presence of a semi-infinite cosmic string, along the accelerating direction. We adopt the expression for the gravitational energy-momentum developed in the teleparallel equivalent of general relativity (TEGR) and obtain a possible explanation for the acceleration of the black hole. The gravitational energy enclosed by surfaces of constant radius around the black hole is evaluated, and in particular the energy contained within the gravitational horizon is obtained. This energy turns out to be proportional to the square root of the area of the horizon. We find that the gravitational energy of the semi-infinite cosmic string is negative and dominant for large values of the radius of integration. This negative energy may explain the acceleration of the black hole, that moves towards regions of lower gravitational energy along the string.

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arXiv2022

On the total energy conservation of the Alcubierre spacetime

In this article, we consider the Alcubierre spacetime, such a spacetime describes a ``bubble'' that propagates with arbitrary global velocity. This setting allows movement at a speed greater than that of light. There are some known problems with this metric, e.g., the source's negative energy and the violation of the source's energy conservation when the bubble accelerates. We address these two issues within the realm of the Teleparallel Equivalent of General Relativity (TEGR). The energy conservation problem can be solved when considering the energy of the gravitational field itself. The total energy of the spacetime, gravitational plus source, is conserved even in accelerated motion. We explicitly show the dependence of energy and gravitational energy flux on the frame of reference, one adapted to a static observer and the other to a free-falling one in the same coordinate system. Addressing the problem of energy negativity of the source, we find that a static observer measures positive energy of the source, while an Eulerian observer measures a negative one. Thus, we surmise that negative energy may be a reference problem.

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arXiv2021

Perturbations of the Gravitational Energy in the TEGR: Quasinormal Modes of the Schwarzschild Black Hole

We calculate the gravitational energy spectrum of the perturbations of a Schwarzschild black hole described by quasinormal modes, in the framework of the teleparallel equivalent of general relativity (TEGR). We obtain a general formula for the gravitational energy enclosed by a large surface of constant radius $r$, in the region $m\,<<\,r\,<<\infty$, where $m$ is the mass of the black hole. Considering the usual asymptotic expression for the perturbed metric components, we arrive at finite values for the energy spectrum. The perturbed energy depends on the two integers $n$ and $l$ that describe the quasinormal modes. In this sense, the energy perturbations are discretised. We also obtain a simple expression for the decrease of the flux of gravitational radiation of the perturbations.

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arXiv2021

Non-linear Plane Gravitational Waves as Space-time Defects

We consider non-linear plane gravitational waves as propagating space-time defects, and construct the Burgers vector of the waves. In the context of classical continuum systems, the Burgers vector is a measure of the deformation of the medium, and at a microscopic (atomic) scale, it is a naturally quantized object. One purpose of the present article is ultimately to probe an alternative way on how to quantize plane gravitational waves.

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arXiv2020

A teleparallel type theory for massless spin 2 fields

We present the Lagrangian and Hamiltonian formulations of a theory for spin 2 fields. The construction is developed in flat space-time. The construction in curved space-time is conceptually straightforward, although it is not unique. The theory is based on a symmetric tensor $S_{μν}$, contains two degrees of freedom of radiation, is motivated by the teleparallel formulation of general relativity, and displays a certain resemblance with Maxwell's theory for the electromagnetic field.

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arXiv2020

Distorted Torsion Tensor, Teleparallelism and Spin 2 Field Equations

A notion of distorted torsion tensor was introduced by Okubo, in the establishment of the Nijenhuis-Bianchi identity and of BRST-like operators. These quantities are constructed with the help of the Nijenhuis tensor, which in turn is defined in terms of a (1,1) tensor $S^λ_μ$. This tensor enters the construction of the distorted torsion tensor. We use this tensor to extend the teleparallel equivalent of general relativity (TEGR) into a theory defined by the tetrad fields and by the tensor $S^λ_μ$. The ordinary TEGR is recovered if $S^λ_μ=δ^λ_μ$. We consider the flat space-time formulation of the theory, in terms of $S^λ_μ$ only, and show that this tensor satisfies the wave equation for massless spin 2 fields.

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arXiv2020

On the Quantization of Burgers Vector and Gravitational Energy in the Space-Time of a Conical Defect

A conical topological defect is the result of translational and/or rotational deformations of spacetime, in particular the Burgers vector describes the translational deformation. Such a configuration represents a discontinuity, that cannot be removed by coordinate transformations, and is related to the spacetime torsion. Using the Teleparallel Equivalent of General Relativity (TERG), a gravitational theory that is dynamically equivalent to General Relativity (GR), we investigate the consequences of assuming a discrete Burgers vector on the geodesic motion of particles around a static conical defect. The result is a helical geodesic motion of a test particle around the defect, with a discrete step that depends on the magnitude of the dislocation.

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arXiv2020

Difficulties of Teleparallel Theories of Gravity with Local Lorentz Symmetry

A brief discussion is made about the relevance of surface terms in the Lagrangian and Hamiltonian formulations of theories of gravity. These surface terms play an important role in the variation of the action integral and in the definition of field quantities such as the gravitational energy-momentum. Then we point out several inconsistencies of a recently proposed formulation of teleparallel theories of gravity with local Lorentz symmetry.

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arXiv2019

The Work-Energy Relation for Particles on Geodesics in the pp-Wave Spacetimes

A non-linear gravitational wave imparts gravitational acceleration to all particles that are hit by the wave. We evaluate this acceleration for particles in the pp-wave space-times, and integrate it numerically along the geodesic trajectories of the particles during the passage of a burst of gravitational wave. The time dependence of the wave is given by a Gaussian, so that the particles are free before and after the passage of the wave. The gravitational acceleration is understood from the point of view of a flat space-time, which is the initial and final gravitational field configuration. The integral of the acceleration along the geodesics is the analogue of the Newtonian concept of work per unit mass. Surprisingly, it yields almost exactly the variation of the non-relativistic kinetic energy per unit mass of the free particle. Therefore, the work-energy relation $ΔK = ΔW$ of classical Newtonian physics also holds for a particle on geodesics in the pp-wave space-times, in a very good approximation, and explains why the final kinetic energy of the particle may be smaller or larger than the initial kinetic energy.

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arXiv2018

Variations of the Energy of Free Particles in the pp-Wave Spacetimes

We consider the action of exact plane gravitational waves, or pp-waves, on free particles. The analysis is carried out by investigating the variations of the geodesic trajectories of the particles, before and after the passage of the wave. The initial velocities of the particles are non-vanishing. We evaluate numerically the Kinetic energy per unit mass of the free particles, and obtain interesting, quasi-periodic behaviour of the variations of the Kinetic energy with respect to the width $λ$ of the gaussian that represents the wave. The variation of the energy of the free particle is expected to be exactly minus the variation of the energy of the gravitational field, and therefore provides an estimation of the local variation of the gravitational energy. The investigation is carried out in the context of short bursts of gravitational waves, and of waves described by normalised gaussians, that yield impulsive waves in a certain limit.

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arXiv2018

Kinetic Energy and Angular Momentum of Free Particles in the Gyratonic pp-Waves Space-times

Gyratonic pp-waves are exact solutions of Einstein's equations that represent non-linear gravitational waves endowed with angular momentum. We consider gyratonic pp-waves that travel in the $z$ direction and whose time dependence on the variable $u={1 \over \sqrt{2}}(z-t)$ is given by gaussians, so that the waves represent short bursts of gravitational radiation propagating in the $z$ direction. We evaluate numerically the geodesics and velocities of free particles in the space-time of these waves, and find that after the passage of the waves both the kinetic energy and the angular momentum per unit mass of the particles are changed. Therefore there is a transfer of energy and angular momentum between the gravitational field and the free particles, so that the final values of the energy and angular momentum of the free particles may be smaller or larger in magnitude than the initial values.

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