arXiv subjects

J. F. da Rocha-Neto

Publications and source records attributed to J. F. da Rocha-Neto.

At least 19 recordsLinked to original sources

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

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 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

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

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

Energy-momentum and angular-momentum of a gyratonic pp-waves spacetime

Gyratonic plane fronted gravitational waves are exact solutions of Einstein's field equations, which correspond to gravitational waves that carry momentum and angular-momentum. Using the definitions of the Hamiltonian formulation of the Teleparallel Equivalent of General Relativity, we explicitly evaluate the general expressions of the energy-momentum and angular-momentum of these space-times. In order to better understand the additional properties of these gravitational waves, we consider the motion of particles in this space-time and obtain an interesting relation between the angular-momentum of the particles and that of the gravitational waves.

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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

Gravitational Pressure and the Accelerating Universe

In the context of the Teleparallel Equivalent of General Relativity (TEGR) one can obtain an alternative insight into General Relativity, as has been shown in addressing properties as energy, momentum and angular momentum of the gravitational field. In this paper, we apply the definition, that arises from the field equation of the the TEGR, for the stress-energy-momentum tensor of the gravitational field, whose spatial components naturally lead to the definition of gravitational pressure, to compute the total space-time pressure, due to the gravitational and matter fields, over a spherical, space-like two-surface of a Friedman-Robertson-Walker (FRW) universe, for any curvature index. In particular, for a spatially flat FRW universe in the actual era (i.e., for "cold matter"), it resulted that the pressure (now due only to the gravitational field) is outwardly directed over any spherical, spatial two-surface. This surface can be, in particular, the apparent horizon of a spatially flat FRW universe (in this case, the apparent horizon coincides with the Hubble horizon). Assuming the validity of the first law of thermodynamics for matter and gravity, and taking into account the contribution of the gravitational field to both the energy and the pressure terms in the first law of the (gravitational) thermodynamics, as well as considering the thermal character of the apparent horizon of the spatially flat FRW universe, we have thus obtained a value of the gravitational pressure that is very close to the observed value. We interpret this result as a possibility that the accelerated expansion of the actual universe might be due to the effect of the pressure of the very gravitational field, instead of an totally unkown (dark) energy.

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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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arXiv2018

Plane Gravitational Waves, the Kinetic Energy of Free Particles and the Memory Effect

It is shown that in the passage of a short burst of non-linear plane gravitational wave, the kinetic energy of free particles may either decrease or increase. The decreasing or increasing of the kinetic energy depends crucially on the initial conditions (position and velocity) of the free particle. Therefore a plane gravitational wave may extract energy from a physical system.

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arXiv2018

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.

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arXiv2013

Gravitational energy, gravitational pressure, and the thermodynamics of a charged black hole in teleparallel gravity

We investigate, in the case of a Reissner-Nordström black hole, the definitions of gravitational energy and gravitational pressure that naturally arise in the framework of the Teleparallel Equivalent of General Relativity. In particular, we calculate the gravitational energy enclosed by the event horizon of the black hole, E, and the radial pressure over it, p. With these quantities we then analyse the thermodynamic relation dE + pdV (as p turns out to be a density, dV is actually given by dV = dr dθdϕ, in spherically-type coordinates). We compare the latter with the standard first law of black hole dynamics. Also, by identifying TdS = dE + pdV, we comment on a possible modification of the standard, Bekenstein-Hawking entropy-area relation due to gravitational energy and gravitational pressure of the black hole. The infinitesimal variations in question refer to the Penrose process for a Reissner-Nordström black hole.

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arXiv2013

Gravitational waves and the breaking of parallelograms in space-time

We show that plane-fronted gravitational waves induce the breaking of parallelograms in space-time, in the context of the teleparallel equivalent of general relativity (TEGR). The breaking of parallelograms can be shown by considering a thought experiment that consists of a simple physical configuration, similar to the experimental setup that is expected to lead to the measurement of gravitational waves with the use of laser interferometers. An incident beam of light splits into two beams running along perpendicular arms, endowed with fixed mirrors at the extremes. The reflected light beams are detected at the same point of the splitting. Along each arm, the two light beams define two null vectors: the forward vector and the reflected vector. We show that the sum of these four vectors, the forward and reflected null vectors along the two arms, do form a parallelogram in flat space-time, but not in the presence of plane-fronted gravitational waves. The non-closure of the parallelogram is a manifestation of the torsion of the space-time, and in this context indicates the existence of gravitational waves.

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arXiv2012

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

We investigate the distribution of gravitational energy on the spacetime of a Schwarzschild black hole immersed in a cosmic magnetic field. This is done in the context of the {\it Teleparallel Equivalent of General Relativity}, which is an alternative geometrical formulation of General Relativity, where gravity is describe by a spacetime endowed with torsion, rather than curvature, with the fundamental field variables being tetrads. 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.

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