arXiv subjects

F. L. Carneiro

Publications and source records attributed to F. L. Carneiro.

At least 19 recordsLinked to original sources

arXiv2026

Analytical and spectral characterization of floral patterns in higher-order polynomial pp-waves

We investigate analytically and numerically the floral deformation of particle rings induced by higher-order polynomial modes of pp-waves. The transverse tidal eigendirections determine $m$ interlaced sectors of radial stretching and compression, while a weak-pulse solution provides the complete first-order response of the ring. Direct geodesic integration for $m=2,3,4$ confirms the predicted orientation and discrete symmetry. A Fourier analysis shows that the response remains overwhelmingly dominated by the angular mode $n=m$; in particular, the loops found for $m=4$ arise from geometrical folding of the fundamental mode rather than strong harmonic mixing. The temporal moments of the pulse further distinguish displacement from velocity memory without changing this angular signature.

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arXiv2026

On correlated noise in the LIGO-Virgo network: a test of the stochastic gravitational-wave background hypothesis

We revisit the inter-detector cross-correlation criterion used in gravitational-wave validation by extending the analysis of Creswell et al.~\cite{Creswell2017} to nine LIGO--Virgo candidate events from the O2 and O3 observing runs. For each event, we analyze all three detector pairs (H1$\times$L1, H1$\times$V1, L1$\times$V1) and compare the normalized cross-correlation function $C(τ)$ in the event window with an empirical ensemble of $N=200$ surrounding off-source windows, using a band-pass-only pipeline. In 26 of 27 pair-measurements, the event peak is statistically indistinguishable from the corresponding noise ensemble, including all pairs involving the independent Virgo detector. The only exception is GW190412 in the H1$\times$L1 pair. We conclude that the cross-correlation statistic does not provide a robust standalone separation between event and noise. We interpret the persistence of comparable correlation structure in the LIGO--Virgo pairs as evidence that the strain data may contain a continuous correlated physical component, for which a stochastic gravitational-wave background is a plausible candidate.

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arXiv2026

Maxwell equations in Schwarzschild spacetime for static and freely falling observers

Classical electrodynamics in curved spacetime is formulated within a tetrad-based framework that preserves the direct physical interpretation of the electromagnetic fields measured by an observer. The formalism is applied to Schwarzschild spacetime for two distinct families of observers described in the same coordinate system: static observers and radially free-falling observers. For static observers, Maxwell equations retain their usual spherical structure, while the gravitational field introduces geometrical corrections in the radial and temporal sectors through the metric function. These corrections are interpreted in terms of proper radial distance, proper time, and the radial variation of the lapse function. For radially free-falling observers, additional kinematical contributions arise from the local radial boost relating the free-falling frame to the static one. As a consequence, charge density mixes with radial current, and the electric and magnetic sectors become intertwined in the temporal-radial projections of Maxwell equations, whereas the angular Ampère-Maxwell and Faraday equations retain the same structure found for the static observer. The weak-field and near-horizon regimes are also examined, and the results are discussed through an effective-medium analogy, in which the Schwarzschild geometry behaves as an inhomogeneous geometrical medium at rest for static observers and as a radially moving effective medium in the temporal-radial sector for free-falling observers.

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arXiv2026

On the Gravitational Energy of Axial Perturbations in Regular Black Holes

The article deals with the gravitational energy associated with axial perturbations of regular black holes. We review the stability of the geometry under odd-parity perturbations and the corresponding quasinormal modes, previously obtained for this class of spacetimes. The perturbative functions describing the metric fluctuations are reconstructed from the master equation. To evaluate the energy content of these perturbations, we employ the Teleparallel Equivalent of General Relativity (TEGR), which provides a well-defined expression for gravitational energy. The gravitational energy is computed up to second order in the perturbation parameter and expressed in terms of the quasinormal mode functions. Our results establish a direct connection between the dynamical response of regular black holes and the energy carried by their gravitational perturbations.

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arXiv2026

Gravitational Energy Creation in the Sandwich pp-Waves Collision

This article investigates the spacetime of two colliding sandwich gravitational waves, focusing on evaluating gravitational energy before and after the collision. In the framework of the Teleparallel Equivalent of General Relativity (TEGR), we derive a true energy-momentum tensor for the gravitational waves and integrate it over a finite region of space, obtaining analytical expressions for the energy of each wave and the resulting spacetime. Our findings reveal that the energy after the collision exceeds the pre-collision, indicating energy creation. We analyze the energy density and ``surface energy density" on the wavefronts, underscoring their divergence near the singularity. Additionally, we observe that the colliding waves drag observers but exert no acceleration at the collision event. This study addresses and resolves longstanding issues raised by Szekeres in his seminal work on colliding pp-waves, offering a more physically realistic framework through the local energy definition provided by TEGR. The implications for gravitational wave interactions and their energy transfer mechanisms are discussed.

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arXiv2026

On the Gravitational Angular Momentum of Axial Perturbations of a Regular Black Hole

This Letter deals with the gravitational angular momentum carried by axial (odd-parity) perturbations of the Bardeen regular black hole within the teleparallel equivalent of general relativity (TEGR). Using the Hamiltonian definition of conserved quantities in TEGR, we derive a closed expression for the perturbative angular momentum $δJ$ in terms of the axial perturbation function $h_0(r,t)$. The result exhibits a sharp multipolar selection rule: $δJ$ vanishes for odd values of the multipole index $\ell$, while even-$\ell$ modes yield a nonzero contribution. The radial and temporal behavior of $δJ$ is illustrated using the known axial quasinormal modes of the Bardeen spacetime.

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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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arXiv2026

Memory effect for generalized modes in pp-waves spacetime

The memory effect of test particles interacting with pp-wave Gaussian pulses is investigated for polarization modes beyond the standard quadrupolar $+$ and $\times$ states. Massive geodesic equations are solved numerically for several values of the multipolar index $m$, allowing the analysis of velocity and energy memory effects. In order to eliminate possible coordinate artifacts, the study is formulated in terms of the relative motion between two test particles. The results show that the relative kinetic energy variation exhibits a quartic dependence on the wave amplitude in the regime of low initial velocities. The coefficient of this scaling is found to depend on the multipolar structure of the wave, reflecting the spatial gradients associated with higher polarization modes. It is further shown that the energy memory effect is determined by the integrated tidal field, linking the permanent change in the relative kinetic energy to the history of the spacetime curvature carried by the wave.13

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arXiv2025

On Nanocones as a Gravitational Analog System

This study delves into the fundamental properties of graphene and boron nitride (BN) nanostructures, exploring their torsional energy characteristics within the framework of Teleparallel Equivalent of General Relativity (TEGR). By constructing nanocones with disclination defects in these materials, we investigate the linear dependence of torsional energy on the disclination angle, as predicted by TEGR. The qualitative validation of TEGR's energy expression is supported by our simulations, which show a strong correlation between the torsional energy and the disclination angle, consistent with the theoretical predictions. Furthermore, we propose a quantitative analysis by estimating the coupling constant $k$ associated with TEGR through molecular simulations and Density Functional Theory (DFT) calculations. Our results suggest that $k$ reflects the interatomic forces within the materials, providing insights into the nature of spacetime and gravitational interactions on a microscopic scale. These findings not only contribute to our understanding of material physics but also offer implications for the precision and validity of TEGR in describing gravitational phenomena.

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arXiv2025

Energy Extraction from Rotating Black Hole with Quintessential Energy through the Penrose Process

We investigate the geometry, dynamics, and collision mechanisms in the ergoregion of KerrNewman-AdS black hole influenced by quintessential energy. Particle splittings within the ergoregion are analyzed, demonstrating their role in energy extraction via the Penrose process. Increased spin elongates the ergosphere, while higher quintessential parameters expand static limits and distort photon regions. Prograde orbits benefit from reduced energy and angular momentum due to frame-dragging, whereas retrograde orbits require higher energy. Quintessential energy weakens the gravitational pull, shifts stable orbit radii, and enhances orbital chaos, as indicated by Lyapunov exponents. The Penrose process demonstrates efficiencies ranging from 5% to 35%, with peak efficiency achieved at high spin, but diminishing with increased charge or quintessential energy due to reduced frame-dragging. We derive the exprssion for irreducible mass and discuss its dependence on cosmological and quintessence parameters, revealing their role in limiting extractable energy.

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arXiv2024

On Reference Frames and Coordinate Transformations

This article explores the differences between frame and coordinate transformations in relativistic theories. We highlight the key role of tetrad fields in connecting spacetime and frame indices. Using Maxwell's electrodynamics as an example, we show that Maxwell's equations are invariant under coordinate transformations but exhibit covariant behavior under frame transformations. We also analyze the energy-momentum of an electromagnetic field in different frames, providing deeper insights into the implications of different frames of reference and coordinate systems.

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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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