arXiv subjects

Fayçal Hammad

Publications and source records attributed to Fayçal Hammad.

At least 19 recordsLinked to original sources

arXiv2025

Spin precession and neutrino helicity flip in various spacetimes

We systematically study spin precession of neutral particles freely moving in spacetime. We first derive the formula describing spin precession within a general stationary and axisymmetric spacetime. We then apply our formula to study spin precession of neutral spinning particles moving within various spacetimes that are among the most ubiquitous ones found in the literature. Our results are then used to extract the helicity flip probability for neutrinos propagating in each one of those selected spacetimes. It is found that low-energy neutrinos acquire a spin-flip probability that is as large as unity in all the spacetimes considered here. The remarkable result, however, is that while spin-flip probability for high-energy neutrinos remains insignificant in most of these spacetimes, some of them do allow spin-flip probability to reach unity even for high-energy neutrinos.

hep-ph↗

arXiv2025

Spin precession and neutrino helicity flip under the influence of a gravitational plane wave

We recently studied spin precession in various stationary and axisymmetric spacetimes and applied it to the case of neutrinos propagating in those spacetimes. In this paper, the study of spin precession is extended to the case of a spinning particle propagating within the spacetime of a time-dependent gravitational plane wave. First, the angular velocity of spin precession of a particle propagating in a geodesic along an arbitrary direction relative to the gravitational wave is derived. Our general result is then used to derive the helicity flip probability for neutrinos freely propagating along such an arbitrary direction within the gravitational wave.

gr-qc↗

arXiv2024

The quantum Hall effect under the influence of gravity and inertia: A unified approach

The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall effects behave under a combined influence of gravity and inertia using a unified Hamiltonian. For that purpose, we first re-derive, using the purely algebraic method, the energy spectrum of charged particles moving in a plane perpendicular to a constant and uniform magnetic field either (i) under the influence of a nonlinear gravitational potential or (ii) under the influence of a constant rotation. The general Hamiltonian for describing the combined effect of gravity, rotation and inertia on the electrons of a Hall sample is then built and the eigenstates are obtained. The electrons mutual Coulomb interaction that gives rise to the familiar fractional quantum Hall effect is also discussed within a such a combination.

cond-mat.mes-hall↗

arXiv2023

Neutrino spin oscillation in screening models revisited

We study, using the Mathisson-Papapetrou-Dixon equations, the spin oscillation of neutrinos when the latter are coupled to the scalar field of screening models of dark energy. First, we derive the transition probability formula for a left-handed neutrino to become a right-handed neutrino within a general static and spherically symmetric metric. We then apply our general formula to neutrinos deflected around a central mass described by the Schwarzschild metric. Our results show that, contrary to what one might expect, the scalar field of chameleon-like and symmetron-like screening models would not show any effect on the spin oscillations of neutrinos. The origin of such an outcome is discussed.

hep-ph↗

arXiv2023

Neutrino flavor oscillations inside matter in conformal coupling models

We recently studied neutrinos flavor oscillations in vacuum within conformal coupling models. In this paper, we extend that analysis by investigating neutrino flavor oscillations inside matter within a general conformal coupling scenario. We first derive the general formula for the flavor transition probability inside matter in arbitrary static and spherically symmetric spacetimes. The modified resonance formula of the MSW effect is derived and the corresponding adiabaticity parameter of the effect is extracted. An application of our results to the case of two-flavor neutrinos within the well-known chameleon and symmetron conformal coupling models is made.

hep-ph↗

arXiv2023

Revisiting the Schrödinger-Dirac equation

In flat spacetime, the Dirac equation is the "square root" of the Klein-Gordon equation in the sense that by applying the square of the Dirac operator to the Dirac spinor, one recovers the Klein-Gordon equation duplicated for each component of the spinor. In the presence of gravity, applying the square of the curved-spacetime Dirac operator to the Dirac spinor does not yield the curved-spacetime Klein-Gordon equation, but yields, instead, the Schrödinger-Dirac covariant equation. First, we show that the latter equation gives rise to a generalization to spinors of the covariant Gross-Pitaevskii equation. Next, we show that while the Schrödinger-Dirac equation is not conformally invariant, there exists a generalization of the equation that is conformally invariant but which requires a different conformal transformation of the spinor than the one required by the Dirac equation. The new conformal factor acquired by the spinor is found to be a matrix-valued factor obeying a differential equation that involves the Fock-Ivanenko line element. The Schrödinger-Dirac equation coupled to the Maxwell field is then revisited and generalized to particles with higher electric and magnetic moments while respecting gauge symmetry. Finally, Lichnerowicz's vanishing theorem in the conformal frame is also discussed.

hep-th↗

arXiv2022

Plane-wave and wavepacket neutrino flavor oscillations in vacuum in conformal coupling models

We investigate neutrino flavor oscillations in vacuum within a general conformal coupling model. We first examine the flavor oscillations within the plane-wave description of neutrinos, and then we extend our analysis to the wavepacket-based formalism. In both cases, we derive the general formulas for the flavor transition probability in arbitrary static and spherically symmetric spacetimes. We thoroughly discuss and assess in both cases the different possible ways -- dictated by the presence of the conformal coupling -- of computing the flavor transition probability. We show that the conformal invariance of the Dirac equation implies that the effect of conformal coupling on neutrino flavor oscillations modifies the oscillation length, but preserves the coherence length and unitarity. A detailed application to two-flavor neutrinos is then made and a numerical analysis is conducted within the well-known chameleon conformal coupling model.

hep-ph↗

arXiv2021

Spin-1/2 particles under the influence of a uniform magnetic field in the interior Schwarzschild solution

The relativistic wave equation for spin-1/2 particles in the interior Schwarzschild solution in the presence of a uniform magnetic field is obtained. The fully relativistic regime is considered, and the energy levels occupied by the particles are derived as functions of the magnetic field, the radius of the massive sphere and the total mass of the latter. As no assumption is made on the relative strengths of the particles' interaction with the gravitational and magnetic fields, the relevance of our results to the physics of the interior of neutron stars, where both the gravitational and the magnetic fields are very intense, is discussed.

gr-qc↗

arXiv2021

Landau levels in a gravitational field: The Schwarzschild spacetime case

We investigate the gravitational effect on Landau levels. We show that the familiar infinite Landau degeneracy of the energy levels of a quantum particle moving inside a uniform and constant magnetic field is removed by the interaction of the particle with a gravitational field. Two independent approaches are used to solve the relevant Schrödinger equation within the Newtonian approximation. It is found that both approaches yield qualitatively similar results within their respective approximations. With the goal of clarifying some results found in the literature concerning the use of a third independent approach for extracting the quantization condition based on a similar differential equation, we show that such an approach cannot yield a general and yet consistent result. We point out to the more accurate, but impractical, way to use such an approach; a way which does in principle yield a consistent quantization condition. We discuss how our results could be used to contribute in a novel way to the existing methods for testing gravity at the tabletop experiments level as well as at the astrophysical observational level by deriving the corrections brought by Yukawa-like and power-law deviations from the inverse-square law. The full relativistic regime is also examined in detail.

gr-qc↗

arXiv2020

Prospects for testing the inverse-square law and gravitomagnetism using quantum interference

We examine a simple tabletop experimental setup for probing the inverse-square law of gravity and detecting eventual deviations therefrom. The nature of the setup allows indeed to effectively reach for shorter distances compared to what is allowed by other methods. Furthermore, we show that the same setup could also in principle be used to probe the interaction between gravitomagnetism and the intrinsic angular spin of quantum particles. Moreover, we show that the setup allows to have a gravitationally induced harmonic oscillator, introducing thus the possibility of studying in a novel way the interaction between gravity and quantum particles.

gr-qc↗

arXiv2020

A simple superconductor quantum interference device for testing gravity

A simple tabletop setup based on a superconducting quantum interference device is proposed for testing the gravitational interaction. A D-shaped superconducting loop has the straight segment immersed inside a massive sphere while the half-circle segment is wrapped around the sphere. The superconducting condensate within the straight arm of the loop thus bathes inside a gravitational simple harmonic oscillator potential while the condensate in the half-circle arm bathes in the constant gravitational potential around the sphere. The resulting phase difference at the Josephson junctions on both sides of the straight arm induces a sinusoidal electric current that has a frequency determined by the precise gravitational potential due to the massive sphere.

gr-qc↗

arXiv2019

Landau levels in a gravitational field: The Levi-Civita and Kerr spacetimes case

We have recently found that the gravitational field of a static spherical mass removes the Landau degeneracy of the energy levels of a particle moving around the mass inside a magnetic field by splitting the energy of the Landau orbitals. In this paper we present the second part of our investigation of the effect of gravity on Landau levels. We examine the effect of the gravitational fields created by an infinitely long massive cylinder and a rotating spherical mass. In both cases, we show that the degeneracy is again removed thanks to the splitting of the particle's orbitals. The first case would constitute an experimental test - which is quantum mechanical in nature - of the gravitational field of a cylinder. The approach relies on the Newtonian approximation of the gravitational potential created by a cylinder but, in view of self-consistency and for future higher-order approximations, the formalism is based on the full Levi-Civita metric. The second case opens up the possibility for a novel quantum mechanical test of the well-known rotational frame-dragging effect of general relativity.

gr-qc↗

arXiv2019

Conformal cosmological black holes: restoring determinism to Einstein theory

A widespread solution-generating technique of general relativity consists of conformally transforming known `seed' solutions. It is shown that these new solutions always solve the field equations of a pathological Brans-Dicke theory. Furthermore, when interpreted as effective Einstein equations,those field equations exhibit, in the case of a cosmological `background', an induced imperfect fluid as an additional effective source besides the original sources of the `seed' solutions. As an application, the charged non-rotating Thakurta black hole conformal to Reissner-Nordstrom is used to demonstrate the fragility of the inner Cauchy horizon when this black hole is embedded in the universe (even accounting for the separation of black hole and Hubble scales). Similarly, the charged McVittie spacetime representing a charged black hole embedded in a cosmological `background' with varying Hubble parameter does not exhibit a real Cauchy horizon. These arguments speak in favor of restoring determinism to Einstein theory, which was questioned in recent research.

gr-qc↗

arXiv2019

More on spacetime thermodynamics in the light of Weyl transformations

It was recently found that, after performing a Weyl conformal transformation, the familiar analogy between black hole mechanics and black hole thermodynamics becomes ambiguous. It was argued that this fact can be traced back to the fundamental dichotomy between matter and geometry, which is at the heart of Einstein's field equations. As a further study of this issue, we investigate here the general link between spacetime thermodynamics and Weyl transformations from two other angles. We first examine the conformal behaviour of the horizon entropy within Wald's approach based on the fundamental diffeomorphism symmetry of $pure$ geometry. We then revisit $-$ using Weyl transformations $-$ Jacobson's derivation of Einstein's field equations, the starting point of which is precisely built on the fundamental dichotomy between matter and geometry. As a result, we show that in order for Jacobson's approach to be able to yield the right Einstein field equations in the conformal frame, a specific conformal behavior of the horizon temperature and its entropy $-$ different from what Wald's approach implies $-$ is required. The two approaches to spacetime thermodynamics become thus incompatible in the conformal frame. In addition, we show $-$ in greater detail in the conformal frame $-$ that in the presence of a null dust the thermodynamics approach for extracting Einstein's field equations necessarily fails. An extensive discussion of the whole issue is given.

gr-qc↗

arXiv2018

Revisiting wormhole energy conditions in Riemann-Cartan spacetimes and under Weyl transformations

We show that the violation of the null energy condition by matter, required by traversable wormholes, can be removed in spacetimes with torsion. In addition, we show that this violation can also be removed in the conformal frame obtained by a Weyl transformation. This comes about because both conformally transformed wormholes and wormholes in spacetimes with torsion become sustained thanks to a combination of 'normal' matter, that satisfies the null energy condition, and an induced 'geometric' energy-momentum tensor that is able to greatly violate the null energy condition.

gr-qc↗

arXiv2018

Black hole mechanics and thermodynamics in the light of Weyl transformations

The fate of black hole thermodynamics under Weyl transformations is investigated by going back to the laws of black hole mechanics. It is shown that the transformed surface gravity, that one would identify with the black hole temperature in the conformal frame, as well as the black hole entropy, that one would identify with the horizon area, cannot be invariant. It is also shown that the conformally invariant surface gravity, attributed to the so-called "conformal Killing horizon", cannot represent the black hole temperature in the conformal frame. Finally, using familiar thought experiments, we find that the effect a Weyl transformation should have on black hole thermodynamics becomes even subtler than what is suggested by the laws of black hole mechanics

gr-qc↗

arXiv2018

Revisiting black holes and wormholes under Weyl transformations

The behavior of black holes horizon and wormholes under the Weyl conformal transformation is investigated. First, a shorter, but more general, derivation of the Weyl transformation of the simple prescription for detecting horizons and wormholes given recently in the literature for spherically symmetric spacetimes is provided. The derivation allows for a simple and intuitive way to understand why and when horizons and wormholes might arise in the conformal frame even if they were absent in the original frame. Then, the conformal behavior of black holes horizon and wormholes in more general spacetimes, based on more "sophisticated" definitions, is provided. The study shows that black holes and wormholes might always arise in the new frame even if they were absent in the original frame. Moreover, it is shown that some of the definitions found in the literature might be transformed into one another under such transformations. Worked-out examples are given.

gr-qc↗

arXiv2017

Density perturbations in $f(R,ϕ)$-gravity with an application to the (varying power)-law model

Density perturbations in the cosmic microwave background within general $f(R,ϕ)$ models of gravity are investigated. The general dynamical equations for the tensor and scalar modes in any $f(R,ϕ)$ gravity model are derived. An application of the equations to the (varying power)-law modified gravity toy-model is then made. Formulas and numerical values for the tensor-to-scalar ratio, the scalar tilt and the tensor tilt are all obtained within this specific model. While the model cannot provide a theoretical reason for the value of the energy scale at which inflation should occur, it is found, based on the latest observations of the density perturbations in the sky, that the model requires inflation to occur at an energy scale less than the GUT-scale; namely, $\sim10^{14}\,{\rm GeV}$. The different energy intervals examined here show that the density perturbations recently obtained from observations are recovered naturally, with very high precision, and without fine tuning the model's parameters.

gr-qc↗