Search Results (53)

This review examines the role of differential forms, Pfaffian systems, and hypersurfaces in general relativity. These mathematical constructions provide the essential tools for general relativity, in which the curvature of spacetime—described by the Einstein field equations—is most elegantly formulated using the Cartan calculus of differential forms. Another important subject in this discussion is the notion of conformal geometry, where the relevant invariants of a metric are characterized by Élie Cartan’s normal conformal connection. The previous analysis is then used to develop the null surface formulation (NSF) of general relativity, a radical framework that postulates the structure of light cones rather than the metric itself as the fundamental gravitational variable. Defined by a central Pfaffian system, this formulation allows the entire spacetime geometry to be reconstructed from a single scalar function, Z, whose level surfaces are null. Full article

In this paper, we provide a complete analysis of the most general spherical solution of the Lyra scalar-tensor (LyST) gravitational theory based on the proper definition of a Lyra manifold. Lyra’s geometry features the metric tensor and a scale function as fundamental fields, resulting in generalizations of geometrical quantities such as the affine connection, curvature, torsion, and non-metricity. A proper action is defined considering the correct invariant volume element and the scalar curvature, obeying the symmetry of Lyra’s reference frame transformations and resulting in a generalization of the Einstein–Hilbert action. The LyST gravity assumes zero torsion in a four-dimensional metric-compatible spacetime. In this work, geometrical quantities are presented and solved via Cartan’s technique for a spherically symmetric line element. Birkhoff’s theorem is demonstrated so that the solution is proven to be static, resulting in the Lyra–Schwarzschild metric, which depends on both the geometrical mass (through a modified version of the Schwarzschild radius $r_S$) and an integration constant dubbed the Lyra radius $r_L$. We study particle and light motion in Lyra–Schwarzschild spacetime using the Hamilton–Jacobi method. The motion of massive particles includes the determination of the $r_{\mathrm{ISCO}}$ and the periastron shift. The study of massless particle motion shows the last photon’s unstable orbit. Gravitational redshift in Lyra–Schwarzschild spacetime is also reviewed. We find a coordinate transformation that casts Lyra–Schwarzschild spacetime in the form of the standard Schwarzschild metric; the physical consequences of this fact are discussed. Full article

This paper is a result of the search for design assumptions for a sensor to detect oil dispersed in the sea waters (oil-in-water emulsions). Our approach is based on analyzing changes in the underwater solar radiance (L) field caused by the presence of oil droplets in the water column. This method would enable the sensor to respond to the presence of oil contaminants dispersed in the surrounding environment, even if they are not located directly at the measurement point. This study draws on both literature sources and the results of current numerical modeling of the spread of solar light in the water column to account for both downward and upward irradiance (Es). The core principle of the analysis involves simulating the paths of a large number of virtual solar photons in a seawater model defined by spatially distributed Inherent Optical Properties (IOPs). The IOPs data were taken from the literature and pertain to the waters of the southern Baltic Sea. The optical properties of the oil used in the model correspond to crude oil extracted from the Baltic shelf. The obtained results were compared with previously published spectral analyses of an analogous polluted sea model, considering vertical downward radiance, vertical upward radiance, and downward and upward irradiance. It was found that the optimal wavelength ratio of 555/412, identified for these quantities, is also applicable to scalar irradiance. The findings indicate that the most effective way to determine this index is by measuring it using a sensor with its window oriented in the direction of upward-traveling light. Full article

A random anisotropic hollow scatterer is discussed and the far-zone characteristics of scalar light waves scattered by this type of medium are theoretically analyzed. The results show that the scattered far-zone spectral density distributions have interesting patterns of “central ellipses and peripheral circles” or “central circles and peripheral ellipses”, which are decided by the outer and inner correlation lengths of the scatterer. This phenomenon provides some new insights into the generation and manipulation of the scattered far field, and can be applied in the reconstruction of the scattering medium’s structure. Full article

Anomaly-free $U\left(1\right)$ extensions of the standard model (SM) predict a new neutral gauge boson $Z^{\prime }$. When $Z^{\prime }$ obtains its mass from the spontaneous breaking of the new $U\left(1\right)$ symmetry by a new complex scalar field, the model also predicts a second real scalar s, and the search for the new scalar and the search for the new gauge boson become intertwined. We present the computation of production cross sections and decay widths of such a scalar s in models with a light $Z^{\prime }$ boson when the decay $h\to Z^{\prime }{Z}^{\prime }$ may have a sizeable branching ratio. We show how the Higgs signal strength measurement in this channel can provide stricter exclusion bounds on the parameters of the model than those obtained from the total signal strength for Higgs boson production. Full article

We compute the evolution of linear perturbations on top of a background solution of a general nonlinear electromagnetic theory. This evolution can be described in terms of two effective metrics, and we analyze under what conditions they are conformally related so that they can be regarded as analog models of non-trivial gravitational fields in the eikonal approximation. This is the case in Born–Infeld theory. For the background created by a static point electric charge in the Born–Infeld theory, the effective metric describes a wormhole geometry for light rays. Depending on the impact parameter, incoming light rays are either scattered to infinity or approach the wormhole slowing down their pace until they hit the charge at vanishing speed. The same effective wormhole geometry is obtained for a magnetic monopole and a dyon and we relate it to the duality invariance of Born–Infeld electromagnetism. Finally, we analyze the scalar Dirac–Born–Infeld theory and show that the effective wormhole geometry is not generated by a particle with scalar charge. Full article

We investigate the interaction of fermion fields with oscillating domain walls, inspired by breather-type solutions of the sine-Gordon equation, a nonlinear system of fundamental importance. Our study focuses on the fermionic bound states and particle production induced by a time-dependent scalar background field. The fermions couple to two domain walls undergoing harmonic motion, and we explore the resulting dynamics of the fermionic wave functions. We demonstrate that while fermions initially form bound states around the domain walls, the energy provided by the oscillatory motion of the scalar field induces an outward flux of fermions and antifermions, leading to particle production and eventual flux propagation toward spatial infinity. Through numerical simulations, we observe that the fermion density exhibits quasiperiodic behavior, with partial recurrences of the bound state configurations after each oscillation period. However, the fermion wave functions do not remain localized, and over time, the density decreases as more particles escape the vicinity of the domain walls. Our results highlight that the sine-Gordon-like breather background, when coupled non-supersymmetrically to fermions, does not preserve integrability or stability, with the oscillations driving a continuous energy transfer into the fermionic modes. This study sheds light on the challenges of maintaining steady-state fermion solutions in time-dependent topological backgrounds and offers insights into particle production mechanisms in nonlinear dynamical systems with oscillating solitons. Full article

We have investigated the Janis–Newman–Winicour spacetime through three fundamental tests of theories of gravity, namely, gravitational lensing, perihelion shift, and redshift due to gravitational force. Focusing initially on the circular motion of a massive particle within the equatorial plane, the analysis disregards external scalar field interactions. The Janis–Newman–Winicour (JNW) spacetime’s unique parameters, mass (M) and the scalar parameter (n), are examined, revealing an intriguing relationship between the innermost stable circular orbit position of the test particle and the scalar field parameter. The study also explores photon motion around a gravitational object in JNW spacetime, revealing the expansion of the photon sphere alongside a diminishing shadow, influenced by the external scalar field. Despite these complexities, gravitational bending of light remains consistent with general relativity predictions. The investigation extends to perihelion precession, where the trajectory of a massive particle in JNW spacetime exhibits eccentricity-dependent shifts, distinguishing it from Schwarzschild spacetime. Finally, oscillatory motion of massive particles in JNW spacetime is explored, providing analytical expressions for epicyclic frequencies using perturbation methods. The study concludes with the application of MCMC analyses to constrain the JNW spacetime parameters based on observational data. Full article

Theoretical studies on the generation of nondiffracting and nondispersive light pulses and their experimental implementation are one of the renowned problems within electromagnetics. Current technologies enable the creation of short-duration pulses of a few cycles with high power and fluency. An application of these techniques to the field of nondiffracting and nondispersive pulses requires a proper mathematical description of highly focused vector pulses. In this work, we study vector optical bullets in a dielectric medium with different polarization structures: linear, azimuthal, and radial. We report the differences caused by the vector model compared to the scalar model. We analyze effects caused by superluminal, subluminal, or even negative group velocity on the properties of vector optical bullets inside a dielectric material. Full article

We review the hadronic light-by-light (HLbL) contribution to the muon anomalous magnetic moment. Upcoming measurements will reduce the experimental uncertainty of this observable by a factor of four; therefore, the theoretical precision must improve accordingly to fully harness such an experimental breakthrough. With regards to the HLbL contribution, this implies a study of the high-energy intermediate states that are neglected in dispersive estimates. We focus on the maximally symmetric high-energy regime and in-quark loop approximation of perturbation theory, following the method of the OPE with background fields proposed by Bijnens et al. in 2019 and 2020. We confirm their results regarding the contributions to the muon $g-2$. For this, we use an alternative computational method based on a reduction in the full quark loop amplitude, instead of projecting on a supposedly complete system of tensor structures motivated by first principles. Concerning scalar coefficients, mass corrections have been obtained by hypergeometric representations of Mellin–Barnes integrals. By our technique, the completeness of such kinematic singularity/zero-free tensor decomposition of the HLbL amplitude is explicitly checked. Full article

Structured light beams have recently attracted enormous research interest for their unique properties and potential applications in optical communications, imaging, sensing, etc. Since most of these applications involve the propagation of structured light beams, which is accompanied by the phenomenon of diffraction, it is very necessary to employ diffraction theories to analyze the obstacle effects on structured light beams during propagation. The aim of this work is to provide a systematic summary and comparison of the scalar diffraction theories for structured light beams. We first present the scalar fields of typical structured light beams in the source plane, including the fundamental Gaussian beams, higher-order Hermite–Gaussian beams, Laguerre–Gaussian vortex beams, non-diffracting Bessel beams, and self-accelerating Airy beams. Then, we summarize and compare the main scalar diffraction theories of structured light beams, including the Fresnel diffraction integral, Collins formula, angular spectrum representation, and Rayleigh–Sommerfeld diffraction integral. Finally, based on these theories, we derive in detail the analytical propagation expressions of typical structured light beams under different conditions. In addition, the propagation of typical structured light beams is simulated. We hope this work can be helpful for the efficient study of the propagation of structured light beams. Full article

Exact models of primordial gravitational waves in the Bianchi type-III universe were constructed on the basis of the quadratic theory of gravity with a scalar field and pure radiation in Shapovalov wave spacetimes of type II (subtype 2). Exact solutions of the field equations and scalar equation were obtained. The characteristics of pure radiation were determined. An explicit form of the scalar field functions included in the Lagrangian of the considered quadratic theory of gravity was found. The trajectories of the propagation of light rays in the considered gravitational wave models were obtained. Full article

In the extension of Maxwell equations based on the Aharonov–Bohm Lagrangian, the e.m. field has an additional degree of freedom, namely, a scalar field generated by charge and currents that are not locally conserved. We analyze the propagation of this scalar field through two different media (a pure dielectric and an ohmic conductor) and study its property over a frequency range where the properties of the media are frequency-independent. We find that an electromagnetic (e.m.) scalar wave cannot propagate in a material medium. If a scalar wave in vacuum impinges on a material medium it is reflected, at most exciting in the medium a pure “potential” wave (which we also call a “gauge” wave) propagating at c, the speed of light in vacuum, with a vector potential whose Fourier amplitude is related to that of the scalar potential by $\omega {\mathbf{A}}_0=\mathbf{k}{\varphi }_0$, where ${\omega }^2=c^2{\left|\mathbf{k}\right|}^2$. Full article

In this work, we look to compare three methods of feedback for the ultimate purpose of measuring the transverse vector components of a magnetic field using a synchronous light-pulse atomic scalar magnetometer with a few tens of fT/$\sqrt{\mathrm{Hz}}$ sensitivity in Earth-field-scale magnetic environments. By applying modulation in the magnetic field to orthogonal axes, the respective vector components may, in principle, be separated from the scalar measurement. Success of this technique depends in significant part on the ability to measure and respond to these perturbations with low measurement uncertainty. Using high-speed least-squares fitting, the phase response of the atomic spins relative to the first harmonic of the optical pump pulse repetition rate is monitored and correspondingly adjusted into resonance with the natural Larmor precession frequency. This paper seeks to motivate and compare three distinct methods of feedback for this purpose. As a first step toward the full development of this technique, the present work uses a simplified version with modulation applied only along the bias field. All three methods investigated herein are shown to provide results that match well with the scalar magnetometer measurements and to depend on both the applied modulation amplitude and optimal feedback response to achieve low relative uncertainty. Full article

We uncover the general mechanism and the nature of today’s dark energy (DE). This is only based on well-known quantum physics and cosmology. We show that the observed DE today originates from the cosmological quantum vacuum of light particles, which provides a continuous energy distribution able to reproduce the data. Bosons give positive contributions to the DE, while fermions yield negative contributions. As usual in field theory, ultraviolet divergences are subtracted from the physical quantities. The subtractions respect the symmetries of the theory, and we normalize the physical quantities to be zero for the Minkowski vacuum. The resulting finite contributions to the energy density and the pressure from the quantum vacuum grow as $loga\left(t\right)$, where $a\left(t\right)$ is the scale factor, while the particle contributions dilute as $1/a^3\left(t\right)$, as it must be for massive particles. We find the explicit dark energy equation of state of today to be $P=w\left(z\right)\mathcal{H}$: it turns to be slightly $w\left(z\right)<-1$ with $w\left(z\right)$ asymptotically reaching the value $-1$ from below. A scalar particle can produce the observed dark energy through its quantum cosmological vacuum provided that (i) its mass is of the order of ${10}^{-3}$ eV = 1 meV, (ii) it is very weakly coupled, and (iii) it is stable on the time scale of the age of the universe. The axion vacuum thus appears as a natural candidate. The neutrino vacuum (especially the lightest mass eigenstate) can give negative contributions to the dark energy. We find that $w(z=0)$ is slightly below $-1$ by an amount ranging from $(-1.5\times {10}^{-3})$ to $(-8\times {10}^{-3})$ and we predict the axion mass to be in the range between 4 and 5 $\mathrm{meV}$. We find that the universe will expand in the future faster than the de Sitter universe as an exponential in the square of the cosmic time. Dark energy today arises from the quantum vacuum of light particles in FRW cosmological space-time in an analogous way to the Casimir vacuum effect of quantum fields in Minkowski space-time with non-trivial boundary conditions. Full article