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A model is proposed for describing the line shape of absorption and dispersion signals from which a recorded signal of nuclear magnetic resonance (NMR) is formed in a weak field. The expediency of using spectral analysis to determine the contributions of absorption and dispersion signals to the recorded NMR signal has been substantiated using a modulation technique. A new method is proposed for determining these contributions. The research results are presented.

The purpose of the present paper is to enquire whether General Relativity (GR) is necessary for the prediction of gravitational waves. It will be shown that in the weak field limit the same predictions come also from the treatment of a zero mass, spin 2 gravitational scattering amplitude. This will also justify the simpler effective vector approach of the author, only the angular distribution differing from that of a tensor theory.

Within the framework of self-force theory, we compute the gravitational-wave energy flux through second order in the mass ratio for compact binaries in quasicircular orbits. Our results are consistent with post-Newtonian calculations in the weak field and they agree remarkably well with numerical-relativity simulations of comparable-mass binaries in the strong field. We also find good agreement for binaries with a spinning secondary or a slowly spinning primary. Our results are key for accurately modelling extreme-mass-ratio inspirals and will be useful in modelling intermediate-mass-ratio systems., 5 pages + supplemental material, 7 figures; Updated to reflect published version

We investigate numerically the role of near-field dipole-dipole interactions on the late-emission dynamics of large disordered cold atomic samples driven by a weak field. Previous experimental and numerical studies of subradiance in macroscopic samples have focused on low-density samples of pure two-level atoms, without internal structure, which corresponds to a scalar representation of the light. The cooperative nature of the late emission of light is then governed by the resonant optical depth. Here, by considering the vectorial nature of the light, we show the detrimental role of the near-field terms on cooperativity in higher-density samples. The observed reduction in the subradiant lifetimes is interpreted as a signature of the inhomogeneous broadening due to the near-field contributions, in analogy with the van der Waals dephasing phenomenon for superradiance.

The principal objective of this project is to investigate the gravitational lensing by asymptotically flat black holes in the framework of Horndeski theory in weak field limits. To achieve this objective, we utilize the Gauss-Bonnet theorem to the optical geometry of asymptotically flat black holes and apply the Gibbons-Werner technique to achieve the deflection angle of photons in weak field limits. Subsequently, we manifest the influence of plasma medium on deflection of photons by asymptotically flat black holes in the context of Horndeski theory. We also examine the graphical impact of deflection angle on asymptotically flat black holes in the background of Horndeski theory in plasma medium as well as non-plasma medium., 13 pages, 4 figures. Accepted for publication in International Journal of Geometric Methods in Modern Physics

Using the previous results on static Green functions we will demonstrate in this chapter how we can utilize them to construct the gravitational field of static and stationary mass distributions in the weak-field limit of non-local ghost-free gravity. This chapter is based on Boos et al. (Phys. Rev. D 97(8), 084021 (2018); Int. J. Mod. Phys. D 27(14), 1847022 (2018); Int. J. Mod. Phys. D 29(14), 2043027 (2020); Phys. Rev. D 101(12), 124065 (2020)).

We study light deflection from a Reissner-Nordstr\"om-de Sitter black hole in the gravitational monopole background. We first calculate the orbit equation and the contribution of the monopole and black hole parameters to the deflection angle up to second-order for the vanishing cosmological constant case using the Rindler-Ishak method. We also obtain the contribution of the cosmological constant to light deflection in this geometry in the weak field limit using the same method., Comment: v2: 10 pages, 2 figures, matches the published version

The role of magnetic fields in the chromospheric heating problem remains greatly unconstrained. Most theoretical predictions from numerical models rely on a magnetic configuration, field strength and connectivity whose details have not been well established with observational studies. High-resolution studies of chromospheric magnetic fields in plage are very scarce or non-existent in general. Our aim is to study the stratification of the magnetic field vector in plage regions. We use high-spatial resolution full-Stokes observations acquired with CRISP instrument at the Swedish 1-m Solar Telescope in the Mg I $\lambda$5173, Na I $\lambda$5896 and Ca II $\lambda$8542 lines. We have developed a spatially-regularized weak-field approximation (WFA) method based on the idea of spatial regularization. This method allows for a fast computation of magnetic field maps for an extended field of view. The fidelity of this new technique has been assessed using a snapshot from a realistic 3D magnetohydrodynamics simulation. We have derived the depth-stratification of the line-of-sight component of the magnetic field from the photosphere to the chromosphere in a plage region. The magnetic fields are concentrated in the intergranular lanes in the photosphere and expand horizontally toward the chromosphere, filling all the space and forming a canopy. Our results suggest that the lower boundary of this canopy must be located around 400-600 km from the photosphere. The mean canopy total magnetic field strength in the lower chromosphere ($z\approx760$ km) is 658 G. At $z=1160$ km we estimate $\approx 417$ G. We propose a modification to the WFA that improves its applicability to data with worse signal-to-noise ratio. These methods provide a quick and reliable way of studying multi-layer magnetic field observations without the many difficulties inherent to other inversion methods., Comment: Accepted for publication on 2020-08-27

In this work, we investigate the weak deflection angle of light from exact black hole within the non-linear electrodynamics. First we calculate the Gaussian optical curvature using the optical spacetime geometry. With the help of modern geometrical way popularized by Gibbons and Werner, we examine the deflection angle of light from exact black hole. For this desire, we determine the optical Gaussian curvature and execute the Gauss-Bonnet theorem on optical metric and calculate the leading terms of deflection angle in the weak limit approximation. Furthermore, we likewise study the plasma medium's effect on weak gravitational lensing by exact black hole. Hence we expose the effect of the non-linear electrodynamics on the deflection angle in the weak gravitational field., Comment: 12 pages. Accepted for publication in Physical Review D (https://journals.aps.org/prd/abstract/10.1103/PhysRevD.101.103521)

We study the dissipative conductivity $\sigma_1$ of a dirty superconductor with a finite Dynes parameter $\Gamma$ under a dc-biased weak time-dependent field. The Usadel equation for the current-carrying state is solved to calculate the pair potential, penetration depth, supercurrent density, and quasiparticle spectrum. It is shown that, while the depairing current density $j_d$ for $\Gamma=0$ is coincident with the Kupriyanov-Lukichev theory, a finite $\Gamma$ decreases the superfluid density, resulting in a reduction of $j_d$. The broadening of the peaks of the quasiparticle density of states induced by a combination of a finite $\Gamma$ and a dc bias can reduce $\sigma_1$ below that for the ideal dirty BCS superconductor with $\Gamma=0$, while subgap states at Fermi level proportional to $\Gamma$ results in a residual conductivity at $T\to 0$. We find the optimum combination of $\Gamma$ and the dc bias to minimize $\sigma_1$ by scanning all $\Gamma$ and all currents up to $j_d$. By using the results, it is possible to improve $j_d$ and reduce electromagnetic dissipation in various superconducting quantum devices., Comment: 9 pages, 8 figures

A Symmetry Principle has been shown to augment unambiguously the Einstein Field Equations, promoting the whole closed-string massless NS-NS sector to stringy graviton fields. Here we consider its weak field approximation, take a non-relativistic limit, and derive the stringy augmentation of Newton Gravity: \[ \begin{array}{lll} {\bf{\nabla}^{2}\Phi}=4\pi G \rho+\bf{H}{\bf{\cdot}}\bf{H}\,, \quad&\qquad\bf{\nabla}\bf{\cdot}\bf{H}=0\,, \quad&\qquad {\bf{\nabla}\bf{\times}\bf{H}}=4\pi G\, \bf{K}\,. \end{array} \] Not only the mass density $\rho$ but also the current density $\mathbf{K}$ is intrinsic to matter. Sourcing $\mathbf{H}$ which is of NS-NS $H$-flux origin, $\mathbf{K}$ is nontrivial if the matter is `stringy'. $\mathbf{H}$ contributes quadratically to the Newton potential, but otherwise is decoupled from the point particle dynamics, i.e. $\bf{\ddot{x}}=-\bf{\nabla}\Phi$. We define `stringization' analogous to magnetization and discuss regular as well as monopole-like singular solutions., Comment: 6 pages, No figure, v2) Refs added

We show that in the weak field limit the light deflection alone cannot distinguish between different R + F [ g ( □ ) R ] models of gravity, where F and g are arbitrary functions. This does not imply, however, that in all these theories an observer will see the same deflection angle. Owed to the need to calibrate the Newton constant, the deflection angle may be model-dependent after all necessary types of measurements are taken into account.

A compact design of a rapid-response nuclear magnetic spectrometer for investigation of condensed media in weak fields is reported. As a result of investigation of different condensed media, special features of recording a nuclear magnetic resonance (NMR) signal in a weak magnetic field from a small volume of the medium under study are established. For the first time the NMR absorption spectra of condensed media in a weak field are collected. Based on the results of experimental studies, the potential of using a compact NMR-spectrometer for condensed media monitoring in a rapid response mode is determined.

A new construction of a magnetic system and a circuit for detecting the signal of nuclear magnetic resonance (NMR) in a weak magnetic field are described. The features of NMR-signal detection from a small volume (less than 0.3 mL) of liquid medium in a weak field using the modulation method are determined. Taking these features into account in the new design of the compact NMR spectrometer has made it possible to provide detection of signals from different nuclei of a condensed medium that possess a magnetic moment. The results of the experimental investigations of various condensed media are presented.

Gravitational waves are regarded as linear waves in the weak field approximation, which ignores the spacetime singularity. In this paper, we analyze singularities in exact gravitational wave solutions. We provide an exact general solution of the gravitational wave with cylindrical symmetry. The general solution includes some known cylindrical wave solutions as special cases. We show that there are two kinds of singularities in the cylindrical gravitational wave solution. The first kind of singularity corresponds to a singular source. The second kind of singularity corresponds to a resonance between different gravitational waves. When two gravitational waves coexist, the interference term in the source may vanish in the sense of time averaging.

The characteristics of signal registration of nuclear-magnetic resonance in a weak magnetic field from a small volume of an investigated medium have been considered. The consideration of the characteristics revealed in a new developed design of a magnetic system for a compact nuclear-magnetic spectrometer, and also in the NMR-signal registration method allows significant extension of the possibility to use the phenomenon of nuclear-magnetic resonance for the study of condensed medium in an express mode. The experimental results of different media studies have been presented.

Photochemistry induced by phase-coherent laser light is an intriguing topic. The possibility of weak-field (one-photon) phase-only control of photoisomerization is controversial. Experimental studies on the weak-field coherent control of cis-trans isomerization have led to conflicting results. Here we address this issue by quantum dynamical calculations, focusing on a mechanism where different "phase-shaped" wave packets are quickly stabilized ("dumped") in the trans configuration because of prompt energy dissipation. We systematically investigate different relaxation rates with the system-bath dynamics described within the time-dependent Hartree approximation leading to a friction-type force. We find evidence for phase control of trans-isomer yields (about 5%) in this model with pure energy dissipation given sufficiently strong dampening.

We explore the implementation of weak field asymptotic theory using orbitals and potentials calculated via Density Functional Theory. This provides a way to calculate strong field ionization rates by assuming that the field is constant.

In this paper we examine the possibility of a Josephson AC effect between two superconductors induced by the Earth's gravitational field, making use of the gravito-Maxwell formalism. The theoretical framework exploits the symmetry between the weak field expansion of the gravitational field and the standard Maxwell formulation, combined with the Josephson junction physics. We also suggest a suitable experimental setup, analysing also the related possible difficulties in measurements., 9 pages, 3 figures

We show that fundamental plane of elliptical galaxies can be used to obtain observational constraints on metric theories of gravity. Being it connected to global properties of ellipticals, it can fix parameters of modified gravity. Specifically, we use fundamental plane to constrain modified theories of gravity with Yukawa-like corrections which commonly emerge in the post-Newtonian limit. After giving examples on how these corrections are derived, we first analyze the velocity distribution of elliptical galaxies comparing theoretical results of modified gravity with Yukawa-like corrections with astronomical data. According to these results, it is possible to constrain the parameters of the corrections discriminating among classes of models compatible with astronomical observations. We conclude that fundamental plane can be used as a standard tool to probe different theories of gravity in the weak field limit., Comment: 13 pages, 7 figures, to be published in Phys. Dark. Univ. (2020)

It was pointed out long ago by Vainshtein [Phys. Lett. 39B, 393 (1972)] that the weak-field perturbation expansion of generic theories (of the nonlinear Fierz-Pauli type) involving massive spin-2 excitations breaks down below a certain distance around a material source ("Vainshtein radius"), scaling as some inverse power of the spin-2 mass $m_2$, i.e., some positive power of the range $m_2^{-1}$. Here we prove that this conclusion does not apply in a generalized Einstein-Cartan theory (called "torsion bigravity") whose spectrum is made (like that of bimetric gravity) of a massless spin-2 excitation and a massive spin-2 one. Working within a static spherically symmetric ansatz, we prove, by reformulating the field equations in terms of new variables, that one can construct an all-order weak-field perturbative expansion where no denominators involving $m_2$ ever appear in the region $r \ll m_2^{-1}$. In particular, we show how the formal large-range limit, $m_2 \to 0$, leads to a well-defined, finite perturbation expansion, whose all-order structure is discussed in some detail., 18 pages, no figures

We discuss an investigation of student difficulties with the corrections to the energy spectrum of the hydrogen atom for the strong and weak field Zeeman effects using degenerate perturbation theory. This investigation was carried out in advanced quantum mechanics courses by administering written free-response and multiple-choice questions and conducting individual interviews with students. We discuss the common student difficulties related to these concepts which can be used as a guide for creating learning tools to help students develop a functional understanding of concepts involving the corrections to the energy spectrum due to the Zeeman effect., Comment: Physics Education Research Conference Proceedings. arXiv admin note: text overlap with arXiv:2006.05000

Accurate cosmological simulations that include the effect of non-linear matter clustering as well as of massive neutrinos are essential for measuring the neutrino mass scale from upcoming galaxy surveys. Typically, Newtonian simulations are employed and the neutrino distribution is sampled with a large number of particles in order to beat down the shot noise. Here we perform very efficient simulations with light massive neutrinos which require virtually no extra cost over matter-only simulations, and furthermore do not require tracer particles for the neutrinos. Instead, we use a weak-field dictionary based on the recently developed Newtonion motion approach, where Newtonian simulations for matter are paired with a linear relativistic Boltzmann code to allow for an absorption of the neutrino evolution into a time-dependent coordinate transformation. For this, only minimal modifications in existing N-body codes are required, which we have explicitly implemented in $\textit{gevolution}$ and $\textit{gadget-2}$. Our fast method determines the non-linear matter power spectrum to permille-level precision when compared against state-of-the-art simulations that have been performed for $0.1\,{\rm eV} \leq \sum m_\nu \leq 0.3\,$eV., Comment: v2, matches published version at JCAP

We study the generalized version of energy-momentum squared gravity (EMSG) in the Palatini formalism. This theory allows the existence of a scalar constructed with energy-momentum tensor as $T_{\alpha\beta}T^{\alpha\beta}$ in the generic action of the theory. We study the most general form of this theory in the Palatini framework and present the underlying field equations. The equations of motion of a massive test particle have been derived. The weak field limit of the theory is explored and the generalized version of the Poisson equation is obtained. Moreover, we explore the cosmological behavior of the theory with emphasis on bouncing solutions. Some new bouncing solutions for the specific Palatini EMSG model given by the Lagrangian density $\mathcal{L}=R+\beta R^2+\eta T_{\mu\nu}T^{\mu\nu}$ are introduced. We show that only the case $\eta>0$ can lead to viable cosmic bounce., Comment: 20 pages, 6 figures, Accepted for publication in PRD

The dynamics of a system that is initially correlated with an environment is almost always non-Markovian. Hence it is important to characterise such initial correlations experimentally and witness them in physically realistic settings. One such setting is weak-field phase control, where chemical reactions are sought to be controlled by the phase of shaped weak laser pulses. In this manuscript, we show how weak quantum controllability can be combined with quantum preparations to witness initial correlations between the system and the environment. Furthermore we show how weak field phase control can be applied to witness when the quantum regression formula does not apply.

We calculate the ultraviolet divergences in a weak field expansion of the Volkov propagator. This is done for the full Lorentz class of gauges. The expected gauge invariance of the vacuum mass shift in each sideband is recovered. However, the renormalisation of the background induced mass shift is shown to be gauge dependent. In particular, we show that it vanishes in Landau gauge. We find that only in that gauge does the vacuum renormalisation remove all ultraviolet divergences., 8 pages, 3 figures, revised version to appear in Physics Letters B

We discuss several recent extensions of quantum radio frequency (RF) electric field sensors to antenna/receiver applications. These Rydberg atom-based sensors have been previously studied for SI-traceable RF field measurements. We demonstrate the reception of modulated signals, including analog audio and pseudorandom bit sequences, RF phase detection, weak field detection, and the recording of musical instruments.

An attempt is made to develop a polarized deuteron source suited for the Van de Graaff accelerator of Czech Technical Universit in Prague. We base on Kaminsky's experiment on channeling deuterons through a Ni single crystal. The setup is described, which contains permanent magnets with a transversal magnetic field to increase the deuteron polarization using the Sona method (zero transition). The measurements of tensor polarization were carried out with a TiT target. The result is Pzz = -0.12±0.04 for a weak field at the target without channeling. The ultimate aim is to produce 14-MeV polarized neutrons which will be used jointly with the frozen-spin polarized deuteron target for measurement of ΔσT and ΔσL asymmetries in the nd-transmission experiment.

We study the local well-posedness of the initial value problem for cubic Horndeski theories. Three different strongly hyperbolic modifications of the Arnowitt-Deser-Misner formulation of the Einstein equations are extended to cubic Horndeski theories in the “weak field” regime. In the first one, the equations of motion are rewritten as a coupled elliptic-hyperbolic system of partial differential equations. The second one is based on the Baumgarte-Shapiro-Shibata-Nakamura formulation with a generalized Bona-Masso slicing (covering the 1+log slicing) and nondynamical shift vector. The third one is an extension of the CCZ4 formulation with a generalized Bona-Masso slicing (also covering the 1+log slicing) and a gamma driver shift condition. This final formulation may be particularly suitable for applications in nonlinear numerical simulations.

It is shown the antisymmetric part of the metric tensor is the potential for the spin field. Various metricity conditions are discussed and comparisons are made to other theories, including Einstein’s. It is shown in the weak field limit the theory reduces to one with a symmetric metric tensor and totally antisymmetric torsion.

A theoretical scheme is proposed to enhance the signal-to-noise ratio in ultrasensitive detection by quantum correlation in a composite optomechanical system. Introducing an auxiliary oscillator and treating it as an added probe for weak-field detection, the additional noise can be greatly suppressed, which may even break the standard quantum limit. A magnetic field is employed as an example to exhibit the detection capability of the scheme. The result shows that, compared with the traditional detection protocol, the scheme has a higher signal-to-noise ratio and a better detection accuracy. Furthermore, the signal intensity detection curve shows a good linearity. The results provide a promising platform for reducing the additional noise by utilizing quantum correlation in ultrasensitive detection.

In this paper, we investigate light bending in the spacetime of regular black holes with cosmic strings in weak field limits. To do so, we apply the Gauss-Bonnet theorem to the optical geometry of the black hole; and, using the Gibbons-Werner method, we obtain the deflection angle of light in the weak field limits which shows that the bending of light is a global and topological effect. Afterwards, we demonstrate the effect of a plasma medium on the deflection of light by RBCS. We discuss that increasing cosmic string parameter $\mu$ and mass $M_0$ will increase the bending angle.

We investigate the linear regime of $f(R)=R+\ensuremath{\alpha}{R}^{2}$ gravity for static, spherically symmetric and asymptotically flat configurations of matter. We show that, in vacuum and deep inside the range of the extra scalar degree of freedom, the post-Newtonian parameter $\ensuremath{\gamma}$ is not equal to $1/2$, as established in the literature, but it assumes larger values depending on the pressure of the star. We provide an explicit expression for $\ensuremath{\gamma}$ in terms of the mass, of the integrated pressure of the star and of the ratio between the star's radius and the range of the extra degree of freedom. We corroborate our results by providing numerical solutions for the case of a neutron star.

We consider one-particle reducible (1PR) contributions to QED and scalar QED processes in external fields, at one-loop and two-loop order. We investigate three cases in detail: constant crossed fields, constant magnetic fields, and plane waves. We find that 1PR tadpole contributions in plane waves and constant crossed fields are non-zero, but contribute only divergences to be renormalised away. In constant magnetic fields, on the other hand, tadpole contributions give physical corrections to processes at one-loop and beyond. Our calculations are exact in the external fields and we give strong and weak field expansions in the magnetic case., Comment: 36 pages, 9 figures, update to journal version

While non-action generated, but identically conserved,-abelian and non-gauge vectors exist, they are unsuitable for building alternate field equations because they have no stress-tensor, hence do not permit Poincare generators and, most phiyically, cannot couple consistently to gravity. Separately, their geometric analogues -covariantly conserved non-Lagrangian symmetric tensors-probably do not exist, but their weak field, abelian counterparts do, and share the vector fields' absence of generators., Comment: Published version

We reconsider the all-optical homodyne-measurement based experimental schemes that aim to reveal Bell nonclassicality of a single photon, often termed `nonlocality'. We focus on the schemes put forward by Tan, Walls and Collett (TWC, 1991) and Hardy (1994). In the light of our previous work the Tan, Walls and Collett setup can be described by a precise local hidden variable model, hence the claimed nonclassicality of this proposal is apparent, whereas the nonclassicality proof proposed by Hardy is impeccable. In this work we resolve the following problem: which feature of the Hardy's approach is crucial for its successful confirmation of nonclassicality. The scheme of Hardy differs from the Tan, Walls and Collett setup in two aspects. (i) It introduces a superposition of a single photon excitation with vacuum as the initial state of one of the input modes of a 50-50 beamsplitter, which creates the superposition state of two separable (exit) modes under investigation. (ii) In the final measurements Hardy's proposal utilises a varying strengths of the local oscillator fields, whereas in the TWC case they are constant. In fact the local oscillators in Hardy's scheme are either on or off (the local setting is specified by the presence or absence of the local auxiliary field). We show that it is the varying strength of the local oscillators, from setting to setting, which is the crucial feature enabling violation of local realism in the Hardy setup, whereas it is not necessary to use initial superposition of a single photon excitation with vacuum as the initial state of the input mode. Neither one needs to operate in the fully on/off detection scheme. Despite the failure of the Tan, Walls and Collett scheme in proving Bell nonclassicality, we show that their scheme can serve as an entanglement indicator., 15 pages, 6 figures. Comments are welcome

We consider the interaction between the Earth's gravitational field and a superconductor in the fluctuation regime. Exploiting the weak field expansion formalism and using time dependent Ginzburg-Landau formulation, we show a possible short-time alteration of the gravitational field in the vicinity of the superconductor., Comment: 5 pages, 4 figures

Recently, He and Ma introduced a generic method to generate static, circular symmetric regular black holes in 2+1-dimensional gravity minimally coupled to nonlinear electrodynamics (NED). In their formalism, they considered spacetimes filled with pure radial electric field and as examples four different cases were studied. In accordance with their method, in the weak field limit, the regular black holes are supposed to reduce to the charged BTZ black hole and the NED Lagrangian admits the Maxwell linear theory. Inspired from their paper, in this Letter we address a common feature of the NED Lagrangian which has not been noticed by the author. It will be shown that the NED Lagrangians are actually hybrid functions whose behaviors at weak and strong field regimes are different. This is in analogy with its 3+1-dimensional counterpart which has been pointed out long ago by Bronnikov.

The Einstein field equations are a complicated set of coupled partial differential equations, which are usually too complicated to find exact solutions. This chapter introduces a simple approximation for weak fields. It discusses the lowest order solution, which gives back Newtonian gravity, and the next order, which includes “gravitomagnetic” or “frame-dragging” effects. The chapter briefly discusses higher order approximations, expansions around a curved background, and the evidence that gravitational energy itself gravitates. It concludes with a brief description of an alternative derivation of the Einstein field equations, starting from flat spacetime and “bootstrapping” the gravitational self-interaction.

The idea of the post-Newtonian formalism is to employ the fact that in the solar system velocities of astronomical bodies are small and gravitational fields are weak. The PN-formalism is a slow motion, weak field approximation to Einstein’s theory of gravity.

We study the behaviour of a superconductor in a weak static gravitational field for temperatures slightly greater than its transition temperature (fluctuation regime). Making use of the time-dependent Ginzburg-Landau equations, we find a possible short time alteration of the static gravitational field in the vicinity of the superconductor, providing also a qualitative behaviour in the weak field condition. Finally, we compare the behaviour of various superconducting materials, investigating which parameters could enhance the gravitational field alteration., Comment: 14 pages, 3 figures

This study deals with the relativity of observer splitting formalism, powerful technique in General Relativity to meaningfully distinguish the contributions of the gravitational effects and fictitious forces on the relative motion of two non-inertial observers. In the weak field limit, this approach has a direct connection with the classical description. This technique is particularly useful to model several astrophysical situations. We show two particular applications related to radiation processes and accretion disc physics.

We derive the gravitational waves for $f\left(T, B\right)$ gravity, an extension of teleparallel gravity containing the torsion scalar $T$ and the boundary term $B$, and demonstrate that it is equivalent to $f(R)$ gravity. Gravitational waves, in this theory, show three polarizations: the two standard, plus and cross, of General Relativity, which are purely transverse, massless tensor polarization modes with two-helicity, and an additional massive scalar mode with zero-helicity. The last one is a mix of a longitudinal mode and a transverse breathing mode. The boundary term $B$ excites the extra scalar polarization and the mass of scalar field breaks the symmetry of the TT gauge by adding a new degree of freedom, namely a single mixed scalar polarization., Comment: 14 pages, accepted for publication in Eur. Phys. J. C

Aims. We aim to investigate the validity of the weak field approximation (WFA) for determining magnetic fields in quiet regions of the solar photosphere using the polarization caused by the Zeeman effect in the Si I10 827 Å line.Methods. We solved the NLTE line formation problem by means of multilevel radiative transfer calculations in a three-dimensional (3D) snapshot model taken from a state-of-the-art magneto-convection simulation of the small-scale magnetic activity in the quiet solar photosphere. The 3D model used is characterized by a surface mean magnetic field strength of about 170 G. The calculated Stokes profiles were degraded because of the atmospheric turbulence of Earth and light diffraction by the telescope aperture. We apply the WFA to the StokesI,Q,U,Vprofiles calculated for different seeing conditions and for the apertures of the VTT, GREGOR, EST and DKIST telescopes. We compare the inferred longitudinal and transverse components of the magnetic field with the original vertical and horizontal fields of the 3D model.Results. We find that with a spatial resolution significantly better than 0.5″ the surface maps of the magnetic field inferred from the Stokes profiles of the Si I10 827 Å line applying the WFA are close to the magnetic field of the model on the corrugated surface, corresponding to line optical depth unity at Δλ ≈ 0.1 Å for a disk-center line of sight. The correlation between them is relatively high, except that the inferred longitudinal and transverse components of the magnetic field turn out to be lower than in the 3D model.Conclusions. The use of the WFA for interpreting high-spatial-resolution spectropolarimetric observations of the Si I10 827 Å line obtained with telescopes like GREGOR, EST, and DKIST allows the longitudinal and transverse components of the magnetic field to be retrieved with reasonable precision over the whole quiet solar photosphere, the result being worse for telescopes of lower aperture.

Physical review / D D 99(9), 096002 (2019). doi:10.1103/PhysRevD.99.096002, In the dynamically assisted Schwinger mechanism, the pair production probability is significantly enhanced by including a weak, rapidly varying field in addition to a strong, slowly varying field. In a previous paper we showed that several features of dynamical assistance can be understood by a perturbative treatment of the weak field. Here we show how to calculate the prefactors of the higher-order terms, which is important because the dominant contribution can come from higher orders. We give a new and independent derivation of the momentum spectrum using the worldline formalism, and extend our WKB approach to calculate the amplitude to higher orders. We show that these methods are also applicable to doubly assisted pair production., Published by Inst.189733, Melville, NY

We give a proof of the equivalence of the electric-magnetic duality on one side and helicity conservation of the tree level amplitudes on the other side within general models of nonlinear electrodynamics. Using modified Feynman rules derived from generalized normal ordered Lagrangian we discuss the interrelation of the above two properties of the theory also at higher loops. As an illustration we present two explicit examples, namely we find the generalized normal ordered Lagrangian for the Born-Infeld theory and derive a semi-closed expression for the Lagrangian of the Bossard-Nicolai model (in terms of the weak field expansion with explicitly known coefficients) from its normal ordered form., Comment: 31 pages

We obtain the deflection angle for a boosted Kerr black hole in the weak field approximation. We also study the behavior of light in the presence of plasma by considering different distributions: singular isothermal sphere, non-singular isothermal gas sphere, and plasma in a galaxy cluster. We find that the dragging of the inertial system along with the boosted parameter $\Lambda$ affect the value of the deflection angle. As an application, we studied the magnification for both uniform and SIS distributions., Comment: 20 pages, 17 figures. v2: refereed version

Basic aspects of the Hamiltonian structure of the parity-violating Poincar\'e gauge theory are studied. We found all possible primary constraints, identified the corresponding critical parameters, and constructed the generic form of the canonical Hamiltonian. In addition to being important in their own right, these results offer dynamical information that is essential for a proper understanding of the particle spectrum of the theory, calculated in the weak field approximation around the Minkowski background., Comment: LaTEx, 36 pages; v2 minor revisions

We find the generalized version of the Toomre's criterion for the stability of a rotating thin disk in the context of Eddington inspired Born-Infeld (EiBI) gravity which possesses one free parameter $\chi$. To do so we use the weak field limit of the theory and find the dispersion relation for the propagation of matter density waves on the surface of a self-gravitating and differentially rotating disk. Finally we find a new version of Toomre's stability criterion for thin disks. We show that EiBI gravity with negative $\chi$ destabilizes all the rotating thin disks. On the other hand EiBI with positive $\chi$ substantially can suppress the local fragmentation, and has stabilizing effects against axi-symmetric perturbations. More specifically, we show that only an annulus remains unstable on the surface of the disk. The width of the annulus directly depends on the magnitude of $\chi$., Comment: Accepted for publication in MNRAS