Weak Field Limit Research Articles

Covariant transport equation and gravito-conductivity in generic stationary spacetimes

We find a near detailed balance solution to the relativistic Boltzmann equation under the relaxation time approximation with a collision term which differs from the Anderson–Witting model and is dependent on the stationary observer. Using this new solution, we construct an explicit covariant transport equation for the particle flux in response to the generalized temperature and chemical potential gradients in generic stationary spacetimes, with the transport tensors characterized by some integral functions in the chemical potential and the relativistic coldness. To illustrate the application of the transport equation, we study probe systems in Rindler and Kerr spacetimes and analyze the asymptotic properties of the gravito-conductivity tensor in the near horizon limit. It turns out that both the longitudinal and lateral parts (if present) of the gravito-conductivity tend to be divergent in the near horizon limit. In the weak field limit, our results coincide with the non-relativistic gravitational transport equation which follows from the direct application of the Drude model.

Observational Signatures of Frame Dragging in Strong Gravity

Objects orbiting in the presence of a rotating massive body experience a gravitomagnetic frame-dragging effect, known as the Lense-Thirring effect, that has been experimentally confirmed in the weak-field limit. In the strong-field limit, near the horizon of a rotating black hole, frame dragging becomes so extreme that all objects must co-rotate with the black hole’s angular momentum. In this work, we perform general relativistic numerical simulations to identify observable signatures of frame dragging in the strong-field limit that appear when infalling gas is forced to flip its direction of rotation as it is being accreted. In total intensity images, infalling streams exhibit “S”-shaped features due to the switch in the tangential velocity. In linear polarization, a flip in the handedness of spatially resolved polarization ticks as a function of radius encodes a transition in the magnetic field geometry that occurs due to magnetic flux freezing in the dragged plasma. Using a network of telescopes around the world, the Event Horizon Telescope collaboration has demonstrated that it is now possible to directly image black holes on event horizon scales. We show that the phenomena described in this work would be accessible to the next-generation Event Horizon Telescope and extensions of the array into space, which would produce spatially resolved images on event horizon scales with higher spatial resolution and dynamic range.

Weak gravitational lensing in dark matter and plasma mediums for wormhole-like static aether solution

In this paper, we study the deflection angle for wormhole-like static aether solution by using Gibbons and Werner technique in non-plasma, plasma, and dark matter mediums. For this purpose, we use optical spacetime geometry to calculate the Gaussian optical curvature, then implement the Gauss–Bonnet theorem in weak field limits. Moreover, we compute the deflection angle by using a technique known as Keeton and Petters technique. Furthermore, we analyze the graphical behavior of the bending angle psi with respect to the impact parameter b, mass m as an integration constant, and parameter q in non-plasma and plasma mediums. We examine that the deflection angle is exponentially increasing as direct with charge. Also, we observe that for small values of b, psi increases, and for large values of b the angle decreases. We also considered analysis to the shadow cast of the wormhole relative to an observer at various locations. Comparing it the Schwarzschild shadow, shadow cast is possible for wormhole as r<2m. At r>2m, the Schwarzschild is larger. As rrightarrow infty , we have seen that the behavior of the shadow, as well as the weak deflection angle, approaches that of the Schwarzschild black hole. Overall, the effect of plasma tends to decrease the value of the observables due to the wormhole geometry.

Weak lensing, Hawking radiation and greybody factor bound by a charged black holes with non-linear electrodynamics corrections

In this paper, we study gravitational lensing in the weak field limits and the shadow by charged black holes in non-linear electrodynamics corrections. To find the deflection angle in vacuum (non-plasma) up to the leading order terms, we compute the optical Gaussian curvature from optical metric and utilize the Gauss–Bonnet theorem by applying Gibbons and Werner’s technique. Also, we derive the bending angle in plasma and dark matter mediums and observe that the bending angle increases by increasing the effects of these mediums. Further, in vacuum and plasma mediums, we investigate the graphical behavior of the bending angle with respect to the impact parameter u and notice that the bending angle exponentially decreases. Moreover, we calculate the Hawking temperature using the Gauss–Bonnet theorem and compare it with a standard method of computing the Hawking temperature. Furthermore, we investigate the bound of the greybody factor and graphically examine that bound converges to the 1. We relate our obtained results with the results of black holes given in the literature. Finally, we have considered exploring the effect of non-linear electrodynamics (NLED), plasma and dark matter on the black hole’s shadow radius to broaden the study’s scope. Results for the shadow indicate that the three parameters give different deviations to the shadow radius. Interestingly, while plasma affects both the photonsphere and shadow, dark matter only influences the shadow.

Weak Deflection Angle by Kalb–Ramond Traversable Wormhole in Plasma and Dark Matter Mediums

This paper is devoted to computing the weak deflection angle for the Kalb–Ramond traversable wormhole solution in plasma and dark matter mediums by using the method of Gibbons and Werner. To acquire our results, we evaluate Gaussian optical curvature by utilizing the Gauss–Bonnet theorem in the weak field limits. We also investigate the graphical influence of the deflection angle α˜ with respect to the impact parameter σ and the minimal radius r0 in the plasma medium. Moreover, we derive the deflection angle by using a different method known as the Keeton and Petters method. We also examine that if we remove the effects of plasma and dark matter, the results become identical to that of the non-plasma case.

Newtonian approximation in (1 + 1) dimensions

We study the possible existence of a Newtonian regime of gravity in 1 + 1 dimensions, considering metrics in both the Kerr-Schild and conformal forms In the former case, the metric gives the exact solution of the Poisson equation in flat space, but the weak-field limit of the solutions and the non-relativistic regime of geodesic motion are not trivial. We show that using harmonic coordinates, the metric is conformally flat and a weak-field expansion is straightforward. An analysis of the non-relativistic regime of geodesic motion remains non-trivial and the weak-field potential only satisfies the flat space Poisson equation approximately.

Weak deflection angle and shadow cast by the charged-Kiselev black hole with cloud of strings in plasma* *Partly supported by the Uzbekistan Ministry for Innovative Development (FZ-20200929344 and F-FA-2021-510). I.H. is grateful to the Institute of Mathematics, University of Aberdeen, Scotland, UK, where a part of this study was done under the IMU-CDC Individual Travel Support Program. G.M. is supported

In this study, the gravitational deflection angle of photons in the weak field limit (or the weak deflection angle) and shadow cast by the electrically charged and spherically symmetric static Kiselev black hole (BH) in the string cloud background are investigated. The influences of the BH charge Q, quintessence parameter γ, and string cloud parameter a on the weak deflection angle are studied using the Gauss-Bonnet theorem, in addition to studying the influences on the radius of photon spheres and size of the BH shadow in the spacetime geometry of the charged-Kiselev BH in string clouds. Moreover, we study the effects of plasma (uniform and non-uniform) on the weak deflection angle and shadow cast by the charged-Kiselev BH surrounded by the clouds of strings. In the presence of a uniform/nonuniform plasma medium, an increase in the string cloud parameter a increases the deflection angle α. In contrast, a decrease in the BH charge Q decreases the deflection angle. Further, we observe that an increase in the BH charge Q causes a decrease in the size of the shadow of the BH. We notice that, with an increase in the values of the parameters γ and a, the size of the BH shadow increases, and therefore, the intensity of the gravitational field around the charged-Kiselev BH in string clouds increases. Thus, the gravitational field of the charged-Kiselev BH in the string cloud background is stronger than the field produced by the pure Reissner-Nordstrom BH. Moreover, we use the data released by the Event Horizon Telescope (EHT) collaboration, for the supermassive BHs M87* and Sgr A*, to obtain constraints on the values of the parameters γ and a.

Atom interferometers and a small-scale test of general relativity

Since the first appearance of general relativity in 1916, various experiments have been conducted to test the theory. Due to the weakness of the interactions involved, all of the documented tests were carried out in a gravitational field generated by objects of an astronomical scale. We propose an idea for an experiment that could detect purely general-relativistic effects in a lab-generated gravitational field. It is shown that a set of dense rapidly-revolving cylinders produce a frame-dragging effect substantial enough to be two orders of magnitude away from the observable range of the next generation of atomic interferometers. The metric tensor due to a uniform rotating axisymmetric body in the weak-field limit is calculated and the phase shift formula for the interferometer is derived. This article is meant to demonstrate feasibility of the concept and stimulate further research into the field of low-scale experiments in general relativity. It is by no means a fully developed experiment proposal.

Quasinormal modes, shadow and thermodynamics of black holes coupled with nonlinear electrodynamics and cloud of strings

We construct an exact black hole solution for the Einstein gravity coupled with the nonlinear electrodynamics (which corresponds to the Maxwell electrodynamics in the weak field limit) in the presence of a cloud of strings as the source. We study the thermodynamical properties of the black hole solutions and derive the corrected first-law of thermodynamics. The presence of a cloud of strings does not affect the stability of the present black hole. However, a second-order phase transition exists for this system at a critical horizon radius. Furthermore, we study the quasinormal modes and their shadow radius. In addition, we find that, upon variation, the parameters of the theory show different aspects of the optical characteristics of the black hole solutions.

The Weyl double copy in vacuum spacetimes with a cosmological constant

We examine the Weyl double copy relation for vacuum solutions of the Einstein equations with a cosmological constant using the approach we previously described, in which the spin-1/2 massless free-field spinors (Dirac-Weyl fields) are regarded as basic units. Based on the exact non-twisting vacuum type N and vacuum type D solutions, the finding explicitly shows that the single and zeroth copies fulfill conformally invariant field equations in conformally flat spacetime. In addition, irrespective of the presence of a cosmological constant, we demonstrate that the zeroth copy connects Dirac-Weyl fields with the degenerate electromagnetic fields in the curved spacetime in addition to connecting gravity fields with the single copy in conformally flat spacetime. Moreover, the study also demonstrates the critical significance the zeroth copy plays in time-dependent radiation solutions. In particular, for Robinson-Trautman (Λ) gravitational waves, unlike the single copy, we find that the zeroth copy carries additional information to specify whether the sources of associated gravitational waves are time-like, null, or space-like, at least in the weak field limit.

Constraints on singularity resolution by nonlinear electrodynamics

One of the long standing problems is a quest for regular black hole solutions, in which a resolution of the spacetime singularity has been achieved by some physically reasonable, classical field, before one resorts to the quantum gravity. The prospect of using nonlinear electromagnetic fields for this goal has been limited by the Bronnikov's no-go theorems, focused on Lagrangians depending on the electromagnetic invariant $F_{ab}F^{ab}$ only. We extend Bronnikov's results by taking into account Lagrangians that depend on both electromagnetic invariants, $F_{ab}F^{ab}$ and $F_{ab}\,{\star F^{ab}}$, and prove that the tension between the Lagrangian's Maxwellian weak field limit and boundedness of the curvature invariants persists in more general class of theories.

Deflection and gravitational lensing of null and timelike signals in the Kiselev black hole spacetime in the weak field limit

In this work we study the deflection and gravitational lensing of null and timelike signals in the Kiselev spacetime in the weak field limit, to investigate the effects of the equation of state parameter ω and the matter amount parameter α. In doing this, we extend a perturbative method previously developed for asymptotically flat spacetimes whose metric functions have integer-power asymptotic expansions to the case that may or may not be asymptotically flat but with non-integer power expansions. It is found that in the asymptotically flat case (−1/3 < ω < 0) the deflection angles are expressable as quasi-power series of the dimensionless quantities M/b, b/r s,d and α/M 1+3ω where M, b, r s,d are respectively the lens mass, impact parameter and source/detector radius. A similar series exists for the non-asymptotically flat case of (−1 < ω < −1/3), but with the closest radius r 0 replacing b. In the asymptotically flat (or non-flat) case, the increase of α or decrease of ω will increase (or increase) the deflection angle. Since the obtained deflection angles naturally take into account the finite distance effect of the source and the detector, we can establish an exact gravitational lensing equation, from which the apparent angles of the images and their magnifications are solved. It is found that generally for the asymptotically flat case, increasing α or decreasing ω will increase the apparent angles of the images. While for the non-asymptotically flat case, increasing α or ω will both lead to smaller apparent angles.

Novel traversable wormhole in general relativity and Einstein-Scalar-Gauss-Bonnet theory supported by nonlinear electrodynamics

Several traversable wormholes (T-WHs) of the Morris-Thorne type have been presented as exact solutions of Einstein-nonlinear electrodynamics gravity (GR-NLED), e.g. \cite{Arellano2009, Bronnikov2018,Bronnikov_Walia2021, Canate_Breton2018, Canate_Breton_Ortiz2020, Canate_Magos_Breton2020}. However, none of these solutions is support by a nonlinear electrodynamics model satisfying plausible conditions. In this work, we present the first traversable wormhole solution of Einstein-nonlinear electrodynamics gravity coupled to a self-interacting phantom scalar field (GR-NLED-SF) with a NLED model such that in the limit of weak field becomes the Maxwell electrodynamics, is presented. Furthermore, we show that this novel T-WH spacetime is also an exact solution of the Einstein-scalar-Gauss-Bonnet (EsGB) theory with a nonlinear electrodynamics source, but now with a real scalar field having a positive kinetic term.

Extended KP equation and solutions with special properties

We present an extended KP equation, which is given by a coupled (2+1)-dimensional nonlinear integrable system derived by the Dbar dressing method. In the limit of weak fields, the symmetry condition about the spectral transformation data is to derive the line-solitons. The rational solutions for the coupled (2+1)-dimensional nonlinear integrable system are also obtained. The dimensional reduction of the extended KP equation is discussed.

Magnetic susceptibility and response time of isotropic and structured magnetorheological elastomers

The response time of magnetorheological elastomers (MREs) depends on the complex interplay of multiple factors. In this study we investigate the response times of silicone rubber based elastomers containing magnetically soft fillers (iron and magnetite) with isotropic, and two types of anisotropic particle structures. The response times of the elastomers were extracted as the characteristic time constant from the time domain dynamic susceptibility response to ramp excitation in the weak field limit ( H&lt; 10 kAm−1). The MREs with both types of filler materials in all particle configurations showed a positive susceptibility response, while an inverse proportionality was observed between the response times and the slope of the ramp excitation in all cases. The dynamics of the structural change is found to be highly sensitive to the type of the filler material, and the anisotropy of the microstructure. The response times of the iron loaded MREs varied from (4.0 ± 0.3) ms up to (60.5 ± 2.3) ms. The magnetite loaded MREs displayed faster response (between (1.2 ± 0.1) ms and (12.1 ± 1.8) ms), which is attributed to the cross-linking inhibitor effect of the magnetite particles. The anisotropic particle structure also favors a decreased response time, however the remanence of the particles can modify the structural effect.

Hofstadter butterflies in magnetically modulated graphene bilayer: An algebraic approach

It has been shown that Bernal stacked bilayer graphene (BLG) in a uniform magnetic field demonstrates integer quantum Hall effect with a zero Landau-level anomaly \cite{Geimbilayer}. In this article we consider such system in a two dimensional periodic magnetic modulation with square lattice symmetry. It is shown algebraically that the resulting Hofstadter spectrum can be expressed in terms of the corresponding spectrum of monolayer graphene in a similar magnetic modulation. In the weak-field limit, using the tight-binding model, we also derive the Harper-Hofstadter equation for such BLG system in a periodic magnetic modulation. We further demonstrate the topological quantisation of Hall conductivity in such system and point out that the quantised Hall plateaus are equally spaced for all quantum numbers for the quantised Hall conductivity.

Constant-r geodesics in the Painlevé–Gullstrand form of Lense–Thirring spacetime

Herein we explore the non-equatorial constant-r (“quasi-circular”) geodesics (both timelike and null) in the Painlevé–Gullstrand variant of the Lense–Thirring spacetime recently introduced by the current authors. Even though the spacetime is not spherically symmetric, shells of constant-r geodesics still exist. Whereas the radial motion is (by construction) utterly trivial, determining the allowed locations of these constant-r geodesics is decidedly non-trivial, and the stability analysis is equally tricky. Regarding the angular motion, these constant-r orbits will be seen to exhibit both precession and nutation — typically with incommensurate frequencies. Thus this constant-r geodesic motion, though integrable in the precise technical sense, is generically surface-filling, with the orbits completely covering a symmetric equatorial band which is a segment of a spherical surface, (a so-called “spherical zone”), and whose latitudinal extent is governed by delicate interplay between the orbital angular momentum and the Carter constant. The situation is qualitatively similar to that for the (exact) Kerr spacetime — but we now see that any physical model having the same slow-rotation weak-field limit as general relativity will still possess non-equatorial constant-r geodesics.

Testing non-local gravity by clusters of galaxies

Extended theories of gravity have been extensively investigated during the last thirty years, aiming at fixing infrared and ultraviolet shortcomings of General Relativity and of the associated varLambda CDM cosmological model. Recently, non-local theories of gravity have drawn increasing attention due to their potential to ameliorate both the ultraviolet and infrared behavior of gravitational interaction. In particular, Integral Kernel theories of Gravity provide a viable mechanism to explain the late time cosmic acceleration so as to avoid the introduction of any form of unknown dark energy. On the other hand, these models represent a natural link towards quantum gravity. Here, we study a scalar-tensor equivalent model of General Relativity corrected with non-local terms, where corrections are selected by the existence of Noether symmetries. After performing the weak field limit and generalizing the results to extended mass distributions, we analyse the non-local model at galaxy cluster scales, by comparing the theoretical predictions with gravitational lensing observations from the CLASH program. We obtain agreement with data at the same level of statistical significance as General Relativity. We also provide constraints for the Navarro–Frenk–White parameters and lower bounds for the non-local length scales. The results are finally compared with those from the literature.

Gravitational lensing for power-Maxwell charged quintessence black hole in Rastall gravity

In this paper, we investigate the gravitational lensing for power-Maxwell charged quintessence black hole (BH) without cosmological constant in Rastall’s theory of gravity in both the strong-field limit and weak-field limit. Furthermore, we discuss the gravitational lensing by the linear electrodynamic (LE) and nonlinear electrodynamic (NLE) Maxwell field with the equation of state (EoS) parameter of the quintessence ([Formula: see text]) and compared to the case with Einstein’s gravity. We discuss the behaviors of the photon sphere radius [Formula: see text], impact parameter [Formula: see text], strong lensing coefficients [Formula: see text], [Formula: see text] and the deflection angle [Formula: see text] on the equatorial plane [Formula: see text] with the different values of Rastall parameter [Formula: see text] for the case of LE and NLE Maxwell field in the strong field limit. We also investigate the angular separation [Formula: see text], angular position [Formula: see text] and the magnification of the relativistic images. Further, we also study about the weak lensing BHs in Rastall gravity. We investigate the behaviors of weak deflection angle with the different values of Rastall parameter [Formula: see text] for the case of LE and NLE Maxwell field in the weak-field limit.

Self-energy problem, vacuum polarization, and dual symmetry in Born–Infeld-type U(1) gauge theories

We extensively explore three different aspects of Born-Infeld (BI) type nonlinear $U(1)$ gauge-invariant modifications of Maxwell's classical electrodynamics (also known as BI-type nonlinear electrodynamics) and bring some new perspectives on these theories. First, within the framework of exponential $U(1)$ gauge theory, it is explicitly proved that although the electric field at the location of the elementary point charges is not finite, but the total electrostatic field energy is finite. Motivated by this observation together with a wealth of evidence, we conjecture that all theories in 4-dimensional spacetime that belong to the BI family result in finite self-energy for elementary charged particles. In higher dimensions, it is found that the weak-field coupling limit of BI-type theories, which is identified as the weak field limit of effective Euler-Heisenberg (EH) theory, does not possess a regularizing ability to make the self-energy of a point charge finite, which implies that the conjecture may not hold for some BI-type theories. However, we explicitly prove that BI, logarithmic and exponential $U(1)$ gauge theories in arbitrary dimensions result in finite self-energy as well. Next, we classically study the problem of vacuum polarization effects and then systematically make a connection between all BI-type theories and QED. It is shown that all the BI-type theories classically predict the vacuum polarization effects, in which the final results are exactly in one-to-one correspondence with QED and the effective EH theory up to the leading order of corrections. Finally, we present a new, simple proof indicating that ...