Effect Of Spacetime Curvature Research Articles

Study of deflection angle and shadow in supergravity black hole theory under the influence of non-magnetic plasma medium

In this paper, we examine models of a black hole’s deflection angle in the context of gauged super-gravity, using the black hole’s optical metric. We compute Gaussian curvature and the Gauss-Bonnet theorem of optical metric and also follow the Gibbons-Werner technique to calculate the deflection angle. The spacetime curvature effects are significant and will have extensive implications for gauged supergravity theory. By incorporating the Gaussian curvature of the optical metric over a four-dimensional surface of light dispersion. Further, we examine the deflection angle in the presence of the non-magnetic plasma medium and how the non-magnetic plasma impacts the deflection angle. Furthermore, we show how the photon sphere influences the gauged supergravity and non-magnetized plasma of the black hole shadow, as well as how to generate black hole shadows by employing the ray tracing approach. Finally, we analyze the shadow cast and address plots of both the deflection angle and the shadow to understand the deflection angle functions and the shadow impact in the non-magnetic plasma medium.

BCS in the sky: signatures of inflationary fermion condensation

We consider a Bardeen-Cooper-Schrieffer (BCS)-like model in the inflationary background. We show that with an axial chemical potential, the attractive quartic fermion self-interaction can lead to a BCS-like condensation. In the rigid-de Sitter (dS) limit of inflation where backreaction from the inflaton and graviton is neglected, we perform the first computation of the non-perturbative effective potential that includes the full spacetime curvature effects in the presence of the chemical potential, subject to the mean-field approximation whose validity has been checked via the Ginzburg criterion. The corresponding BCS phase transition is always first-order, when the varying Hubble is interpreted as an effective Gibbons-Hawking temperature of dS spacetime. In the condensed phase, the theory can be understood from UV and IR sides as fermionic and bosonic, respectively. This leads to distinctive signatures in the primordial non-Gaussianity of curvature perturbations. Namely, the oscillatory cosmological collider signal is smoothly turned off at a finite momentum ratio, since different momentum ratios effectively probe different energy scales. In addition, such BCS phase transitions can also source stochastic gravitational waves, which are feasible for future experiments.

Photon motion and weak gravitational lensing in black-bounce spacetime* *Supported by Grant F-FA-2021-510 of the Uzbekistan Ministry for Innovative Development

The effect of spacetime curvature on photon motion may offer an opportunity to propose new tests on gravity theories. In this study, we investigate and focus on the massless (photon) particle motion around black-bounce gravity. We analyze the horizon structure around a gravitational compact object described by black-bounce spacetime. The photon motion and the effect of gravitational weak lensing in vacuum and plasma are discussed, and the shadow radius of the compact object is also studied in black-bounce spacetime. Additionally, the magnification of the image is studied using the deflection angle of light rays.

Weak Gravitational Lensing around Bardeen Black Hole with a String Cloud in the Presence of Plasma

The effect of spacetime curvature on optical properties may provide an opportunity to suggest new tests for gravity theories. In this paper, we investigated gravitational weak lensing around a Bardeen black hole with the string clouds parameter. First, we examined the horizon structure in the presence of string clouds around the gravitational compact object defined by Bardeen spacetime. The effect of gravitational weak lensing in a plasma medium is also discussed. According to the findings, the influence of the string cloud parameter on the circular orbits of a light ray around the black hole is greater than that in the Schwarzschild case, while the influence of the charge is reversed. The deflection angle of light rays in weak lensing is also used to study how much the image is magnified.

Optical realization of one-dimensional generalized split-step quantum walks

Quantum walks are more than tools for building quantum algorithms. They have been used effectively to model and simulate quantum dynamics in many complex physical processes. Particularly, a variant of discrete-time quantum walk known as split-step quantum walk is closely related to Dirac cellular automata and topological insulators, whose realizations rely on position-dependent control of evolution operators. Owing to the ease of manipulating multiple degrees of freedom of photons, we provide an optical setup of split-step operators which, in combination with position-dependent coin (PDC) operation, can accomplish a table-top setup of generalized split-step walks. Also, we propose an optical implementation for PDC operation that allows, for instance, realizing electric quantum walks, control localization dynamics, and emulate space-time curvature effects. In addition, we propose a setup to realize any t-step split-step quantum walk involving 2 J-plates, 2 variable waveplates, a half-waveplate, an optical switch, and an optical delay line.

Hawking temperature for 4D-Einstein-Gauss-Bonnet black holes from uncertainty principle

Inspired by string theory, Heisenberg's uncertainty principle can be generalized to include the photon-electron gravitational interaction, which leads to the Generalized Uncertainty Principle (GUP). Although GUP considers gravitational uncertainty at the minimum fundamental length scale in physics, it does not consider the effects of spacetime curvature on quantum mechanical uncertainty relations. The Extended Uncertainty Principle (EUP) is a generalization of Heisenberg's Uncertainty Principle that, unlike the GUP, applies to large length scales. GEUP is also a linear combination of EUP and GUP that creates minimal uncertainty on large length scales. The Einstein-Gauss-Bonnet theory (EGB) can be considered as one of the most promising candidates for modified gravity. In this paper, by using GUP, EUP, and GEUP, we intend to obtain the Hawking temperature of a four-dimensional EGB black hole in the asymptotically flat and (Anti)-de Sitter spacetime. We show that coupling constant, cosmological constant, mass, and radius significantly affect Hawking temperature and decrease or increase Hawking temperature depending on the chosen horizons.

Equivalence principle violation from large scale structure

We explore the interplay between the equivalence principle and a generalization of the Heisenberg uncertainty relations known as extended uncertainty principle, that comprises the effects of spacetime curvature at large distances. Specifically, we observe that, when the modified uncertainty relations hold, the weak formulation of the equivalence principle is violated, since the inertial mass of quantum systems becomes position-dependent whilst the gravitational mass is left untouched. To obtain the above result, spinor and scalar fields are separately analyzed by considering the non-relativistic limit of the Dirac and the Klein-Gordon equations in the presence of the extended uncertainty principle. In both scenarios, it is found that the ratio between the inertial and the gravitational mass is the same.

The effect of spacetime curvature on statistical distributions

The Boltzmann distribution of an ideal gas is determined by the Hamiltonian function generating single particle dynamics. Systems with higher complexity often exhibit topological constraints, which are independent of the Hamiltonian and may affect the shape of the distribution function as well. Here, we study a further source of heterogeneity, the curvature of spacetime arising from the general theory of relativity. The present construction relies on three assumptions: first, the statistical ensemble is made of particles obeying geodesic equations, which define the phase space of the system. Next, the metric coefficients are time-symmetric, implying that, if thermodynamic equilibrium is achieved, all physical observables are independent of coordinate time. Finally, ergodicity is enforced with respect to proper time, so that ambiguity in the choice of a time variable for the statistical ensemble is removed. Under these hypothesis, we derive the distribution function of thermodynamic equilibrium, and verify that it reduces to the Boltzmann distribution in the non-relativistic limit. We further show that spacetime curvature affects physical observables, even far from the source of the metric. Two examples are analyzed: an ideal gas in Schwarzschild spacetime and a charged gas in Kerr–Newman spacetime. In the Schwarzschild case, conservation of macroscopic constraints, such as angular momentum, combined with relativistic distortion of the distribution function can produce configurations with decreasing density and growing azimuthal rotation velocity far from the event horizon of the central mass. In the Kerr–Newman case, it is found that kinetic energy associated with azimuthal rotations is an increasing function of the radial coordinate, and it eventually approaches a constant value corresponding to non-relativistic equipartition, even though spatial particle density decreases.

Chiral magnetism: a geometric perspective

We discuss a geometric perspective on chiral ferromagnetism. Much like gravity becomes the effect of spacetime curvature in theory of relativity, the Dzyaloshinski-Moriya interaction arises in a Heisenberg model with nontrivial spin parallel transport. The Dzyaloshinskii-Moriya vectors serve as a background SO(3) gauge field. In 2 spatial dimensions, the model is partly solvable when an applied magnetic field matches the gauge curvature. At this special point, solutions to the Bogomolny equation are exact excited states of the model. We construct a variational ground state in the form of a skyrmion crystal and confirm its viability by Monte Carlo simulations. The geometric perspective offers insights into important problems in magnetism, e.g., conservation of spin current in the presence of chiral interactions.

Mathematical modelling and analysis of gravitational collapse in curved geometry

Background and objectives: In the visible universe, it is believed that mass and energy are interchangeable. However, the physical and chemical processes in the hidden world put the scientist into the thought of matter and energy contents that are responsible for these phenomena. These are regarded as dark matter and dark energy. In this article, we study the effects of spacetime curvature on the gravitational collapse of dark energy in modified gravity, considering the collapse of the spherically symmetric star, which is composed of perfect and homogeneous fluid. We studied the collapse for closed, flat and hyperbolic geometry.Method: As a result of mathematical modeling, we achieved highly non-linear differential equations. For the solution, we needed the assumption of physical significance. Specifically, we have taken the dark energy collapse. Then we achieved a simple system and solved for the analytic solutions of the field equations.Results: It is shown that the possible collapse is visibly influenced by spatial curvature. The collapse time is advanced for closed spacetime, delayed for the hypersurface, and the flat space behaves intermediately. We have taken here the equation of state in linear form to discuss the exhibition of fluid profile and a specific necessary criterion for the occurrence of spacetime singularity.Conclusion: In this paper, we study the mathematical model of gravitational collapse in modified gravity, which derives the field equations using the principle of least action. The significant outcomes are the influences of the spatial curvature on the collapsing process and the time of formation of spacetime singularity. The matching of boundary and the fundamental continuity of the 1-form and 2-form are discussed.

Cylindrical gravitational waves: C-energy, super-energy and associated dynamical effects

The energy content of cylindrical gravitational wave spacetimes is analyzed by considering two local descriptions of energy associated with the gravitational field, namely those based on the C-energy and the Bel–Robinson super-energy tensor. A Poynting–Robertson-like effect on the motion of massive test particles, beyond the geodesic approximation, is discussed, allowing them to interact with the background field through an external force which accounts for the exchange of energy and momentum between particles and waves. In addition, the relative strains exerted on a bunch of particles displaced orthogonally to the direction of propagation of the wave are examined, providing invariant information on spacetime curvature effects caused by the passage of the wave. The explicit examples of monochromatic waves with either a single or two polarization states as well as pulses of gravitational radiation are discussed.

Geometric optics in general relativity using bilocal operators

We consider the standard problem of observational astronomy, i.e. the observations of light emission from a distant region of spacetime in general relativity. The goal is to describe the changes between the measurements of the light performed by a sample of observers slightly displaced with respect to each other and moving with different 4-velocities and 4-accelerations. In our approach, all results of observations can be expressed as functions of the kinematic variables, describing the motions of the observers and the emitting bodies with respect to their local inertial frames, and four linear bilocal geodesic operators, describing the influence of the spacetime geometry on light propagation. The operators are functionals of the curvature tensor along the line of sight. The results are based on the assumption that the regions of emissions and observations are sufficiently small so that the spacetime curvature effects are negligible within each of them, although they are significant for the light propagation between them. The new formulation provides a uniform approach to optical phenomena in curved spacetimes and, as an application, we discuss the problem of a fully relativistic definition of the parallax and position drifts (or proper motions). We then use the results to construct combinations of observables which are completely insensitive to the motion of both the observer and the emitter. These combinations by construction probe the spacetime geometry between the observation and emission regions and in our formalism we may express them as functionals of the Riemann tensor along the line of sight. For short distances one of these combinations depends only on the matter content along the line of sight. This opens up the possibility to measure the matter content of a spacetime in a tomography-like manner irrespective of the motions of the emitter and the observer.

Efimov physics in curved spacetime: Field fluctuations and exotic matter

Several experimental detections have demonstrated the existence of Borromean states predicted by Vitaly Efimov within a nuclear physics context, that is, trimers bound despite the absence of bound states of any of the two-body subsystems. I show that novel Efimov Physics is expected in gravitationally polarizable nonbaryonic dark matter beyond the Standard Model with van der Waals-like forces driven by quantum gravitational fluctuations. I also discuss ground and space-based tests of spacetime curvature effects on weakly bound, highly diffuse quantum three-body systems with standard electrodynamical van der Waals forces. Finally, I consider exotic gravitational quantum matter from higher-order Brunnian structures and analogies with classical systems, already proven in three-stranded DNA, driven by the stochastic gravitational wave background.

Relativistic Magnetic Reconnection in Kerr Spacetime.

The magnetic reconnection process is analyzed for relativistic magnetohydrodynamical plasmas around rotating black holes. A simple generalization of the Sweet-Parker model is used as a first approximation to the problem. The reconnection rate, as well as other important properties of the reconnection layer, has been calculated taking into account the effect of spacetime curvature. Azimuthal and radial current sheet configurations in the equatorial plane of the black hole have been studied, and the case of small black hole rotation rate has been analyzed. For the azimuthal configuration, it is found that the black hole rotation decreases the reconnection rate. On the other hand, in the radial configuration, it is the gravitational force created by the black hole mass that decreases the reconnection rate. These results establish a fundamental interaction between gravity and magnetic reconnection in astrophysical contexts.

Observer dependence of angular momentum in general relativity and its relationship to the gravitational-wave memory effect

We define a procedure by which observers can measure a type of special-relativistic linear and angular momentum $({P}^{a},{J}^{ab})$ at a point in a curved spacetime using only the spacetime geometry in a neighborhood of that point. The method is chosen to yield the conventional results in stationary spacetimes near future null infinity. We also explore the extent to which spatially separated observers can compare the values of angular momentum that they measure and find consistent results. We define a generalization of parallel transport along curves which gives a prescription for transporting values of angular momentum along curves that yields the correct result in special relativity. If observers use this prescription, then they will find that the angular momenta they measure are observer dependent, because of the effects of spacetime curvature. The observer dependence can be quantified by a kind of generalized holonomy. We show that bursts of gravitational waves with memory generically give rise to a nontrivial generalized holonomy: there is, in this context, a close relation between the observer dependence of angular momentum and the gravitational-wave memory effect.

Neutrino Oscillation in a Curved Schwarzschild-de Sitter Space-Time

The quantum mechanical phases associated with the neutrinos oscillation associated to the propagation phenomenon in a Schwarchild-de Sitter gravitational fields using the WKB approximation are studied and the space-time curvature effects are discussed.

Gravity from refraction of CMB photons using the optical-mechanical analogy in general relativity

Relativistic light bending and gravitational lensing have traditionally been viewed purely as effects of spacetime curvature. Yet for many years they have also been treated as a quasi-refraction of light in a special optical medium, wherein the refractive index is considered proportional to the gravitational potential. We now propose that this ‘optical-mechanical analogy’ in general relativity can also account for gravity. Using classical optics we show that a photon moving through the refractive medium about a mass transfers momentum first to the medium and then to the mass itself. Due to transfer of momentum primarily from ultra-remote CMB photons, masses are then subject to a cosmic pressure on all sides. Where two masses occur, mutual screening by their respective envelopes of refractive medium is shown to result in an attractive force of the Le Sage or ‘pushing gravity’ type. We suggest that the gravito-optical medium is comprised of gravitons, which may be modeled as a quasi-Einstein-Bose conjugate interconnecting all the masses of the visible universe.

Size of the Gribov region in curved spacetime

Recent work in the literature has argued that the joint effect of spacetime curvature and the Gribov ambiguity may introduce further modifications to the Green functions in the infrared. This paper focuses on a simple criterion for studying the effect of spacetime curvature on the size of the Gribov region, improving the accuracy of the previous analysis. It is shown that, depending on the sign of the scalar and Riemann curvature, the Gribov horizon moves inward or, instead, outward with respect to the case of flat spacetime. This is made clear by two novel inequalities here derived for the first time.

The Structure Lacuna

Molecular symmetry is intimately connected with the classical concept of three-dimensional molecular structure. In a non-classical theory of wave-like interaction in four-dimensional space-time, both of these concepts and traditional quantum mechanics lose their operational meaning, unless suitably modified. A required reformulation should emphasize the importance of four-dimensional effects like spin and the symmetry effects of space-time curvature that could lead to a fundamentally different understanding of molecular symmetry and structure in terms of elementary number theory. Isolated single molecules have no characteristic shape and macro-biomolecules only develop robust three-dimensional structure in hydrophobic response to aqueous cellular media.

Dynamo effect of spacetime curvature in force-free magnetospheres

We study the possibility of growth of the electric and magnetic fields in a force-free plasma due strictly to the gravitational curvature of the spacetime domain where those fields lie. To this end, we identify a total energy by analogy with the results of classical magnetohydrodynamics. After obtaining the general evolution equation for the total energy, we apply to it to the fiducial observers in a number of classical metrics: Schwarzschild, Boyer-Lindquist, Kerr-Schild, Robertson-Walker, and post-Newtonian approximation. As a rule the shift velocity plays the role of minus the fluid velocity in Newtonian MHD, but the details are often highly intricate.