Conformal Spacetime Research Articles

Probing the effect of time conformal factor on the particle dynamics around AdS Reissner–Nordström black hole

This study entails the effect of time on particle dynamics (both charged and uncharged) in the surrounding of the Reissner–Nordström AdS black hole in light of a general time conformal factor by acquiring Noether symmetry relation using the Lagrangian of the considered black hole spacetime. Upon acquiring the required time conformal spacetime as well as the Noether and approximated Noether symmetries along with their respective laws of conservation, the study further aims at investigating different parameters, like effective potential, effective force, and trajectories of escape velocity for the particle dynamics of the specified black hole. Additionally, in order to investigate orbit stability, the study employs the Lyapunov exponent.

On the holographic dual of a topological symmetry operator

We study the holographic dual of a topological symmetry operator in the context of the AdS/CFT correspondence. Symmetry operators arise from topological field theories localized on a subspace of the boundary conformal field theory spacetime. We use bottom up considerations to construct the topological sector associated with their bulk counterparts. In particular, by exploiting the structure of entanglement wedge reconstruction we argue that the bulk counterpart has a nontopological world volume action, i.e., it describes a dynamical object. As a consequence, we find that there are no global p-form symmetries for p≥0 in asymptotically anti–de Sitter spacetimes, which includes the case of noninvertible symmetries. Provided one has a suitable notion of subregion-subregion duality, our argument for the absence of bulk global symmetries applies to more general spacetimes. These considerations also motivate us to consider for general QFTs (holographic or not) the notion of lower-form symmetries, namely, (−m)-form symmetries for m≥2. Published by the American Physical Society 2024

Exact Solution for Rotating Black Holes in Parity-Violating Gravity

Abstract It has recently been pointed out that one can construct invertible conformal transformations with a parity-violating conformal factor, which can be employed to generate a novel class of parity-violating ghost-free metric theories from general relativity. We obtain exact solutions for rotating black holes in such theories by performing the conformal transformation on the Kerr solution in general relativity, which we dub conformal Kerr solutions. We explore the geodesic motion of a test particle in the conformal Kerr spacetime. While null geodesics remain the same as those in the Kerr spacetime, timelike geodesics exhibit interesting differences due to an effective external force caused by the parity-violating conformal factor.

Solitary wave solutions of the conformable space–time fractional coupled diffusion equation

In the realm of spatio-temporal fractional dynamics in a predator–prey system, we investigate fractional solitary wave-like solutions using the conformable space–time fractional coupled diffusion equation. To achieve this goal, we utilize the fractional derivative wave transformation approach to convert the conformable space–time fractional coupled nonlinear partial differential equations into equivalent ordinary differential equations. Subsequently, employing the G′G expansion technique, we obtain exact solutions for the transformed coupled ordinary differential equations. With the aid of these solutions and the fractional wave transformation, we construct three distinct fractional solitary wave-like solutions, namely kink-type, periodic, and rational for the considered fractional diffusive predator–prey model. Furthermore, we explore the dynamic attributes of prey and predator population densities by manipulating the space and time fractional-order parameters. Our findings reveal a significant insight: an increase in the fractional order can lead to system stabilization and foster the coexistence of both prey and predator species.

Distinct exact solutions for the conformable fractional derivative Gerdjikov-Ivanov equation via three credible methods

This paper reveals the conformable fractional space-time perturbed Gerdjikov-Ivanov (GI) equation, which is applied to nonlinear fibre optics together with photonic crystal fibres. The foremost intent of our operation is adopting the unified method, the modified F-expansion method and the modified Kudryashov method to hunt for definite solutions to the equation. In addition, by selecting fairish values, fluctuation behaviours of the solutions are drafted.

Propagation of optical pulses in fiber optics modelled by coupled space-time fractional dynamical system

This article focuses on securing distinct optical solitons to optical fiber with the coupled nonlinear Schrödinger equation. The examined equation is analyzed with the aid of conformable space–time fractional and is known to have a significant role in the propagation of pulses through a two-mode optical fiber and the soliton wavelength division multiplexing. The fractional nonlinear partial differential equations have garnered increased interest since they may be utilized to explain a wide range of complicated physical phenomena and have more dynamic structures of localized wave solutions. New extended direct algebraic method, a relatively recent integration tool, is used to obtain the solutions. The diverse pulses as bright, dark, combo, and singular soliton solutions have been extracted. In addition to aiding in the clarification of fractional nonlinear partial differential equations, the employed method provides previously extracted solutions and extracts new exact solutions. Given the correct parameter values, numerous graph forms are sketched to provide information on the visual presentation of the obtained findings. The achieved solutions are to be attractive to researchers for understanding the complexity of the considered model. The findings of this research validate the effectiveness of the proposed method for increasing nonlinear dynamical behavior. It is anticipated that, the research will be of interest to all engineers who work with engineering models. Results demonstrate the efficacy, simplicity, and generalizability of the selected computational method.

MODIFIED FINITE ELEMENT NUMERICAL METHOD FOR SOLVING CONFORMABLE SPACE-TIME FRACTIONAL NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

This paper shows how to approximate the solution to a nonlinear conformable space-time fractional partial differential equations. The proposed method is based on the Cubic B-spline polynomials and Galerkin method. Two test problems show that the approach we use to approximate the proposed equation is accurate and efficient. We apply the Von Neumann approach to show that stability requires some conditions.

Further results about the exact solutions of conformable space–time fractional Boussinesq equation (FBE) and breaking soliton (Calogero) equation

Seeking for the exact solutions of fractional nonlinear partial differential equations (FNPDE) has penetrated into almost every discipline of the natural, engineering, mathematics, and social sciences. In this article, with the aid of Maple software, using the (G′G2)-expansion method and the unified F-expansion method, we successfully investigate the exact solutions about conformable space–time fractional Boussinesq equation (FBE) and breaking soliton (Calogero) equation. Consequently, three types traveling wave solutions are found such as Jacobian double periodic elliptic, simply periodic and the rational function solutions. The (G′G2)-expansion and unified F-expansion methods are relatively complex, but we can find more solutions that have not been seen before. We give the some specific examples solutions such as double-periodic Jacobian elliptic functions which can be molted into single-periodic functions. Also we point the bridge linking among the Weierstrass elliptic, hyperbolic, trigonometric functions and Jacobian elliptic functions. The connection and distinction between these three formal solutions are also indicated in our paper.

Optical solitons for conformable space-time fractional nonlinear model

In search of the exact solutions of nonlinear partial differential equations in solitons form has become most popular to understand the internal features of physical phenomena. In this paper, we discovered various type of solitons solutions for the conformable space-time nonlinear Schrodinger equation (CSTNLSE) with Kerr law nonlinearity. To seek such solutions, we applied two proposed methods which are Sardar-subequation method and new extended hyperbolic function method. In this way several types of solitons obtained for example bright, dark, periodic singular, combined dark-bright, singular, and combined singular solitons. Some of the acquired solutions are interpreted graphically. These solutions are specific, novel, correct and may be beneficial for edifying precise nonlinear physical phenomena in nonlinear dynamical schemes. It is revealed that the proposed methods offer a straightforward and mathematical tool for solving nonlinear conformable space-time nonlinear Schrodinger equation. These results support in attaining nonlinear optical fibers in the future.

Two Reliable Techniques for Solving Conformable Space-Time Fractional PHI-4 Model Arising in Nuclear Physics via β-derivative

Nowadays, nonlinear fractional partial differential equations have been highly using for modelling of physical phenomena. Therefore, it is very important to achieve exact solutions of fractional differential equations for understanding complex phenomena in mathematical physics. In this study, new exact traveling wave solutions are reached of space-time fractional Phi-4 equation indicated by Atangana’s conformable derivative using two powerful different techniques. These are the functional variable method and the first integral method. Obtaining new solutions of this equation show that method is effective to understanding other nonlinear complex problems in particle and nuclear physics.

Deformed hopfion-Rañada knots in ModMax electrodynamics

Source-free so-called ModMax theories of nonLinear electrodynamics (NLE) in the four dimensional Minkowski spacetime vacuum are the only possible continuous deformations—and as a function of a single real and positive parameter—of source-free Maxwell linear electrodynamics (MLE) in the same vacuum, which preserve all the same Poincaré and conformal spacetime symmetries as well as the continuous duality invariance of Maxwell’s theory. Null field configurations of the latter however, including null electromagnetic knots, are singular for the Lagrangian formulation of any spacetime Poincaré and conformal invariant theory of NLE. In particular null hopfion-Rañada (HR) knots are a distinguished and fascinating class on their own of topologically nontrivial solutions to Maxwell’s equations. This work addresses the fate of these configurations within ModMax theories. A doubled class of ModMax deformed HR knots is thereby identified, each of which coalescing back in a continuous fashion to the original HR knot when the nonlinear deformation parameter is turned off.

Numerical solution of the nonlinear conformable space–time fractional partial differential equations

Numerical solution of the nonlinear conformable space–time fractional partial differential equations

Variable Coefficient Exact Solutions for Some Nonlinear Conformable Partial Differential Equations Using an Auxiliary Equation Method

The objective of this present paper is to utilize an auxiliary equation method for constructing exact solutions associated with variable coefficient function forms for certain nonlinear partial differential equations (NPDEs) in the sense of the conformable derivative. Utilizing the specific fractional transformations, the conformable derivatives appearing in the original equation can be converted into integer order derivatives with respect to new variables. As for applications of the method, we particularly obtain variable coefficient exact solutions for the conformable time (2 + 1)-dimensional Kadomtsev–Petviashvili equation and the conformable space-time (2 + 1)-dimensional Boussinesq equation. As a result, the obtained exact solutions for the equations are solitary wave solutions including a soliton solitary wave solution and a bell-shaped solitary wave solution. The advantage of the used method beyond other existing methods is that it provides variable coefficient exact solutions covering constant coefficient ones. In consequence, the auxiliary equation method based on setting all coefficients of an exact solution as variable function forms can be more extensively used, straightforward and trustworthy for solving the conformable NPDEs.

Numerical simulations of stochastic conformable space–time fractional Korteweg-de Vries and Benjamin–Bona–Mahony equations

Abstract In this paper, we investigate the effect of white noise on conformable time and space fractional KdV and BBM equations. For this purpose, we convert these equations with external noise to homogeneous conformable time and space fractional KdV and BBM equations with defined transformation and then we solve them by modified Kudryashov method. We bring our numerical results in some figures in the last section.

The conformable space–time fractional Fokas–Lenells equation and its optical soliton solutions based on three analytical schemes

This paper is about the study of space–time fractional Fokas–Lenells equation that describes nonlinear wave propagation in optical fibers. Three prominent schemes are employed for extracting different types of exact soliton solutions. In particular, the [Formula: see text] function method, the hyperbolic function method and the simplest Riccati equation scheme are investigated for the said model. As a sequel, a series of soliton solutions are obtained and verified through MATHEMATICA. The obtained solutions are significant additions in some specific fields of physics and engineering. Furthermore, the 3D graphical descriptions are left to analyze the pulse propagation for the reader.

Charged fluids encircling compact objects: force representations and conformal geometries

Charged fluids rotating around compact objects can form unique equilibrium structures when ambient large-scale electromagnetic fields combine with strong gravity. Equatorial as well as off-equatorial toroidal structures are among such figures of equilibrium with a direct relevance for astrophysics. To investigate their geometrical shapes and physical properties in the near-horizon regime, where effects of general relativity play a significant role, we commonly employ a scheme based on the energy–momentum conservation written in a standard representation. Here, we develop its interesting alternatives in terms of two covariant force representations, both based on a hypersurface projection of the energy–momentum conservation. In a proper hypersurface, space-like forces can be defined, following from a decomposition of the fluid four-acceleration. Each of the representations provides us with an insight into properties of the fluid flow, being well reflected in related conformal hypersurface geometries; we find behaviour of centrifugal forces directly related to geodesics of these conformal hypersurfaces and their embedding diagrams. We also reveal correspondence between the charged fluid flow world-lines from an ordinary spacetime, and world-lines determined by a charged test particles equation of motion in a conformal spacetime.

Computational solutions of conformable space-time derivatives dynamical wave equations: Analytical mathematical techniques

In this article, the instigator sets up the profuse traveling wave solutions four types of fractional nonlinear equations in the sense of conformable derivatives by using the novel form of modified mathematical technique. The constructed traveling wave solutions are articulated in terms of trigonometric, hyperbolic and exponential functions. The derived results are fruitful for the physical demonstrations of problems in mathematical physics and engineering.

Particles dynamics around time conformal quintessential Schwarzschild black hole

In this paper, the effect of time is explored on the dynamics of neutral and charged particles around the Schwarzschild (Sch) black hole (BH) environed by quintessence. We introduce a general time conformal factor [Formula: see text] to the quintessential Sch spacetime, where [Formula: see text] is a time ([Formula: see text])-dependent function and [Formula: see text], a small parameter, that causes perturbation in the corresponding spacetime. The Noether symmetry equation is obtained with the help of Lagrangian corresponding to time conformal Sch spacetime environed by quintessence. Consequently, we get a 19 partial differential equations (PDEs) system. The solution of this system gives Noether symmetries, Noether approximate symmetries, and the corresponding conservation laws. The dynamics of neutral/charged particles are studied as well as graphically analyzed at the foot of these invariants.

The null-timelike boundary problems of linear wave equations in asymptotically anti-de Sitter spacetime

In this paper, we study the initial-boundary problem of the massive wave equation which is conformal regular on an asymptotically anti-de Sitter spacetime, where the initial-boundary data are given on an outgoing null hypersurface and a timelike hypersurface, and the asymptotic information is given on the future null infinity. After a conformal rescaling, this problem will reduce to a null-timelike boundary problem of linear wave equation on the conformal compactificated spacetime, where the initial data is given on a null hypersurface and the boundary data are given on two timelike hypersurfaces. We demonstrate well posedness for the associated null-timelike boundary problems. The proofs rely on energy estimates (weighted energy estimates for null-timelike boundary problems) and local existence of solution for initial-boundary problems. This is a toy model motivated by AdS/CFT correspondence.

New Exact Solutions of the Conformable Space-Time Sharma–Tasso–Olver Equation Using Two Reliable Methods

The major purpose of this article is to seek for exact traveling wave solutions of the nonlinear space-time Sharma–Tasso–Olver equation in the sense of conformable derivatives. The novel ( G ′ G ) -expansion method and the generalized Kudryashov method, which are analytical, powerful, and reliable methods, are used to solve the equation via a fractional complex transformation. The exact solutions of the equation, obtained using the novel ( G ′ G ) -expansion method, can be classified in terms of hyperbolic, trigonometric, and rational function solutions. Applying the generalized Kudryashov method to the equation, we obtain explicit exact solutions expressed as fractional solutions of the exponential functions. The exact solutions obtained using the two methods represent some physical behaviors such as a singularly periodic traveling wave solution and a singular multiple-soliton solution. Some selected solutions of the equation are graphically portrayed including 3-D, 2-D, and contour plots. As a result, some innovative exact solutions of the equation are produced via the methods, and they are not the same as the ones obtained using other techniques utilized previously.