Search Results (79)

Applying the Parikh–Wilczek method and based on the thermodynamics laws of black holes, we investigate the structure of the entropy of rotating Bardeen black holes. We find that entropy includes three terms and thus violates the area law. The first two terms depend on all of the black hole characteristics, while the third one is solely dependent on the charge of a magnetic monopole arising from nonlinear electrodynamics. The existence of the additional term means that the entropy of regular black holes has a different structure from that of classical ones, so it cannot be considered as a constant and disregarded, as was implemented in the previous literature. Full article

We investigate the transport coefficients $\alpha$ and $\beta$ in plasma systems with varying Reynolds numbers while maintaining a unit magnetic Prandtl number (${Pr}_{\mathrm{M}}$). The $\alpha$ and $\beta$ tensors parameterize the turbulent electromotive force (EMF) in terms of the large-scale magnetic field $\overline{\mathbf{B}}$ and current density as follows: $⟨\mathbf{u}\times \mathbf{b}⟩=\alpha \overline{\mathbf{B}}-\beta \nabla \times \overline{\mathbf{B}}$. In astrophysical plasmas, high fluid Reynolds numbers ($Re$) and magnetic Reynolds numbers ($R{e}_{\mathrm{M}}$) drive turbulence, where $Re$ governs flow dynamics and $R{e}_{\mathrm{M}}$ controls magnetic field evolution. The coefficients ${\alpha }_{\mathrm{semi}}$ and ${\beta }_{\mathrm{semi}}$ are obtained from large-scale magnetic field data as estimates of the $\alpha$ and $\beta$ tensors, while ${\beta }_{\mathrm{theo}}$ is derived from turbulent kinetic energy data. The reconstructed large-scale field $\overline{B}$ agrees with simulations, confirming consistency among $\alpha$, $\beta$, and $\overline{B}$ in weakly nonlinear regimes. This highlights the need to incorporate magnetic effects under strong nonlinearity. To clarify $\alpha$ and $\beta$, we introduce a field structure model, identifying $\alpha$ as the electrodynamic induction effect and $\beta$ as the fluid-like diffusion effect. The agreement between our method and direct simulations suggests that plasma turbulence and magnetic interactions can be analyzed using fundamental physical quantities. Moreover, ${\alpha }_{\mathrm{semi}}$ and ${\beta }_{\mathrm{semi}}$, which successfully reproduce the numerically obtained magnetic field, provide a benchmark for future theoretical studies. Full article

We study the charged black-hole solutions of a 2 + 1 nonlinear electrodynamical theory with a cosmological constant. Considered as a one-parameter group of theories (the exponent of the squared Maxwell tensor), the causal structure of all possible black holes is scrutinized. We analyze the singularity character that each theory delivers, together with their horizons and the plausible limitations in black-hole charges. The investigation demonstrates a rich structure of three different groups of theories according to the qualitative behavior of the singularity, horizons and limitations in the geometric charges. For such groups, we study the effect of a scalar field propagating in the spacetime of fixed black holes. All analyzed geometries are stable to such linear perturbations, evolving as usual quasinormal spectra of the black holes calculated for the different cases. Full article

We investigate a quantum electrodynamics system consisting of two coupled single-mode cavities. The left cavity couples with a two-level atom, while the right cavity incorporates a second-order nonlinear medium, activated by a pumping field. In the absence of nonlinear medium, we show that the transmitted field intensity reveals only classical asymmetric behavior at the central frequency. However, the parametric interaction induced by the nonlinear medium leads to various quantum asymmetric behaviors at single photon excitation frequencies, including the squeezing, quantum statistics, and phase-space characteristics of the transmitted photons. These asymmetric behaviors arise from additional excitation pathways enabled by the parametric interaction-induced two-photon processes. We demonstrate these asymmetric behaviors through Klyshko’s figures of merit, the Wigner function, and the steady-state second-order correlation function of the transmitted photons. These results present promising applications for remote quantum-state manipulation and contribute significantly to the advancement of quantum networking. Full article

Under the framework of classical electrodynamics, this article investigates the nonlinear Thomson scattering generated by the cross-collision between a tightly focused linearly polarized Gaussian laser pulse and a relativistic electron through numerical simulation and emulation. The oscillation direction and emission angle of the electron’s trajectory are influenced by the beam waist radius and the delay time. The spatial radiation distribution of electrons exhibits a comet-shaped pattern, with the radiation being concentrated in the forward position. This is attributed to the high laser intensity at the focus, resulting in intense electron motion. As the beam waist radius keeps increasing continuously, the maximum radiation polar angle in the spatial distribution decreases. The time spectrum exhibits a symmetrical three-peak structure, with a high secondary peak. Meanwhile, the supercontinuum spectrum gradually transforms into a multi-peak distribution spectrum. In the multi-peak mode, the main peak and the secondary peak will interchange during the increase in the waist radius, generating rays with higher frequencies and energies. The aforementioned research findings reveal a portion of the mechanism of the nonlinear Thomson scattering theory and are beneficial for generating X-rays of higher quality. Full article

The Bronnikov generalization of the Fisher naked singularity and Dilatonic black hole spacetimes attracts high interest, as it combines two fundamental transitions of the solutions of Einstein equations. These are the black hole/wormhole “black bounce” transition of geometry, and the phantom/canonical transition of the scalar field, called trapped ghost scalar, combined with an electromagnetic field described by a non-linear electrodynamics. In the present paper, we put restrictions on the parameters of the Fisher (wormhole) and Dilatonic (black hole or wormhole) regularized spacetimes by using frequencies of the epicyclic orbital motion in the geodesic model for explanation of the high-frequency oscillations observed in microquasars or active galactic nuclei, where stellar mass or supermassive black holes are usually assumed. Full article

In recent decades, many researchers have pointed out that derivatives and integrals of the non-integer order are well suited for describing various real-world materials, for example, polymers. It has also been shown that fractional-order mathematical models are more effective than integer-order mathematical models. Thereby, given these considerations, the investigation of qualitative properties, in particular, Ulam-type stabilities of fractional differential equations, fractional integral equations, etc., has now become a highly attractive subject for mathematicians, as this represents an important field of study due to their extensive applications in various branches of aerodynamics, biology, chemistry, the electrodynamics of complex media, polymer science, physics, rheology, and so on. Meanwhile, the qualitative concepts called Ulam–Hyers–Mittag-Leffler (U-H-M-L) stability and Ulam–Hyers–Mittag-Leffler–Rassias (U-H-M-L-R) stability are well-suited for describing the characteristics of fractional Ulam-type stabilities. The Banach contraction principle is a fundamental tool in nonlinear analysis, with numerous applications in operational equations, fractal theory, optimization theory, and various other fields. In this study, we consider a nonlinear fractional Volterra integral equation (FrVIE). The nonlinear terms in the FrVIE contain multiple variable delays. We prove the U-H-M-L stability and U-H-M-L-R stability of the FrVIE on a finite interval. Throughout this article, new sufficient conditions are obtained via six new results with regard to the U-H-M-L stability or the U-H-M-L-R stability of the FrVIE. The proofs depend on Banach’s fixed-point theorem, as well as the Chebyshev and Bielecki norms. In the particular case of the FrVIE, an example is delivered to illustrate U-H-M-L stability. Full article

The unified Einstein–Euler–Heisenberg theory is utilized to investigate the particle motion and weak gravitational lensing characteristics of black holes. This black hole solution is developed using spherically symmetric possessing electric and magnetic charges. Quantum electrodynamics corrections reveal a screening effect for BH electric charges and paramagnetic impacts on magnetic charges. We analyzed the motion of massive as well as massless particles by studying their effective potential, event horizon, photon orbit and inner circular orbit. It was demonstrated that magnetic and electric fields of spherically symmetric black holes have significant impact. Then, we also delve to study the weak gravitational lensing phenomenon. A comprehensive approach was employed to investigate this phenomenon and explore the angle of deflection of light rays near magnetically and electrically charged black holes. Full article

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

This paper explores the optical approach to simplifying complex concepts in general relativity (GR) and nonlinear vacuum electrodynamics. The focus is on using optical analogies to simplify the understanding of spacetime curvature and interactions in strong gravitational and magnetic fields. We demonstrate how applying concepts of effective refractive index can facilitate the teaching and comprehension of GR optical effects, such as gravitational lensing and the behavior of light around massive objects. Additionally, the paper covers the application of optical analogies in the context of nonlinear vacuum electrodynamics, showing how strong magnetic fields affect light propagation. This interdisciplinary approach provides a more natural understanding and modeling of complex physical phenomena, making them better accessible for study and teaching. Full article

We analyze Hayward black holes (BHs) with a negative cosmological constant surrounded by a cloud of strings, which we designate Hayward–Letelier AdS BHs. These solutions can be obtained by coupling the Einstein equations with nonlinear electrodynamics and the energy–momentum tensor of clouds of strings. We show that these solutions are no longer regular and have a curvature singularity at the center. In turn, we analyze the thermodynamics associated with these BHs by establishing the form of the Smarr formula and the first law of thermodynamics. We derive the expressions for the thermodynamic quantities such as pressure, temperature, heat capacity, Gibbs free energy, and isothermal compressibility. We explore the phase structure of these solutions by analyzing the behavior of the heat capacity and Gibbs free energy. These solutions exhibit a first-order phase transition, similar to van der Waals fluids. We also check the behavior of the thermodynamic quantities near the critical points and calculate the values of the critical exponents. This illustrates a robust analogy between our solutions and van der Waals fluids. Full article

We obtain exact black hole solutions to Einstein gravity coupled with a nonlinear electrodynamics field, in the presence of a cloud of strings and quintessence, as sources. The solutions have four parameters, namely m, k, a, and $\alpha$, corresponding to the physical mass of the black hole, the nonlinear charge of a self-gravitating magnetic field, the cloud of strings, and the intensity of the quintessential fluid. The consequences of these sources on the regularity or singularity of the solutions, on their horizons, as well as on the energy conditions, are discussed. We study some aspects concerning the thermodynamics of the black hole, by taking into account the mass, Hawking temperature, and heat capacity and show how these quantities depend on the presence of the cloud of strings and quintessence, in the scenario considered. Full article

In this article, exact solutions of the Biswas–Arshed equation are obtained using the extended Weierstrass transformation method (EWTM). This method is widely used in solid-state physics, electrodynamics, and mathematical physics, and it yields exact solution functions involving trigonometric, rational trigonometric, Weierstrass elliptic, wave, and rational functions. The process involves expanding the solution functions of an elliptic differential equation into finite series by transforming them into Weierstrass functions. Furthermore, it generates parametric solutions for nonlinear algebraic equation systems, which are particularly useful in mathematical physics. These solutions are derived using the Mathematica package program. To analyze the behavior of these determined solution functions, the article employs separate two- and three-dimensional graphs showing the real and imaginary components, along with contour and density graphs. These visuals aid in comprehending the physical characteristics exhibited by these solution functions. Full article

We apply a combined study in order to investigate the dynamics of cosmological models incorporating nonlinear electrodynamics (NLED). The study is based on the simultaneous investigation of such fundamental aspects as stability and causality, complemented with a dynamical systems investigation of the involved models, as well as Bayesian inference for parameter estimation. We explore two specific NLED models: the power-law and the rational Lagrangian. We present the theoretical framework of NLED coupled with general relativity, followed by an analysis of the stability and causality of the various NLED Lagrangians. We then perform a detailed dynamical analysis to identify the ranges where these models are stable and causal. Our results show that the power-law Lagrangian model transitions through various cosmological phases, evolving from a Maxwell radiation-dominated state to a matter-dominated state. For the rational Lagrangian model, including the Maxwell term, stable and causal behavior is observed within specific parameter ranges, with critical points indicating the evolutionary pathways of the universe. To validate our theoretical findings, we perform Bayesian parameter estimation using a comprehensive set of observational data, including cosmic chronometers, baryon acoustic oscillation (BAO) measurements, and supernovae type Ia (SNeIa). The estimated parameters for both models align with the expected values for the current universe, particularly the matter density ${\Omega }_m$ and the Hubble parameter h. However, the parameters of the models are not tightly constrained within the prior ranges. Our combined studies approach rules out the mentioned models as an appropriate description of the cosmos. Our results highlight the need for further refinement and exploration of NLED-based cosmological models to fully integrate them into the standard cosmological framework. Full article

We study Einstein’s gravity in AdS space coupled to nonlinear electrodynamics. Thermodynamics in extended phase space of magnetically charged black holes is investigated. We compute the metric and mass functions and their asymptotics, showing that black holes may have one or two horizons. The metric function is regular, $f\left(0\right)=1$, and corrections to the Reissner–Nordström solution are in the order of $\mathcal{O}\left(r^{-3}\right)$ when the Schwarzschild mass is zero. We prove that the first law of black hole thermodynamics and the generalized Smarr relation hold. The magnetic potential and vacuum polarization conjugated to coupling are computed and depicted. We calculate the Gibbs free energy and the heat capacity showing that first-order and second-order phase transitions take place. Full article