Maxwell Source Research Articles

Nonlinearly charged black hole chemistry with massive gravitons in the grand canonical ensemble

In the context of Black Hole Chemistry (BHC), holographic phase transitions of asymptotically anti-de Sitter (AdS) charged topological black holes (TBHs) in massive gravity coupled to Power Maxwell Invariant (PMI) electrodynamics are discussed in the grand canonical (fixed $U(1)$ potential, $\Phi$) ensemble. Considering all higher-order graviton's self-interactions of (dRGT) massive gravitational field theory in arbitrary dimensions, exact TBH solutions are derived, the explicit form of the on-shell action is computed, and the associated thermodynamic quantities in the Grand Canonical Ensemble (GCE) are calculated. In addition, the validity of the first law of thermodynamics and Smarr relation are examined in the extended phase space. Regarding this model, it is shown that a van der Waals (vdW) behavior takes place in $d \ge 4$ dimensions, a typical reentrant phase transition is observed in $d \ge 5$, and both anomalous vdW and triple point phenomena are recognized in $d \ge 6$. So, the results are quite different from their counterparts in the GCE of Maxwell-massive gravity. Besides, we briefly study the critical behaviors of higher-dimensional TBHs with a conformally invariant Maxwell source as a special subgroup of our solutions for both Einstein and massive gravity theories in various ensembles.

Instability and no-hair paradigm in d-dimensional charged-AdS black holes

Is it possible the no-hair paradigm is violated when a black hole undergoes an instability? Employing massless charged scalar perturbations, we address this question within the context of conformally invariant Einstein-Maxwell theory for some allowed d-dimensional (d=4n+4 with conformal parameter n=0,1,2,...) topological small AdS black-holes. We provide numerical analyses that show the non trivial scalar hairy black hole solutions to include planar and spherical horizon topologies in higher dimensions with an even conformal parameter n. It is also shown that the solutions presented here cannot be considered as scalar hairs for a Reissner-Nordstrom background. As a result, for d-dimensional small AdS black holes in the presence of a conformally invariant Maxwell source, the no-scalar hair paradigm seems to be supported.

Conformally mapped polynomial chaos expansions for Maxwell's source problem with random input data

AbstractGeneralized Polynomial Chaos (gPC) expansions are well established for forward uncertainty propagation in many application areas. Although the associated computational effort may be reduced in comparison to Monte Carlo techniques, for instance, further convergence acceleration may be important to tackle problems with high parametric sensitivities. In this work, we propose the use of conformal maps to construct a transformed gPC basis, in order to enhance the convergence order. The proposed basis still features orthogonality properties and hence, facilitates the computation of many statistical quantities such as sensitivities and moments. The corresponding surrogate models are computed by pseudo‐spectral projection using mapped quadrature rules, which leads to an improved cost accuracy ratio. We apply the methodology to Maxwell's source problem with random input data. In particular, numerical results for a parametric finite element model of an optical grating coupler are given.

ENHANCED ADAPTIVE SURROGATE MODELS WITH APPLICATIONS IN UNCERTAINTY QUANTIFICATION FOR NANOPLASMONICS

We propose an efficient surrogate modeling technique for uncertainty quantification. The method is based on a well-known dimension-adaptive collocation scheme. We improve the scheme by enhancing sparse polynomial surrogates with conformal maps and adjoint error correction. The methodology is applied to Maxwell's source problem with random input data. This setting comprises many applications of current interest from computational nanoplasmonics, such as grating couplers or optical waveguides. Using a non-trivial benchmark model we show the benefits and drawbacks of using enhanced surrogate models through various numerical studies. The proposed strategy allows us to conduct a thorough uncertainty analysis, taking into account a moderately large number of random parameters.

Exact ghost-free bigravitational waves

We study the propagation of exact gravitational waves in the ghost-free bimetric theory. Our focus is on type N spacetimes compatible with the cosmological constants provided by the bigravity interaction potential, and particularly in the single class known by allowing at least a Killing symmetry: the AdS waves. They have the advantage of being represented by a generalized Kerr-Schild transformation from AdS spacetime. This means a notorious simplification in bigravity by allowing to straightforwardly compute any power of its interaction square root matrix, opening the door to explore physically meaningful exact configurations. For these exact gravitational waves the complex dynamical structure of bigravity decomposes into elementary exact massless or massive excitations propagating on AdS. We use a complexified formulation of the Euler-Darboux equations to provide for the first time the general solutions to the massive version of the Siklos equation which rules the resulting AdS-waves dynamics, using an integral representation originally due to Poisson. Inspired in this progress we tackle the subtle problem on how matter couples to bigravity and concretely if this occurs through a composite metric, which is hard to handle in a general setting. Surprisingly, the Kerr-Schild ansatz brings again a huge simplification in how the related energy-momentum tensors are calculated. This allows us to explicitly characterize AdS waves supported in one case by a massless free scalar field and by a wavefront-homogeneous Maxwell field in another. Considering the most general allowed Maxwell source instead is a highly nontrivial task, that we accomplish by exploiting again the complexified Euler-Darboux description and taking advantage of the classical Riemann method. In fact, this allow us to find at the end the most general configurations for any matter source.

Q − Φ criticality and microstructure of charged AdS black holes in f(R) gravity

The phase transition and critical behaviors of charged AdS black holes in [Formula: see text] gravity with a conformally invariant Maxwell (CIM) source and constant curvature are further investigated. As a highlight, this research is carried out by employing new state parameters [Formula: see text] and contributes to deeper understanding of the thermodynamics and phase structure of black holes. Our analyses manifest that the charged [Formula: see text]-CIM AdS black hole undergoes a first-order small–large black hole phase transition, and the critical behaviors qualitatively behave like a Van der Waals liquid–vapor system. However, differing from the case in Einstein’s gravity, phase structures of the black holes in [Formula: see text] theory exhibit an interesting dependence on gravity modification parameters. Moreover, we adopt the thermodynamic geometry to probe the black hole microscopic properties. The results show that, on the one hand, both the Ruppeiner curvature and heat capacity diverge exactly at the critical point, on the other hand, the [Formula: see text]-CIM AdS black hole possesses the property as ideal Fermi gases. Of special interest, we discover a microscopic similarity between the black holes and a Van der Waals liquid–vapor system.

F(R)Gravity’s Rainbow and Its Einstein Counterpart

Motivated by UV completion of general relativity with a modification of a geometry at high energy scale, it is expected to have an energy dependent geometry. In this paper, we introduce charged black hole solutions with power Maxwell invariant source in the context of gravity’s rainbow. In addition, we investigate two classes ofF(R)gravity’s rainbow solutions. At first, we study energy dependentF(R)gravity without energy-momentum tensor, and then we obtainF(R)gravity’s rainbow in the presence of conformally invariant Maxwell source. We study geometrical properties of the mentioned solutions and compare their results. We also give some related comments regarding thermodynamical behavior of the obtained solutions and discuss thermal stability of the solutions.

Dynamical analysis of charged anisotropic spherical star in f(R) gravity

We consider a modified gravity theory, \(f(R) = R + \alpha R^n - \tfrac{{\mu ^4 }} {{R^m }}\), in the metric formulation and analyze the contribution of the electromagnetic field on the range of dynamical instability of a star filled with anisotropic matter. The collapse equation is developed by applying conservation on anisotropic matter, Maxwell source and dark source terms arising due to f(R) gravity. A specific perturbation scheme is implemented and it is observed that the inclusion of Maxwell source slows down the collapse and makes the system more stable in Newtonian regime. Also, we make a comparison of our results with the existing literature.

Thermodynamics of higher dimensional topological dilation black holes with a power-law Maxwell field

In this paper, we extend the study on the nonlinear power-law Maxwell field to dilaton gravity. We introduce the $(n+1)$-dimensional action in which gravity is coupled to a dilaton and power-law nonlinear Maxwell field, and obtain the field equations by varying the action. We construct a new class of higher dimensional topological black hole solutions of Einstein-dilaton theory coupled to a power-law nonlinear Maxwell field and investigate the effects of the nonlinearity of the Maxwell source as well as the dilaton field on the properties of the spacetime. Interestingly enough, we find that the solutions exist provided one assumes three Liouville-type potentials for the dilaton field, and in case of the Maxwell field one of the Liouville potential vanishes. After studying the physical properties of the solutions, we compute the mass, charge, electric potential and temperature of the topological dilaton black holes. We also study thermodynamics and thermal stability of the solutions and disclose the effects of the dilaton field and the power-law Maxwell field on the thermodynamics of these black holes. Finally, we comment on the dynamical stability of the obtained solutions in four-dimensions.

Higher-dimensional chargedf(R)black holes

We construct a new class of higher-dimensional black hole solutions of $f(R)$ theory coupled to a nonlinear Maxwell field. In deriving these solutions the traceless property of the energy-momentum tensor of the matter filed plays a crucial role. In $n$-dimensional spacetime the energy-momentum tensor of conformally invariant Maxwell field is traceless provided we take $n=4p$, where $p$ is the power of conformally invariant Maxwell Lagrangian. These black hole solutions are similar to higher-dimensional Reissner-Nordstrom anti-de Sitter black holes but only exist for dimensions which are multiples of four. We calculate the conserved and thermodynamic quantities of these black holes and check the validity of the first law of black hole thermodynamics by computing a Smarr-type formula for the total mass of the solutions. Finally, we study the local stability of the solutions and find that there is indeed a phase transition for higher-dimensional $f(R)$ black holes with conformally invariant Maxwell source.

The effects of conformally invariant Maxwell source on the magnetic wormhole solutions in Gauss–Bonnet gravity

In this paper we introduce a new class of nonsingular higher dimensional conformally invariant magnetic solutions that may be interpreted as traversable wormholes, which could be supported by matter not violating the weak energy conditions. The electromagnetic source is chosen in which the expression of the Maxwell field does not depend on the dimension and its value coincides with the Reissner–Nordström solution in four dimensions. We generalize this class of solutions to the case of rotating solutions and show that the rotating wormhole solutions have a net electric charge that is proportional to the magnitude of the rotation parameter, while the static wormhole has no net electric charge. Finally, we use the counterterm method and compute the conserved quantities of these spacetimes.

Isogeometric Discrete Differential Forms in Three Dimensions

The concept of isogeometric analysis (IGA) was first applied to the approximation of Maxwell equations in [A. Buffa, G. Sangalli, and R. Vazquez, Comput. Methods Appl. Mech. Engrg., 199 (2010), pp. 1143-1152]. The method is based on the construction of suitable B-spline spaces such that they verify a De Rham diagram. Its main advantages are that the geometry is described exactly with few elements, and the computed solutions are smoother than those provided by finite elements. In this paper we develop the theoretical background to the approximation of vector fields in IGA. The key point of our analysis is the definition of suitable projectors that render the diagram commutative. The theory is then applied to the numerical approximation of Maxwell source problems and eigenproblems, and numerical results showing the good behavior of the scheme are also presented.

The relation between [formula omitted] gravity and Einstein-conformally invariant Maxwell source

In this Letter, we consider the special case of F(R) gravity, in which F(R)=RN and obtain its topological black hole solutions in higher dimensions. We show that, the same as higher-dimensional charged black hole, these solutions may be interpreted as black hole solutions with two event horizons, extreme black hole and naked singularity provided the parameters of the solutions are chosen suitably. But, the presented black hole is different from the standard higher-dimensional Reissner–Nordström solutions. Next, we present the conformally invariant Maxwell field coupled to Einstein gravity and discuss about its black hole solutions. Comparing these two class of solutions, shows that there is a correspondence between the Einstein-conformally invariant Maxwell solutions and the solutions of F(R) gravity without matter field in arbitrary dimensions.

Isogeometric analysis in electromagnetics: B-splines approximation

We introduce a new discretization scheme for Maxwell equations in two space dimension. Inspired by the new paradigm of Isogeometric analysis introduced in Hughes et al. (2005) [16], we propose an algorithm based on the use of bivariate B-splines spaces suitably adapted to electromagnetics. We construct B-splines spaces of variable interelement regularity on the parametric domain. These spaces (and their push-forwards on the physical domain) form a De Rham diagram and we use them to solve the Maxwell source and eigen problem. Our scheme has the following features: (i) is adapted to treat complex geometries, (ii) is spectral correct, (iii) provides regular (e.g., globally C 0 ) discrete solutions of Maxwell equations.

Topological black holes in Gauss–Bonnet gravity with conformally invariant Maxwell source

In this Letter, we present a class of rotating solutions in Gauss–Bonnet gravity in the presence of cosmological constant and conformally invariant Maxwell field and study the effects of the nonlinearity of the Maxwell source on the properties of the spacetimes. These solutions may be interpret as black brane solutions with inner and outer event horizons provide that the mass parameter m is greater than an extremal value mext, an extreme black brane if m=mext and a naked singularity otherwise. We investigate the conserved and thermodynamics quantities for asymptotically flat and asymptotically AdS with flat horizon. We also show that the conserved and thermodynamic quantities of these solutions satisfy the first law of thermodynamics.

Ricci flat rotating black branes with a conformally invariant Maxwell source

We consider Einstein gravity coupled to an $U(1)$ gauge field for which the density is given by a power of the Maxwell Lagrangian. In $d$-dimensions the action of Maxwell field is shown to enjoy the conformal invariance if the power is chosen as $d/4$. We present a class of charge rotating solutions in Einstein-conformally invariant Maxwell gravity in the presence of a cosmological constant. These solutions may be interpreted as black brane solutions with inner and outer event horizons or an extreme black brane depending on the value of the mass parameter. Since we are considering power of the Maxwell density, the black brane solutions exist only for dimensions which are multiples of four. We compute conserved and thermodynamics quantities of the black brane solutions and show that the expression of the electric field does not depend on the dimension. Also, we obtain a Smarr-type formula and show that these conserved and thermodynamic quantities of black branes satisfy the first law of thermodynamics. Finally, we study the phase behavior of the rotating black branes and show that there is no Hawking--Page phase transition in spite of conformally invariant Maxwell field.

Spherically symmetric solutions of Einstein + non-polynomial gravities

We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to maintain the (first) derivative order of the Einstein equations in Schwarzschild gauge. Generically, the solutions exhibit both horizons and a singularity at the origin, except for one model that forbids spherical symmetry altogether. Extensions to arbitrary dimension with a cosmological constant, Maxwell source and Gauss-Bonnet terms are also considered.

Representation of the main geomagnetic field using Maxwell's theory of poles

SUMMARY The spatio-temporal variations in the main geomagnetic field are analysed using Maxwell's source representation of the potential function defined by Maxwell's theory of poles. Maxwell sources up to order 4 are obtained for three main geomagnetic field models. The temporal variations in the main geomagnetic field are shown in terms of the variations in the parameters defined in Maxwell's source representation, for example, the Maxwell moments, the Maxwell axes, the intrinsic energy of the Maxwell source, etc. The characteristics of these variations are discussed. Applications of Maxwell's source representation of the potential function to the studies of the earth's magnetic field are suggested.

Higher-dimensional black holes with a conformally invariant Maxwell source

We consider an action for an Abelian gauge field for which the density is given by a power of the Maxwell Lagrangian. In $d$ spacetime dimensions this action is shown to enjoy conformal invariance if the power is chosen as $d/4$. We take advantage of this conformal invariance to derive black hole solutions electrically charged with a purely radial electric field. Since we are considering a power of the Maxwell density, the black hole solutions exist only for dimensions which are multiples of four. The expression for the electric field does not depend on the dimension and corresponds to the four-dimensional Reissner-Nordstr\om field. Using the Hamiltonian action we identify the mass and the electric charge of these black hole solutions.

Kaluza-Klein black hole with negatively curved extra dimensions in string-generated gravity models

We obtain a new exact black-hole solution in Einstein-Gauss-Bonnet gravity with a cosmological constant which bears a specific relation to the Gauss-Bonnet coupling constant. The spacetime is a product of the usual 4-dimensional manifold with a $(n-4)$-dimensional space of constant negative curvature, i.e., its topology is locally ${\ma M}^n \approx {\ma M}^4 \times {\ma H}^{n-4}$. The solution has two parameters and asymptotically approximates to the field of a charged black hole in anti-de Sitter spacetime. The most interesting and remarkable feature is that the Gauss-Bonnet term acts like a Maxwell source for large $r$ while at the other end it regularizes the metric and weakens the central singularity.