Maxwell Field Research Articles

Action growth of dyonic black holes and electromagnetic duality

Electromagnetic duality of Maxwell theory is a symmetry of equations but not of the action. The usual application of the “complexity = action” conjecture would thus lose this duality. It was recently proposed in arXivid:1901.00014 that the duality can be restored by adding some appropriate boundary term, at the price of introducing the mixed boundary condition in the variation principle. We present universal such a term in both first-order and second-order formalism for a general theory of a minimally-coupled Maxwell field. The first-order formalism has the advantage that the variation principle involves only the Dirichlet boundary condition. Including this term, we compute the on-shell actions in the Wheeler-De Witt patch and find that the duality is preserved in these actions for a variety of theories, including Einstein-Maxwell, Einstein-Maxwell-Dilaton, Einstein-Born-Infeld and Einstein-Horndeski-Maxwell theories.

A note on spinor form of Lovelock differential identity

The paper is devoted to 2-spinor calculus methods in general relativity. New spinor form of the Lovelock differential identity is suggested. This identity is second-order identity for the Riemann curvature tensor. We provide an example that our spinorial treatment of Lovelock identity is effective for the description of solutions of Einstein–Maxwell equations. It is shown that the covariant divergence of Lipkin’s zilch tensor for the free Maxwell field vanishes on the solutions of Einstein–Maxwell equations if and only if the energy–momentum tensor of the electromagnetic field is Weyl-compatible.

Ultra-compact spherically symmetric dark matter charged star objects

We study the properties of ultra-compact spherically symmetric dark matter sector star objects, being the solution of Einstein equations with two U(1)-gauge fields. One of them is the ordinary Maxwell field, while the auxiliary gauge field pertains to the hidden sector, and mimics the properties of dark matter. The visible and hidden sectors are coupled by a kinetic mixing term with a coupling constant α. We also investigate the possibility of condensation of charged scalar field around the reflecting dark matter star object. It happens that dark matter sector, both dark matter charge and coupling constant, cause shrinking of the star radius for which the condensation may occur.

Duality invariant self-interactions of abelian p-forms in arbitrary dimensions

We analyze non-linear interactions of 2N -form Maxwell fields in a space-time of dimension D = 4N.Based on the Pasti-Sorokin-Tonin (PST) method, we derive the general consistency condition for the dynamics to respect both manifest SO(2)-duality invariance and manifest Lorentz invariance. For a generic dimension D = 4N, we determine a canonical class of exact solutions of this condition, which represent a generalization of the known non-linear duality invariant Maxwell theories in D = 4. The resulting theories are shown to be equivalent to a corresponding class of canonical theories formulated à la Gaillard-Zumino-Gibbons-Rasheed (GZGR), where duality is a symmetry only of the equations of motion. In dimension D = 8, via a complete solution of the PST consistency condition, we derive new non-canonical manifestly duality invariant quartic interactions. Correspondingly, we construct new non-trivial quartic interactions also in the GZGR approach, and establish their equivalence with the former. In the presence of charged dyonic p-brane sources, we reveal a basic physical inequivalence of the two approaches. The power of our method resides in its universal character, reducing the construction of non-linear duality invariant Maxwell theories to a purely algebraic problem.

Models of lightlike charges with nongeodesic worldlines

Massless particles in General Relativity move with the speed of light, their trajectories in spacetime are described by null geodesics. This is independent of the electrical charge of the particle being considered, however, the charged light-like case is less well understood. Starting with the Maxwell field of a charged particle having a light-like geodesic world line in Minkowskian space-time we construct the Maxwell field of such a particle having a non-geodesic, light-like world line. The necessary geometry in the neighbourhood of an arbitrary null world line in Minkowskian space-time is described and properties of the resulting electromagnetic field are discussed. The electromagnetic field obtained represents a light-like analogue of the Lienard-Wiechert field, which generalises the Coulomb field of a charge having a time-like geodesic world line to the field of a charge having an accelerated world line.

Finite field formalism for bulk electrolyte solutions

The manner in which electrolyte solutions respond to electric fields is crucial to understanding the behavior of these systems both at, and away from, equilibrium. The present formulation of linear response theory for such systems is inconsistent with common molecular dynamics (MD) implementations. Using the finite field formalism, suitably adapted for finite temperature MD, we investigate the response of bulk aqueous NaCl solutions to both finite Maxwell (E) and electric displacement (D) fields. The constant E Hamiltonian allows us to derive the linear response relation for the ionic conductivity in a simple manner that is consistent with the forces used in conventional MD simulations. Simulations of a simple point charge model of an electrolyte solution at constant E yield conductivities at infinite dilution within 15% of experimental values. The finite field approach also allows us to measure the solvent’s dielectric constant from its polarization response, which is seen to decrease with increasing ionic strength. Comparison of the dielectric constant measured from polarization response vs polarization fluctuations enables direct evaluation of the dynamic contribution to this dielectric decrement, which we find to be small but not insignificant. Using the constant D formulation, we also rederive the Stillinger-Lovett conditions, which place strict constraints on the coupling between solvent and ionic polarization fluctuations.

Electromagnetic effects on complexity factor for static cylindrical system

This paper investigates the phenomenon of complexity factor for static charged anisotropic cylindrical configuration. We formulate some basic equations such as Einstein–Maxwell field equations, Tolman–Opphenheimer–Volkoff equation and mass equation. Further, the orthogonal splitting of the Riemann tensor is used to obtain the structure scalars that lead to the complexity factor. Finally, we investigate some theoretical models with vanishing complexity condition. It is found that the complexity of the system increases for α ≤ 1 in the presence of the electromagnetic field.

Maxwell quantum mechanics

We extend classical Maxwell field theory to a first quantized theory of the photon by deriving a conserved Lorentz four-current whose zero component is a positive definite number density. Fields are real and their positive (negative) frequency parts are interpreted as absorption (emission) of a positive energy photon. With invariant plane wave normalization, the photon position operator is Hermitian with instantaneously localized eigenvectors that transform as Lorentz four-vectors. Reality of the fields and wave function ensure causal propagation and zero net absorption of energy in the absence of charged matter. The photon probability amplitude is the real part of the projection of the photon's state vector onto a basis of position eigenvectors and its square implements the Born rule. Manifest covariance and consistency with quantum field theory is maintained through use of the electromagnetic four-potential and the Lorenz gauge.

Conformal wave equations for the Einstein-tracefree matter system

Inspired by a similar analysis for the vacuum conformal Einstein field equations by Paetz (Ann Henri Poincaré 16:2059, 2015), in this article we show how to construct a system of quasilinear wave equations for the geometric fields associated to the conformal Einstein field equations coupled to matter models whose energy-momentum tensor has vanishing trace. In this case, the equation of conservation for the energy-momentum tensor is conformally invariant. Our analysis includes the construction of a subsidiary evolution which allows to prove the propagation of the constraints. We discuss how the underlying structure behind these systems of equations is the set of integrability conditions satisfied by the conformal field equations. The main result of our analysis is that both the evolution and subsidiary equations for the geometric part of the conformal Einstein-tracefree matter field equations close without the need of any further assumption on the matter models other that the vanishing of the trace of the energy-momentum tensor. Our work is supplemented by an analysis of the evolution and subsidiary equations associated to three basic tracefree matter models: the conformally invariant scalar field, the Maxwell field and the Yang–Mills field. As an application we provide a global existence and stability result for de Sitter-like spacetimes. In particular, the result for the conformally invariant scalar field is new in the literature.

Cosmological Einstein–Maxwell model with g-essence

In this paper, we study the model of the late universe with the homogeneous, isotropic and flat Friedmann–Robertson–Walker metric, where the source of the gravitational field is based on the fermion and boson fields, with the Maxwell term [Formula: see text] in four dimensions. The actuation of the Maxwell term for the Einstein gravity makes it possible to find new approaches to solve the problem of the observed accelerated expansion of the universe. Energy conditions have been obtained and studied. These conditions impose very simple and model-independent restrictions on the behavior of energy density and pressure since they do not require a specific equation-of-state of matter. To consider the model, the energy conditions NEC, WEC, DEC are realized, and the SEC condition is violated. The boson and fermion fields are responsible for the accelerated regime at early times, but since the total pressure tends toward zero for large times, a transition to a decelerated regime occurs. Maxwell field is crucial only in the early times.

Representation independent boundary conditions for a piecewise-homogeneous linear magneto-dielectric medium

At a boundary between two transparent, linear, isotropic, homogeneous materials, derivations of the electromagnetic boundary conditions and the Fresnel relations typically proceed from the Minkowski {E,B,D,H} representation of the macroscopic Maxwell equations. However, equations of motion for macroscopic fields in a transparent linear medium can be written using Ampère {E,B}, Chu {E,H}, Lorentz, Minkowski, Peierls, and other formulations of continuum electrodynamics. We present a representation-independent derivation of electromagnetic boundary conditions and Fresnel relations for the propagation of monochromatic radiation through a piecewise-homogeneous, transparent, linear, magneto-dielectric medium. The electromagnetic boundary conditions and the Fresnel relations are derived from energy conservation coupled with the application of Stokes’s theorem to the wave equation. Our representation-independent formalism guarantees the general applicability of the Fresnel relations. Specifically, the new derivation is necessary so that a valid derivation of the Fresnel equations exists for alternative, non-Minkowski formulations of the macroscopic Maxwell field equations.

Spontaneous scalarisation of charged black holes: coupling dependence and dynamical features

Spontaneous scalarisation of electrically charged, asymptotically flat Reissner–Nordström black holes (BHs) has been recently demonstrated to occur in Einstein–Maxwell–Scalar (EMS) models. This phenomenon is allowed by a non-minimal coupling between the scalar and the Maxwell fields, and does not require non-minimal couplings of the scalar field to curvature invariants. EMS BH scalarisation presents a technical simplification over the BH scalarisation that has been conjectured to occur in extended scalar–tensor Gauss–Bonnet (eSTGB) models. It is then natural to ask: (1) how universal are the conclusions extracted from the EMS model? And (2) how much do these conclusions depend on the choice of the non-minimal coupling function? Here we address these questions by performing a comparative analysis of several different forms for the coupling function including: exponential, hyperbolic, power-law and a rational function (fraction) couplings. In all of them we obtain and study the domain of existence of fundamental, spherically symmetric, scalarised BHs and compute, in particular, their entropy. The latter shows that scalarised EMS BHs are always entropically preferred over the RN BHs with the same total charge to mass ratio q. This contrasts with the case of eSTGB, where for the same power-law coupling the spherical, fundamental scalarised BHs are not entropically preferred over the Schwarzschild solution. Also, while the scalarised solutions in the EMS model for the exponential, hyperbolic and power-law coupling are very similar, the rational function coupling leads to a transition in the domain of existence, by virtue of a pole in the coupling function, into a region of ‘exotic’ solutions that violate the weak energy condition. Furthermore, fully non-linear dynamical evolutions of unstable RN BHs with different values of q are presented. These show: (1) for sufficiently small q, scalarised solutions with (approximately) the same q form dynamically; (2) for large q, spontaneous scalarisation visibly decreases q; thus evolutions are non-conservative; (3) despite the existence of non-spherical, static scalarised solutions, the evolution of unstable RN BHs under non-spherical perturbations leads to a spherical scalarised BH.

Dyonic Field Equations in Arbitrary Media

Starting with the generalized Maxwell field equation of dyon, the matrix form of generalized Maxwell field equation is formulated in a compact manner. The Maxwell field equations and Lorentz force for dyon in term of the matrix are also derived in arbitrary media (material media). It represents an additional field, which shows polarization and magnetization for the electric and magnetic charge. Finally, the Continuity equation for dyon is also derived.

Further evidence for the weak gravity \u2014 cosmic censorship connection

We have recently shown that a class of counterexamples to (weak) cosmic censorship in anti-de Sitter spacetime is removed if the weak gravity conjecture holds. Surprisingly, the minimum value of the charge to mass ratio necessary to preserve cosmic censorship is precisely the weak gravity bound. To further explore this mysterious connection, we investigate two generalizations: adding a dilaton or an additional Maxwell field. Analogous counterexamples to cosmic censorship are found in these theories if there is no charged matter. Even though the weak gravity bound is modified, we show that in each case it is sufficient to remove these counterexamples. In most cases it is also necessary.

Dyonic Field Equations in Arbitrary Media

Starting with the generalized Maxwell field equation of dyon, the matrix form of generalized Maxwell field equation is formulated in a compact manner. The Maxwell field equations and Lorentz force for dyon in term of the matrix are also derived in arbitrary media (material media). It represents an additional field, which shows polarization and magnetization for the electric and magnetic charge. Finally, the Continuity equation for dyon is also derived.

Entropy Evolution in the Interior Volume of a Charged f(R) Black Hole**Supported by the National Natural Science Foundation of China under Grant No. 11235003

Based on the 4-dimensional black hole solution of f(R) theory coupled to a nonlinear Maxwell field, we calculate the interior volume of a charged f(R) black hole using the method proposed by Christodoulou and Rovelli. Considering massless scalar field in the interior volume and Hawking radiation carrying only energy, we calculate the entropy of the scalar field inside a charged f(R) black hole and investigate the evolution of the entropy under Hawking radiation. In the meantime, the evolution of the Bekenstein-Hawking entropy under Hawking radiation has also been calculated. Based on these results, the proportional relation is obtained between the evolution of the scalar field entropy and the evolution of Bekenstein-Hawking entropy under Hawking radiation. According to the result, we investigate and discuss how the modified coefficient b in f(R) gravity theory affects the evolution relation between the two types of entropy. It is shown that the radiation rate for Hawking radiation of a charged f(R) black hole can increase with the modified coefficient b.

Black holes that repel

The recent observation that black holes in certain Einstein-Maxwell-Dilaton (EMD) theories can violate the entropy super-additivity led to the suggestion that these black holes might repel each other. In this paper, we consider EMD theories with two Maxwell fields $A_i$, with general exponential couplings $\exp(a_i \phi)$ in their kinetic terms. We calculate the gravi-electrostatic force between charged black holes $(m_1,e_1)$ and $(M_2,Q_2)$; the former is sufficiently small and can be treated as a point-like object. We find there is a potential barrier caused by the dilaton coupling at $r_0$ outside the back hole horizon $r_+$, provided that $-a_1 a_2> 2(D-3)/(D-2)$. As the black hole approaches extremality, both $r_+$ and $r_0$ vanish, the barrier becomes infinitesimally thin but infinitely high, and the two black holes repel each other in the whole space. There is no electrostatic force between them; the dilaton is the antigravity agent. Furthermore we find that the exact constraint on $a_1 a_2$ can be derived from the requirements that two-charged extremal black holes have a fusion bomb like mass formula and the violation of entropy super-additivity can occur. The two very different approaches give a consistent picture of the black hole repulsion.

Dirac star in the presence of Maxwell and Proca fields

We consider configurations consisting of a gravitating nonlinear spinor field $\psi$, with a nonlinearity of the type $\lambda\left(\bar\psi\psi\right)^2$, minimally coupled to Maxwell and Proca fields through the coupling constants $Q_M$ [U(1) electric charge] and $Q_P$, respectively. In order to ensure spherical symmetry of the configurations, we use two spin-$1/2$ fields having opposite spins. By means of numerical computations, we find families of equilibrium configurations with a positive Arnowitt-Deser-Misner (ADM) mass described by regular zero-node asymptotically flat solutions for static Maxwell and Proca fields and for stationary spinor fields. For the case of the Maxwell field, it is shown that, with increasing charge $Q_M$, the masses of the objects increase and diverge as the charge tends to a critical value. For negative values of the coupling constant $\lambda$, we demonstrate that, by choosing physically reasonable values of this constant, it is possible to obtain configurations with masses comparable to the Chandrasekhar mass and with effective radii of the order of kilometers. It enables us to speak of an astrophysical interpretation of such systems, regarding them as charged Dirac stars. In turn, for the system with the Proca field, it is shown that the mass of the configurations also grows with increasing both $|\lambda|$ and the coupling constant $Q_P$. Although in this case the numerical calculations do not allow us to make a definite conclusion about the possibility of obtaining masses comparable to the Chandrasekhar mass for physically reasonable values of $\lambda$, one may expect that such masses can be obtained for certain values of free parameters of the system under consideration.

Cosmology of a higher derivative scalar theory with non-minimal Maxwell coupling

Higher derivative scalar field theory in curved space-time belongs to the GLPV theory coupled non-minimally to the Maxwell field is considered. We will show that the theory admits two independent exact de Sitter solutions in the FRW background, one driven by the cosmological constant and the other by the GLPV scalar field. The dynamical system analysis of the theory shows that these two exact solutions are stable fixed points. Also, cosmological perturbations over these solutions shows that the cosmological constant based solution is healthy at linear level but the GLPV based solution suffers from a gradient instability in the scalar sector. This proves that the cosmological constant is needed in the GLPV-Maxwell system in order to have a healthy de Sitter solution.

Axionic charged black branes with arbitrary scalar nonminimal coupling

In this paper, we construct four-dimensional charged black branes of a nonminimally coupled and self-interacting scalar field. In addition to the scalar and Maxwell fields, the model involves two axionic fields homogeneously distributed along the two-dimensional planar base manifold providing in turn a simple mechanism of momentum dissipation. Interestingly enough, the horizon of the solution can be located at two different positions depending on the sign of the parameter associated to the axionic field, and in both cases there exists a wide range of values of the nonminimal coupling parameter yielding to physical acceptable solutions. For a negative parameter that sustains the axionic fields, the allowed nonminimal coupling parameters take discrete values and the solution turns out to be extremal since its has zero temperature. A complete analysis of the thermodynamic features of the solutions is also carried out. Finally, thanks to the mechanism of momentum dissipation, the holographic DC conductivities of the solutions are computed in terms of the black hole horizon data, and we analyze the effects of the nonminimal coupling parameter on these conductivities. For example, in the purely electric case, we notice that as long as the nonminimal coupling parameter takes the discrete values associated to the extremal solution, the DC conductivity vanishes identically reproducing in turn an insulator behavior. In the non extremal case, we point out the existence of a particular value of the nonminimal coupling parameter (which is greater than the conformal one in four dimensions) yielding an infinite conductivity; this is due to the fact that the translation invariance is restored at this point. Finally, in the dyonic case, we show that the conductivity matrix for the extremal solution has a Hall effect-like behavior.