We obtain electrically charged black hole solutions of the Einstein equations in arbitrary dimensions with a nonlinear electrodynamics source. The matter source is deriving from a Lagrangian given by an arbitrary power of the Maxwell invariant. The form of the general solution suggests a natural partition for the different ranges of this power. For a particular range, we exhibit a class of solutions whose behavior resemble to the standard Reissner-Nordstrom black holes. There also exists a range for which the black hole solutions approach asymptotically the Minkowski spacetime slower than the Schwarzschild spacetime. We have also found a family of not asymptotically flat black hole solutions with an asymptotic behavior growing slower than the Schwarzschild (anti) de Sitter spacetime. In odd dimensions, there exists a critical value of the exponent for which the metric involves a logarithmic dependence. This critical value corresponds to the transition between the standard behavior and the solution decaying to Minkowski slower than the Schwarzschild spacetime.
In the probe limit, we investigate the nonlinear electrodynamical effects of the both exponential form and the logarithmic form on the holographic paramagnetism-ferromagnetism phase transition in the background of a Schwarzschild-AdS black hole spacetime. Moreover, by comparing the exponential form of nonlinear electrodynamics with the logarithmic form of nonlinear electrodynamics and the Born-Infeld nonlinear electrodynamics which has been presented in Ref.~\cite{Wu:2016uyj}, we find that the higher nonlinear electrodynamics correction makes the critical temperature smaller and the magnetic m…
We study quasinormal modes related to gravitational and electromagnetic perturbations of spherically symmetric charged black holes in nonlinear electrodynamics. Beyond the linear Maxwell electrodynamics, we consider a class of Lagrangian with higher-order corrections written by the electromagnetic field strength and its Hodge dual with arbitrary coefficients, and we parametrize the corrections for quasinormal frequencies in terms of the coefficients. It is confirmed that the isospectrality of quasinormal modes under parity is generally violated due to nonlinear electrodynamics. As applications…
We study a non-local ghost-free Lorentz invariant modification of the Maxwell equations in four- and higher-dimensional flat spacetimes. We construct solutions of these equations for stationary charged and magnetized objects and use them to find the field created by such objects moving with the speed of light.
Recently Bandos, Lechner, Sorokin, and Townsend [arXiv:2007.09092] have discovered that Maxwell's electrodynamics can be generalized so that the resulting nonlinear theory preserves both conformal invariance and SO(2) duality-rotation invariance. Their result can be derived in a simpler way.
A theory of quantum electrodynamics with nonlocal interaction
In this paper, we present a theory of quantum electrodynamics with nonlocal interaction, a main characteristic of the theory is that a charged particle situated x^{mu} interacts with electromagnetic field situated y^{mu}, where x^{mu}=y^{mu}+aA^{mu}, A^{mu} reads electromagnetic 4-potential, a is a constant. All the action, the equations of motion of charged particle and electromagnetic field are given. For the case of free fields, charged particle and electromagnetic field obey the Dirac equation and the Maxwell equation of free fields, respectively; for the case with interaction, both the eq…
After many years of efforts, the first nonlinearly charged rotating black hole has been finally reported by Garcia-Diaz in two recent works. This is an important result that was pending in General Relativity, since nonlinear generalizations of the Kerr-Newman solution were not yet known. Unfortunately, the Lagrangian supporting this configuration cannot be expressible in terms of the standard invariants using elementary functions. In the present work we circumvent this problem by using the formulations of nonlinear electrodynamics in terms of mixed electromagnetic eigenvalues, introduced by Sa…
We have performed a complete study of BPS vortex solutions in the Abelian sector of the standard model extension (SME). Specifically, we have coupled the SME electromagnetism with a Higgs field which is supplemented with a Lorentz-violating CPT-even term. We have verified that Lorentz violation (LV) belonging to the Higgs sector allows to interpolate between some well known models like, Maxwell-Higgs, Chern-Simons-Higgs and Maxwell-Chern-Simons-Higgs. We can also observed that the electrical charged density distribution is nonnull in both CPT-even and CPT-odd models; however, the total electri…
We prove a no Cauchy horizon theorem for general nonlinear electrodynamics black holes with charged scalar hairs. By constructing a radially conserved charged, we show that there is no inner Cauchy horizon for both spherical and planar symmetric cases, independent of the form of scalar potential and nonlinear electrodynamics. After imposing the null energy condition, we are also able to rule out the existence of the Cauchy horizon for the hyperbolic black holes. We take the Born-Infeld black hole as a concrete example to study the interior dynamics beyond the event horizon. When the contributi…
We consider both generalized Born-Infeld and Exponential Electrodynamics. The field-energy of a point-like charge is finite only for Born-Infeld-like Electrodynamics. However, both Born-Infeld-type and Exponential Electrodynamics display the vacuum birefringence phenomenon. Subsequently, we calculate the lowest-order modifications to the interaction energy for both classes of Electrodynamics, within the framework of the gauge-invariant path-dependent variables formalism. These are shown to result in long-range ($1/r^5$- type) corrections to the Coulomb potential. Once again, for their non-comm…
In the present work we study the scale dependence at the level of the effective action of charged black holes in Einstein-Maxwell as well as in Einstein-power-Maxwell theories in (2+1)-dimensional spacetimes without a cosmological constant. We allow for scale dependence of the gravitational and electromagnetic couplings, and we solve the corresponding generalized field equations imposing the "null energy condition". Certain properties, such as horizon structure and thermodynamics, are discussed in detail.
New five-dimensional charged AdS black hole solutions are found in Einstein-Gauss-Bonnet gravity and the nonlinear electrodynamics. These solutions include regular black holes as well as extremal black holes. The first law of the black hole thermodynamics is confirmed in the extended phase space where the cosmological constant is treated as the pressure. The first and second order phase transitions are investigated by observing the behavior of the heat capacity at constant pressure and the Gibbs free energy. In addition, the equation of state for the black holes and their $P-V$ criticality are…
The field of a moving pointlike charge is determined in nonlinear local electrodynamics. As a model Lagrangian for the latter we take the one whose nonlinearity is the Euler-Heisenberg Lagrangian of quantum electrodynamics truncated at the leading term of its expansion in powers of the first field invariant. The total energy of the field produced by a point charge is finite in that model; thereby its field configuration is a soliton. We define a finite energy-momentum vector of this field configuration to demonstrate that its components satisfy the standard mechanical relation characteristic o…
Recently, an interesting mechanism [Phys.Rev.Lett.106:231101,2011] has been proposed which produces all nonlinear terms in massive gravity to all orders . In this work, we reproduce these results in M-theory and consider the process of birth and growth of nonlinear gravity during the construction of Mp-branes. It has been shown that Mp brane are built up of p- M1-branes which each of them are connected to M1-branes of other Mp-brane through a wormhole. In this model, by increasing the number of dimensions, the number of nonlinear terms in relevant action of branes enhances and some theories li…
The Bronnikov model of nonlinear electrodynamics is investigated in general relativity. The magnetic black hole is considered and we obtain a solution giving corrections to the Reissner-Nordström solution. In this model spacetime at $r\rightarrow\infty$ becomes Minkowski's spacetime. We calculate the magnetic mass of the black hole and the metric function. At some parameters of the model there can be one, two or no horizons. The Hawking temperature and the heat capacity of black holes are calculated. We show that a second-order phase transition takes place and black holes are thermodynamically…
Recently, it has been observed that the Noether-Gaillard-Zumino (NGZ) identity holds order by order in $α'$ expansion in nonlinear electrodynamics theories as Born-Infeld (BI) and Bossard-Nicolai (BN). The nonlinear electrodynamics theory that couples to an axion field is invariant under the $SL(2,R)$ duality in all orders of $α'$ expansion in the Einstein frame. In this paper we show that there are the $SL(2,R)$ invariant forms of the energy momentum tensors of axion-nonlinear electrodynamics theories in the Einstein frame. These $SL(2,R)$ invariant structures appear in the energy momentum te…
We derive the classical dynamics of massless charged particles in a rigorous way from first principles. Since due to ultraviolet divergences this dynamics does not follow from an action principle, we rely on a) Maxwell's equations, b) Lorentz- and reparameterization-invariance, c) local conservation of energy and momentum. Despite the presence of pronounced singularities of the electromagnetic field along Dirac-like strings, we give a constructive proof of the existence of a unique distribution-valued energy-momentum tensor. Its conservation requires the particles to obey standard Lorentz equa…
We first obtain the $D$-dimensional asymptotically AdS charged black hole solution in general nonlinear electrodynamics (NLED). We then use the Hamilton-Jacobi method to describe the motion in curved spacetime of a scalar particle and a fermion, which, as we show, satisfy the same Hamilton-Jacobi equation. With absorbing a charged particle, the variation of the generic charged NLED black hole is calculated in the normal and extended phase spaces. In the normal phase space, where the cosmological constant and dimensionful parameters in NLED are fixed, the first and second laws of thermodynamics…
We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and a U(1) nonlinear electromagnetic field. Solving analytically and numerically the coupled system for both power-law and Born-Infeld type electrodynamics, we find charged hairy black hole solutions. Then, we study the thermodynamics of these solutions and we find that at a low temperature the topological charged black hole with scalar hair is thermodynamically preferred, whereas the topological charged black hole without scalar hair is thermodynamically preferred at a …
Using a modified expression for the electric potential in the context of T-duality (Gaete and Nicolini, Phys. Lett. B, 2022) we obtain an exact charged solution within 4D Einstein-Gauss-Bonnet (4D EGB) theory of gravity in the presence of a cosmological constant. We show that the solution exists in the regularized 4D EGB theory as well and we point out a correspondence between the black hole solution in 4D EGB theory and the solution in the non-relativistic Horava--Lifshitz theory. The black hole solution is regular and free from singularity and as a special case we recover a class of well-kno…
We consider Heisenberg-Euler-type model of nonlinear electrodynamics with two parameters. Heisenberg-Euler electrodynamics is a particular case of this model. Corrections to Coulomb's law at $r\rightarrow\infty$ are obtained and energy conditions are studied. The total electrostatic energy of charged particles is finite. The charged black hole solution in the framework of nonlinear electrodynamics is investigated. We find the asymptotic of the metric and mass functions at $r\rightarrow\infty$. Corrections to the Reissner-Nordström solution are obtained.
A regular static, spherically symmetric electrically charged black hole solution of general relativity coupled to a new theory for nonlinear electrodynamics is presented. This theory has the interesting feature that, at far distances from the black hole, in the weak field limit, the theory reduces to Maxwell Lagrangian with Heisenberg-Euler correction term of quantum electrodynamics. The singular center of the black hole is replaced by flat, de Sitter, or anti de Sitter space, if the spacetime in which the black hole is embedded is asymptotically flat, de Sitter, or anti de Sitter, respectivel…
Charged Lifshitz black holes for the Einstein-Proca-Maxwell system with a negative cosmological constant in arbitrary dimension $D$ are known only if the dynamical critical exponent is fixed as $z=2(D-2)$. In the present work, we show that these configurations can be extended to much more general charged black holes which in addition exist for any value of the dynamical exponent $z>1$ by considering a nonlinear electrodynamics instead of the Maxwell theory. More precisely, we introduce a two-parametric nonlinear electrodynamics defined in the more general, but less known, so-called $(\mathcal{…
We present exact black hole solutions endowed with magnetic charge coming from exponential and logarithmic nonlinear electrodynamics (NLED). Classically, we analyze the null and timelike geodesics, all of which contain both the bound and the scattering orbits. Using the effective geometry formalism, we found that photon can have nontrivial stable (both circular and non-circular) bound orbits. The noncircular bound orbits for the one-horizon case mostly take the form of precessed ellipse. For the extremal and three-horizon cases we find many-world orbits where photon crosses the outer horizon b…
Light propagation and gravitational lensing effects in charged Kalb-Ramond spacetime in nonlinear electrodynamics
Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学）；University of Valladolid UVA（巴利亚多利德大学）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）；Universidade Federal de Campina Grande（坎皮纳格兰德联邦大学）；Khazar University（阿塞拜疆卡扎尔大学）；Universidade Estadual do Maranhão（马拉尼昂州立大学）；Universidade Federal do Pará（帕拉联邦大学）
We consider couplings of electrically and magnetically charged sources to the maximally symmetric non-linear extension of Maxwell's theory called ModMax. The aim is to reveal physical effects which distinguish ModMax from Maxwell's electrodynamics. We find that, in contrast to generic models of non-linear electrodynamics, Lienard-Wiechert fields induced by a moving electric or magnetic particle, or a dyon are exact solutions of the ModMax equations of motion. We then study whether and how ModMax non-linearity affects properties of electromagnetic interactions of charged objects, in particular …
In the context of the dRGT massive gravity coupled with nonlinear electrodynamics, we present new dRGT black hole solutions. Together with the thermodynamical properties of the solutions, we study the greybody factor of the corresponding black hole solution. To this end, we compute the rigorous bound on the greybody factor for the obtained dRGT black holes. The obtained results are graphically represented for different values of the theory's physical parameters. Our analysis shows that the charged dRGT black holes of nonlinear electrodynamics evaporate quicker than the charged dRGT black holes…
