Related papers: Global strong solution to Maxwell-Dirac equations …
We solve the Dirac equation in one space dimension for the case of a linear, Lorentz-scalar potential. This extends earlier work of Bhalerao and Ram [Am. J. Phys. 69 (7), 817-818 (2001)] by eliminating unnecessary constraints. The spectrum…
We study the global existence of Einstein-Maxwell(EM) equations on $\mathbb{R}^4$. We use the method, which relies on wave and Lorentzian gauge conditions, to obtain some exquisite estimates. Our main conclusion is that if the initial data…
The Maxwell-Dirac equations in one space dimension are proved to be well posed in the charge class, that is, with $L^2$ data for the spinor. We also prove that this result is sharp, in the sense that well-posedness fails for spinor data in…
The solutions of $U(1)$ gauge-gravity coupling is one of the interesting models for analyzing the semi-classical nature of spacetime. In this regard, different well-known singular and nonsingular solutions have been taken into account. The…
We prove the existence and uniqueness of global finite energy solutions of the Maxwell-scalar field system in Lorenz gauge on the Einstein cylinder. Our method is a combination of a conformal patching argument, the finite energy existence…
We study the Cauchy problem of higher dimensional Einstein-Maxwell-Higgs system in the framework of Bondi coordinates. As a first step, the problem is reduced to a single first-order integro-differential equation by defining a generalized…
The solutions of the Einstein-Maxwell-Chern-Simons theory are studied in (1+2) dimensions with the self-duality condition imposed on the Maxwell field. We give a closed form of the general solution which is determined by a single function…
We define and study the Cauchy problem for a 1-D nonlinear Dirac equation with nonlinearities concentrated at one point. Global well-posedness is provided and conservation laws for mass and energy are shown. Several examples, including…
A self consistent solution to Dirac equation in a Kerr Newman space-time with $M^2 > a^2 + Q^2$ is presented for the case when the Dirac particle is the source of the curvature and the electromagnetic field. The solution is localised,…
The time local and global well-posedness for the Maxwell-Schr{\"o}dinger equations is considered in Sobolev spaces in three spatial dimensions. The Strichartz estimates of Koch and Tzvetkov type are used for obtaining the solutions in the…
We prove that the charge-scalar field (also known as the massless Maxwell-Klein-Gordon) equations are globally stable on (3+1) dimensional Minkowski space for small initial data in certain gauge covariant weighted Sobolev spaces. These…
This paper studies an initial boundary value problem for a class of nonlinear Dirac equations with cubic terms and moving boundary. For the initial data with bounded $L^2$ norm and the suitable boundary conditions, the global existence and…
The Cauchy problem for the Maxwell-Klein-Gordon equations in Lorenz gauge in two and three space dimensions is locally well-posed for low regularity data without finite energy. The result relies on the null structure for the main bilinear…
In this paper we discuss global existence of the solution of the Maxwell and Newton system of equations, describing the interaction of a rigid charge distribution with the electromagnetic field it generates. A unique solution is proved to…
The field equations for Einstein-Maxwell-dilaton gravity in $D$ dimensions are reduced to an effective one-dimensional system under the influence of exponential potentials. Various cases where exact solutions can be found are explored. With…
The Cauchy problem for the Maxwell-Klein-Gordon equations in Lorenz gauge in $n$ space dimensions ($n \ge 2$) is locally well-posed for low regularity data, in two and three space dimensions even for data without finite energy. The result…
In this paper we report some results obtained by applying the radial gauge to 2+1 dimensional gravity. The general features of this gauge are reviewed and it is shown how they allow the general solution of the problem in terms of simple…
We report a new class of rotating charged solutions in 2+1 dimensions. These solutions are obtained for Einstein-Maxwell gravity coupled to a dilaton field with selfdual electromagnetic fields. The mass and the angular momentum of these…
We report a new family of solutions to Einstein-Maxwell-dilaton gravity in 2+1 dimensions and Einstein-Maxwell gravity with cylindrical symmetry in 3+1 dimensions. A set of static charged solutions in 2+1 dimensions are obtained by a…
We introduce a class of solutions in $2+1-$dimensional Einstein-Power-Maxwell theory for circularly symmetric electric field. The electromagnetic field is considered with an angular component given by $% F_{\mu \nu }=E_{0}\delta_{\mu…