Related papers: Rainich theory for type D aligned Einstein-Maxwell…
Given an algebraic differential equation of order greater than one, it is shown that if there is any nontrivial algebraic relation amongst any number of distinct nonalgebraic solutions, along with their derivatives, then there is already…
We present a new class of expanding and twisting solutions to the Einstein-Maxwell equations of algebraic type D, where the null eigendirections of the Faraday tensor are not aligned with PNDs of the Weyl tensor. After deriving this novel…
This paper presents a set of complete solutions of a nonconvex variational problem with a double-well potential. Based on the canonical duality-triality theory, the associated nonlinear differential equation with either Dirichlet/Neumann or…
We study Robinson-Trautman spacetimes in the presence of an aligned p-form Maxwell field and an arbitrary cosmological constant in n>=4 dimensions. As it turns out, the character of these exact solutions depends significantly on the…
The gauge-theoretical method introduced in our previous paper is applied to solve the axisymmetric and static Einstein-Maxwell equations. We obtain the solutions of the non-Weyl class, where the gravitational and electric or magnetic…
We speculate on the role of relativistic versions of delayed differential equations in fundamental physics. Relativistic invariance implies that we must consider both advanced and retarded terms in the equations, so we refer to them as…
We construct infinite families of Lifshitz solutions of D=10 and D=11 supergravity with dynamical exponent z=2. The new solutions are based on five- and seven-dimensional Einstein manifolds and are dual to theories in 1+2 and 1+1 spacetime…
Writing the metric of an asymptotically flat spacetime in Bondi coordinates provides an elegant way of formulating the Einstein equation as a characteristic value problem. In this setting, we find that a specific class of asymptotically…
We prove area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory. Our inspiration comes on the one hand from a corresponding upper bound for the area in terms of the charges obtained recently by…
The system of Einstein-Maxwell equations for fields mentioned in the title is simplified. Known pure radiation solutions are systematized and new solutions are given by separating the variables.
We find and analyse solutions of Einstein's equations in arbitrary d dimensions and in the presence of a scalar field with a Liouville potential coupled to a Maxwell field. We consider spacetimes of cylindrical symmetry or again subspaces…
The purpose of this article is to develop an algebraic approach to the problem of integrable classification of differential-difference equations with one continuous and two discrete variables. As a classification criterion, we put forward…
We summarize the global geometric formulation of Einstein-Scalar-Maxwell theories twisted by flat symplectic vector bundle which encodes the duality structure of the theory. We describe the scalar-electromagnetic symmetry group of such…
We present a solution of the Weiss operator family generalized for the case of $\mathbb{R}^{d}$ and formulate a d-dimensional analogue of the Weiss Theorem. Most importantly, the generalization of the Weiss Theorem allows us to find a…
A fundamental result that characterizes elliptic-hyperbolic equations of Tricomi type, the uniqueness of classical solutions to the open Dirichlet problem, is extended to a large class of elliptic-hyperbolic equations of Keldysh type. The…
We describe a class of unified theories of electromagnetism and gravity. The Lagrangian is of the BF type, with a potential for the B-field, the gauge group is U(2) (complexified). Given a choice of the potential function the theory is a…
It is shown that bivectors are not necessary to satisfy the Rainich conditions in the null case.
Abstract differential-algebraic equations (ADAEs) of a semilinear type are studied. Theorems on the existence and uniqueness of solutions and the maximal interval of existence, on the global solvability of the ADAEs, the boundedness of…
In this paper, we search the existence of invariant solutions of Bianchi type I space-time in the context of $f\left(R,T\right)$ gravity. The exact solution of the Einstein's field equations are derived by using Lie point symmetry analysis…
We study static spherically symmetric solutions of Einstein gravity plus an action polynomial in the Ricci scalar, $R$, of arbitrary degree, $n$, in arbitrary dimension, $D$. The global properties of all such solutions are derived by…