Related papers: Twisting algebraically special solutions in five d…
This article explores solutions to a generalised form of the Seiberg--Witten equations in higher dimensions, first introduced by Fine and the author. Starting with an oriented $n$ dimensional Riemannian manifold with a…
In this paper we analyze the conformal Einstein equations to all orders at null infinity without imposing any restriction on the spacetime dimension, the topology of $\mathscr{I}$, or fall-off conditions for the Weyl tensor. In particular,…
We construct new supersymmetric solutions to the Euclidean Einstein-Maxwell theory with a non-vanishing cosmological constant, and for which the Maxwell field strength is neither self-dual or anti-self-dual. We find that there are three…
We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…
A unitary gravitational action up to third order of curvature in which respects to the holographic $a-$theorem has been constructed in \cite{myers}. In particular, its third order term is just the Weyl-cubed term in four dimensions. In this…
We study the problem of asymptotically flat bi-axially symmetric stationary solutions of the vacuum Einstein equations in $5$-dimensional spacetime. In this setting, the cross section of any connected component of the event horizon is a…
Using the Ehlers transformation, we derive an exact solution for a doubly rotating black ring in five-dimensional vacuum Einstein theory. It is well-known that the vacuum Einstein theory with three commuting Killing vector fields can be…
An extension to higher dimensions of the Bel-Debever characterization of the Weyl tensor is considered. This provides algebraic conditions that uniquely determine the multiplicity of a Weyl aligned null direction (WAND), and thus the…
We study the class of generalized Kerr-Schild (GKS) spacetimes in dimensions $n\geq 3$ and analyze their geometric and algebraic properties in a completely theory-independent setting. First, considering the case of a general null vector…
We establish the status of the Weyl double copy relation for radiative solutions of the vacuum Einstein equations. We show that all type N vacuum solutions, which describe the radiation region of isolated gravitational systems with…
We study various classical aspects of the Weyl transverse (WTDiff) gravity in a general space-time dimension. First of all, we clarify a classical equivalence among three kinds of gravitational theories, those are, the conformally-invariant…
This is an elementary and self--contained review of twistor theory as a geometric tool for solving non-linear differential equations. Solutions to soliton equations like KdV, Tzitzeica, integrable chiral model, BPS monopole or Sine-Gordon…
Five-dimensional Einstein-Maxwell-Chern-Simons equations are investigated in the framework of an extended Kerr-Schild strategy to search for black holes solutions. The fulfillment of Einstein equations constrains the Chern-Simons coupling…
Classes of exact static solutions in four-dimensional Einstein-Maxwell-Dilaton gravity are found. Besides of the well-known solutions previously found in the literature, new solutions are presented.It's shown that spherically symmetric…
We examine the effective field equations that are obtained from the axi-dilaton gravity action with a second order Euler-Poincare term and a cosmological constant in all higher dimensions. We solve these equations for five-dimensional…
We present a large family of twisting and expanding solutions to the Einstein-Maxwell equations of algebraic type D, for which the two double principal null directions (PNDs) of the Weyl tensor are not aligned with the null eigendirections…
We obtain explicitly all solutions of the SU(infinity) Toda field equation with the property that the associated Einstein-Weyl space admits a 2-sphere of divergence-free shear-free geodesic congruences. The solutions depend on an arbitrary…
We derive exact solutions to the vacuum Einstein field equations in 5D, under the assumption that (i) the line element in 5D possesses self-similar symmetry, in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the…
In present work the generalization of Einstein's special theory of relativity on 5-dimentional space is considered, in which as fifth coordinates we consider the interval s of a particle. 5-dimentional vectors in this space are isotropic…
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on…