Related papers: The Einstein-Maxwell Equations and Conformally Kae…
We present a new class of near-horizon geometries which solve Einstein's vacuum equations, including a negative cosmological constant, in all even dimensions greater than four. Spatial sections of the horizon are inhomogeneous S^2-bundles…
For conformally K\"ahler Riemannian four-manifolds with a Killing field, we present a framework to solve the field equations for generalised gravitational instantons corresponding to conformal self-duality and to cosmological…
We discuss smooth metric measure spaces admitting two weighted Einstein representatives of the same weighted conformal class. First, we describe the local geometries of such manifolds in terms of certain Einstein and quasi-Einstein warped…
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 study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We…
We construct two classes of exact solutions to six and higher dimensional Einstein-Maxwell theory in which the metric functions can be written as convolution-like integrals of two special functions. The solutions are regular everywhere and…
We consider a family of critical elliptic equations which arise as the Euler-Lagrange equation of Caffarelli-Kohn-Nirenberg inequalities, possibly in convex cones in $\mathbb{R}^d$, with $d\geq 2$. We classify positive solutions without…
Four-dimensional colliding plane wave (CPW) solutions have played an important role in understanding the classical non-linearities of Einstein's equations. In this note, we investigate CPW solutions in $2n+2$--dimensional Einstein gravity…
New exact solution of the cylindrically symmetric Einstein-Maxwell equations is presented. The solution is singular on the axis of symmetry and at the radial infinity, where sources should be placed. The accepted source at the origin can be…
This article considers the existence and regularity of Kahler-Einstein metrics on a compact Kahler manifold $M$ with edge singularities with cone angle $2\pi\beta$ along a smooth divisor $D$. We prove existence of such metrics with…
A new solution to the Einstein-Maxwell field equations is presented describing a cylindrically symmetric homogeneous cosmology. The solution is conformally flat, it possesses seven Killing vectors of which the timelike one is rotating and…
A new infinite series of Einstein metrics is constructed explicitly on S^2 x S^3, and the non-trivial S^3-bundle over S^2, containing infinite numbers of inhomogeneous ones. They appear as a certain limit of a nearly extreme 5-dimensional…
We present and discuss a 4-parameter stationary axisymmetric solution of the Einstein-Maxwell equations able to describe the exterior field of a rotating magnetized deformed mass. The solution arises as a system of two overlapping…
Static, spherically symmetric solutions to the semi-classical Einstein equation are studied, including the effect of the quantum energy-momentum tensor for conformal matters with 4D Weyl anomaly. Through both perturbative and…
We report on a new two-parameter class of cosmological solutions to the Einstein-Maxwell equations. The solutions have everywhere regular curvature invariants. We prove that the solutions are geodesically complete and globally hyperbolic.
In this paper, we establish a compactness result for a class of conformally compact Einstein metrics defined on manifolds of dimension $d\ge 4$. As an application, we derive the global uniqueness of a class of conformally compact Einstein…
In the first part of this note we study compact Riemannian manifolds (M,g) whose Riemannian product with R is conformally Einstein. We then consider compact 6--dimensional almost Hermitian manifolds of type W_1+W_4 in the Gray--Hervella…
We use direct products of Einstein Metrics to construct new solutions to Einstein's Equations with cosmological constant. We illustrate the technique with three families of solutions having the geometries Kerr/de Sitter X de Sitter,…
In this paper, we present a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can…
We consider the inverse problem of determining all extreme black hole solutions to the Einstein equations with a prescribed near-horizon geometry. We investigate this problem by considering infinitesimal deformations of the near-horizon…