The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities φ : R \Σ → H C into the (k+1)-dimensional complex hyperbolic space. In this paper, we prove the existence and uniqueness of harmonic maps with prescribed singularities φ : R \ Σ → H, where Σ is an unbounded smooth closed submanifold of R of codimension at...

In this note, we prove that there is a canonical continuous Hermitian metric on the CM line bundle over the proper moduli space M of smoothable Kähler-Einstein Fano varieties. The curvature of this metric is the Weil-Petersson current, which exists as a positive (1,1)-current on M and extends the canonical Weil-Petersson current on the moduli space parametrizing smooth Kähler-Einstein Fano mani...

We use a gauge fixing for the Rarita-Schwinger equations for helicity 3/2 fields in curved space that leads to a straightforward Hilbert space framework for their study and prove global existence and uniqueness of solutions to the Rarita-Schwinger evolution equations compatible with the constraints inthis framework. We discuss how these results might be applied to the global analysis of the ful...

The structure of the general, inhomogeneous solution of (bosonic) Einstein-matter systems in the vicinity of a cosmological singularity is considered. We review the proof (based on ideas of BelinskiiKhalatnikov-Lifshitz and technically simplified by the use of the ArnowittDeser-Misner Hamiltonian formalism) that the asymptotic behaviour, as one approaches the singularity, of the general solutio...

A black hole solution in a teleparallel theory of (2+1)-dimensional gravity, given in a previous paper, is examined. This solution is also a solution of the three-dimensional vacuum Einstein equation with a vanishing cosmological constant. Remarkable is the fact that this solution gives a black hole in a “flat-land” in the Einstein theory and a Newtonian limit. Coordinate transformations to “Mi...

For a homogeneous space G/P , where P is a parabolic subgroup of a complex semisimple group G, an explicit Kähler–Einstein metric on it is constructed. The Einstein constant for the metric is 1. Therefore, the intersection number of the first Chern class of the holomorphic tangent bundle of G/P coincides with the volume of G/P with respect to this Kähler–Einstein metric, thus enabling us to com...

For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein-Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational functions of an auxiliary complex parameter. They are constructed using the so-called "monodromy transform" approach and our new method for the solution of the l...