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This paper is concerned with the construction of special metrics on non-compact 4-manifolds which arise as resolutions of complex orbifold singularities. Our study is close in spirit to the construction of the hyperkaehler gravitational…

We construct local, in spacetime, singular solutions to the Einstein vacuum equations that exhibit Kasner-like behavior in their past boundary. Our result can be viewed as a localization (in space) of the construction in \cite{FL}. We also…

We prove the uniqueness theorem for static spherically symmetric traversable wormholes with two asymptotically flat ends, constituting the solutions of Einstein-phantom-electric-magnetic equations of motion. For the completeness of the…

The one-dimensional Klein-Gordon equation is investigated with the most general Lorentz structure for the external potentials. The analysis and calculation of the reflection and transmission coefficients for the scattering of particles in a…

We improve the upper bound for the consistency strength of stationary reflection at successors of singular cardinals.

Recently, no-go theorems for the existence of solitonic solutions in Einstein-Maxwell-scalar (EMS) models have been established in arXiv:1902.07721. Here we discuss how these theorems can be circumvented by a specific class of non-minimal…

This article is a guide to the literature on existence theorems for the Einstein equations which also draws attention to open problems in the field. The local in time Cauchy problem, which is relatively well understood, is treated first.…

The note contains the proof of the uniqueness theorem for the inverse problem in the case of $n$-th order differential equation.

This work studies the direct and inverse fixed energy scattering problem for two-dimensional Schroedinger equation with rather general nonlinear index of refraction. In particular, using the Born approximation we prove that all…

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…

We construct a class of Einstein-vector theories where the vector field couples bilinearly to the curvature polynomials of arbitrary order in such a way that only Riemann tensor rather than its derivative enters the equations of motion. The…

We construct a scattering theory for the linearised Einstein equations on a Schwarzschild background in a double null gauge. We build on the results of Part I \cite{Mas20}, where we used the energy conservation enjoyed by the Regge--Wheeler…

The purpose of the present expository paper is to give an account of the recent progress and present status of the classification of solvable Lie groups admitting an Einstein left invariant Riemannian metric, the only known examples so far…

Singular solutions of the harmonic Einstein evolution equation are constructed which are related to spatially global and time-local solutions for a certain class of quasilinear hyperbolic systems of second order. The constructed…

We investigate some aspects of anomaly cancellation realized by the subtraction of an anomaly pole, stressing on some of its properties in superspace. In a local formulation these subtractions can be described in terms of a physical scalar,…

We prove exponential stability theorems of Nekhoroshev type for motion in the neighbourhood of an elliptic fixed point in Hamiltonian systems having an additional transverse component of arbitrary dimension.

We classify all stationary axi-symmetric solutions of topologically massive gravity into Einstein, Schr\"odinger, warped and generic solutions. We construct explicitly all local solutions in the first three sectors and present an algorithm…

We consider the problem of extending the integrals of motion of soliton equations to the space of all finite-gap solutions. We consider the critical points of these integrals on the moduli space of Riemann surfaces with marked points and…

The theorem on the existence of bifurcation points of the stationary solutions for the Vlasov-Maxwell system with bifurcation direction is proved.

This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein field equations using the 1+3 tetrad formalism. This approach reformulates the Einstein equations into first order scalar equations,…