Related papers: 5D Axisymmetric Stationary Solutions as Harmonic M…
It is formulated a new 'anholonomic frame' method of constructing exact solutions of Einstein equations with off--diagonal metrics in 4D and 5D gravity. The previous approaches and results are summarized and generalized as three theorems…
We construct generating technique for 5D minimal and $U(1)^3$ supergravities based on hidden symmetries arising in dimensional reduction to three dimensions. In the three-vector case the symmetry is SO(4,4), and the minimal case corresponds…
We analyse the most general bosonic supersymmetric solutions of type IIB supergravity whose metrics are warped products of five-dimensional anti-de Sitter space AdS_5 with a five-dimensional Riemannian manifold M_5. All fluxes are allowed…
This work concerns an alignment problem that has applications in many geospatial problems such as resource allocation and building reliable disease maps. Here, we introduce the problem of optimally aligning $k$ collections of $m$ spatial…
We review some aspects of the spinorial geometry approach to the classification of supersymmetric solutions of supergravity theories. In particular, we explain how spinorial geometry can be used to express the Killing spinor equations in…
Within the framework of Lagrangian variables, we develop a method for deriving explicit solutions to the 2D Boussinesq equations using harmonic mapping theory. By reformulating the characterization of flow solutions described by harmonic…
Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schrodinger equations in dimensions $n\neq 1$. Both focusing and defocusing cases of a power nonlinearity are considered,…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
We consider linearized 5-d gravity in the Randall-Sundrum brane world. The class of static solutions for linearized Einstein equations is found. Also we obtaine wave solutions describing radiation from an imaginary point source located at…
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 review some aspects of biaxially symmetric solutions to Vasiliev's equations in four dimensional spacetime with negative cosmological constant. The solutions, which activate bosonic fields of all spins, are constructed using gauge…
The Riemann-Hilbert approach to studying solutions of supergravity theories allows us to associate spacetime independent monodromy matrices (matrices in the Geroch group) with solutions that effectively only depend on two spacetime…
The timelike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to an arbitrary number of abelian vector multiplets are classified using spinorial geometry techniques. We show that the generalized holonomy group for vacua…
Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or…
We derive a first-order formalism for solving $(2+1)$ gravity on Riemann surfaces, analogously to the recently discovered classical solutions for $N$ moving particles. We choose the York time gauge and the conformal gauge for the spatial…
We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main strategy in both…
In this paper, an attempt is made to represent 5+1 dimensional gravity (via ADM formalism) in terms of the loop constructions introduced by the author in a companion paper. The "momenta" and "velocity" from the earlier paper, which were…
Necessary and sufficient conditions are provided for a class of warped product manifolds with non-vanishing flux to be supersymmetric solutions of 11D supergravity. Many noncompact, but complete solutions can be obtained in this manner,…
We give a formulation of linearized minimal 5-dimensional supergravity in N = 1 superspace. Infinitesimal local 5D diffeomorphisms, local 5D Lorentz transformations, and local 5D supersymmetry are all realized as off-shell superfield…
We define gravitational mass and current multipoles for five-dimensional, stationary, and asymptotically flat vacuum metrics. We do this by generalizing Thorne's asymptotically Cartesian and mass-centered (ACMC) coordinate formalism to five…