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We present interesting relationship between what are called stationary axisymmetric black hole solutions for the vacuum Einstein equations in the ordinary four-dimensions and exact solutions for self-dual Yang-Mills fields in flat $2+2$…
A new family of analytical solutions in a four dimensional static spacetime is presented for $f\left( R\right) $-gravity. In contrast to General Relativity, we find that a non trivial black string/ring solution is supported in vacuum power…
In this Thesis we investigate properties of stability, rigidity and unitarity of the string landscape in ten and lower dimensions. The dissertation explores these aspects by intertwining a detailed analysis of string vacua, with and without…
The exact axisymmetric and static solution of the Einstein equations coupled to axisymmetric and static gravitating scalar (or phantom) field is presented. The spacetimes modified by the scalar field are explicitly given for the so called…
In this paper, we introduce new methods for solving the vacuum Einstein constraints equations: the first one is based on Schaefer's fixed point theorem (known methods use Schauder's fixed point theorem) while the second one uses the concept…
We consider the classical equations of the Einstein-Yang-Mills model in five space-time dimensions and in the presence of a cosmological constant. We assume that the fields do not depend on the extra dimension and that they are spherically…
A positive cosmological constant simplifies the asymptotics of forever expanding cosmological solutions of the Einstein equations. In this paper a general mathematical analysis on the level of formal power series is carried out for vacuum…
We numerically simulate gravitational collapse in asymptotically anti-de Sitter spacetimes away from spherical symmetry. Starting from initial data sourced by a massless real scalar field, we solve the Einstein equations with a negative…
In this lecture, I explain the gauge-invariant formulation for perturbations of background spacetimes with untwisted homologous Einstein fibres, which include lots of practically important spacetimes such as static black holes, static black…
The static, cylindrically symmetric vacuum solutions with a cosmological constant in the framework of the Brans-Dicke theory are investigated. Some of these solutions admitting Lorentz boost invariance along the symmetry axis correspond to…
We construct and study general static, spherically symmetric, magnetically charged solutions in Einstein-Maxwell-dilaton gravity in four dimensions. That is, taking Einstein gravity coupled to a ${\rm U}(1)$ gauge field and a massless…
We make a systematic investigation of stationary cylindrically symmetric solutions to the five-dimensional Einstein and Einstein-Gauss-Bonnet equations. Apart from the five-dimensional neutral cosmic string metric, we find two new exact…
The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a non-positive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants.…
We give an infinite number of exact solutions to the 5-dimensional static Einstein equation with axial symmetry by using the inverse scattering method. The solutions are characterized by two integers representing the soliton numbers. The…
Four-dimensional cylindrically symmetric spacetimes with homothetic self-similarity are studied in the context of Einstein's Theory of Gravity, and a class of exact solutions to the Einstein-massless scalar field equations is found. Their…
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…
By studying singularities in stationary axisymmetric Kerr and Tomimatsu-Sato solutions with distortion parameter \d = 2, 3, ... in general relativity, we conclude that these singularities can be regarded as nothing other than closed…
New exact vacuum solutions with various singularities in the plane-symmetric spacetime are shown, and they are applied to the analysis of inhomogeneous cosmological models and colliding gravitational waves. One of the singularities can be…
In this paper, we study solutions to the linearized vacuum Einstein equations centered at higher-dimensional Schwarzschild met- rics. We employ Hodge decomposition to split solutions into scalar, co-vector, and two-tensor pieces; the first…
We find solutions of Einstein's field equation for topologically stable strings associated with the breaking of a U(1) symmetry. Strings form in many GUTs and are expected whenever the homotopy group $\Pi_1(M_0)$ is non-trivial. The…