相关论文: Stationary solutions in the small-$c$ expansion of…
We study the large-$c$ expansion of general relativity in ADM variables. Using a unified even $\omega$-expansion, the ADM formulation gives a common starting point for Galilean and Carrollian limits. We focus on the Galilean branch and…
Physically admissible choice of the "essential" coordinates identified with components of the metric tensor and co-moving frame of reference reduced to the formulation of the stationary axisymmetric GR problem. Such nontraditional approach…
We study stationary and axisymmetric solutions of General Relativity, i.e. pure gravity, in four or higher dimensions. D-dimensional stationary and axisymmetric solutions are defined as having D-2 commuting Killing vector fields. We derive…
The wide applications of higher dimensional gravity and gauge/gravity duality have fuelled the search for new stationary solutions of the Einstein equation (possibly coupled to matter). In this topical review, we explain the mathematical…
Chern-Simons (CS) modified gravity is an extension to general relativity (GR) in which the metric is coupled to a scalar field, resulting in modified Einstein field equations. In the dynamical theory, the scalar field is itself sourced by…
A modification of General Relativity that is based on the gravitational Standard-Model Extension and incorporates nondynamical background fields has recently been studied via the ADM formalism. Our objective in this paper is to develop a…
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…
Massive gravity is a good theoretical laboratory to study modifications of General Relativity. The theory offers a concrete set-up to study models of dark energy, since it admits cosmological self-accelerating solutions in the vacuum, in…
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 $2+2$…
This work presents the foundations of Singular Semi-Riemannian Geometry and Singular General Relativity, based on the author's research. An extension of differential geometry and of Einstein's equation to singularities is reported.…
We investigate f(R)-gravity models performing the ADM-slicing of standard General Relativity. We extract the static, spherically-symmetric vacuum solutions in the general case, which correspond to either Schwarzschild de-Sitter or…
This thesis focuses on the application of numerical relativity methods to the solutions of problems in strong gravity. Our goal is the study of mergers of compact objects in the strong field regime where non-linear dynamics manifest and…
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 develop a theory of nonlinear cosmological perturbations on superhorizon scales where a characteristic length scale of perturbations is longer than the Hubble radius, in general theoretical frameworks. Our formalism is based on the…
We study the stability of three-dimensional numerical evolutions of the Einstein equations, comparing the standard ADM formulation to variations on a family of formulations that separate out the conformal and traceless parts of the system.…
Modified gravity theories (MGTs) have long been studied as alternatives to general relativity (GR) and the standard Lambda CDM cosmological model. For example, exponential f(R) models often yield better fits to observational data,…
The non-linear superposition of the stationary euclidon solution with an arbitrary axially symmetric stationary gravitational field on the basis of the method of variation of parameters was constructed. Stationary soliton solution of the…
We consider stationary axisymmetric solutions of general relativity that asymptote to five dimensional Minkowski space. It is known that this system has a hidden SL(3,R) symmetry. We identify an SO(2,1) subgroup of this symmetry group that…
This article is a status report on the Anholonomic Frame and Connection Deformation Method, AFCDM, for constructing generic off-diagonal exact and parametric solutions in general relativity, GR, relativistic geometric flows, and modified…
The Klein-Gordon equation for a massive scalar field in the background of a rapidly-rotating Kerr black hole is studied analytically. In particular, we derive a simple formula for the stationary (marginally-stable) resonances of the field…