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The so-called $\Gamma\Gamma$-form of the gravitational Lagrangian, long known to provide its most compact expression as well as the most efficient generation of the graviton vertices, is taken as the starting point for discussing General…
Based on the study of the simple Abelian Higgs model in $1+1$ dimensions we will present a new method to identify and localize extended instantons. The idea is to measure the topological charge on regions somewhat larger than the extended…
Presented are exactly integrable models with pure radiation in R^2 gravity with a cosmological constant, related to wave-like Shapovalov spacetimes type II. Spatially homogeneous models of Shapovalov spaces were considered. The obtained…
An alternative approach to Einstein's theory of General Relativity (GR) is reviewed, which is motivated by a range of serious theoretical issues inflicting the theory, such as the cosmological constant problem, presence of non-Machian…
We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally…
We consider vacuum anisotropic spatially homogeneous models in certain modified gravity theories (such as Ho\v{r}ava-Lifshitz, $\lambda$-$R$ or $f(R)$ gravity), which are expected to describe generic spacelike singularities for these…
In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form…
We address the homogeneous in space and time (ST-homogeneous) G\"{o}del-type metrics within the cubic galileon theory, a particular class of generalized galileon theories. We check the consistency of such spacetimes for a physically…
The role of instantons in describing non-perturbative aspects of globally supersymmetric gauge theories is reviewed. The cases of theories with N=1, N=2 and N=4 supersymmetry are discussed. Special attention is devoted to the intriguing…
An introduction to the instanton formalism in supersymmetric gauge theories is given. We explain how the instanton calculations, in conjunction with analyticity in chiral parameters and other general properties following from supersymmetry,…
We calculate the scalar potential in the gauged N=2 supergravity with a single hypermultiplet, whose generic quaternionic moduli space metric has an abelian isometry. This isometry is gauged by the use of a graviphoton gauge field. The…
By defining a regular gauge which is conformal-like and provides instantaneous field propagation, we investigate classical solutions of (2+1)-Gravity coupled to arbitrarily moving point-like particles. We show how to separate field…
In this paper, we study Einstein gravity with a minimally coupled scalar field accompanied with a potential, assuming an O(4) symmetric metric ansatz. We call an Euclidean instanton is to be an oscillating instanton, if there exists a point…
A century after its formulation by Einstein, it is time to incorporate special relativity early in the physics curriculum. The approach advocated here employs a simple algebraic extension of vector formalism that generates Minkowski…
Using ideas from continuum mechanics we construct a theory of gravity. We show that this theory is equivalent to Einstein's theory of general relativity; it is also a much faster way of reaching general relativity than the conventional…
We discuss instantons on noncommutative four-dimensional Euclidean space. In commutative case one can consider instantons directly on Euclidean space, then we should restrict ourselves to the gauge fields that are gauge equivalent to the…
It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "open" model $H^ 3$ for this…
In a recent paper [16], the authors proposed a BGK model for relativistic gas mixtures based on the Marle-type approximation, which satisfies the fundamental kinetic properties: non-negativity of distribution functions, conservation laws,…
We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four and…
Euclidean random matrices appear in a broad class of physical problems involving disorder. The problem of determining their spectra can be mapped, using the replica method, into the study of a scalar field theory with an interaction of the…