相关论文: A note on static metrics: the degenerate case
We express the vacuum Einstein constraints in terms of differential forms - the forms include one-forms constituting an orthonormal coframe of the spatial metric. We show that if the metric is real-analytic, then the constraints can be…
Considering an action in F(G) modified gravity, the static spherically symmetric solutions are investigated. Introducing the Lagrangian multipliers {\alpha} we obtain the Lagrangian and equations of motion. we obtain two type solutions for…
We establish the asymptotic behavior and decay of solutions near vacuum to the Hartree equation with the Coulomb interaction potential in three dimensions. Our approach is direct, which consists of independently deriving the sharp…
In this paper, we have considered flat Friedmann-Lema\^{i}tre-Robertson-Walker metric in the framework of perfect fluid models and modified $f(G)$ gravity (where $G$ is the Gauss Bonnet invariant). Particularly, we have considered…
In this article, we demonstrate the common fixed point theorems for three transformations on vector S-metric space by utilizing weakly compatible and point of coincidence. Moreover, some of our results generalize the existing results in the…
In this article we study the pointwise decay properties of solutions to the wave equation on a class of nonstationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form…
The stability issue of a large class of modified gravitational models is discussed with particular emphasis to de Sitter solutions. Three approaches are briefly presented and the generalization to more general cases is mentioned.
We consider conditions for existence and stability of a static cosmological solution in quadratic gravity. It appears that such a solution for a Universe filled by only one type of perfect fluid is possible in a wide range of the equation…
Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which…
In this paper we are concerned with the stability of equilibrium solutions of periodic Hamiltonian systems with one degree of freedom in the case of degeneracy, which means that the characteristic exponents of the linearized system have…
The following problem is addressed: A $3$-manifold $M$ is endowed with a triple $\Omega = \big(\Omega^1,\Omega^2,\Omega^3\big)$ of closed $2$-forms. One wants to construct a coframing $\omega = \big(\omega^1,\omega^2,\omega^3\big)$ of $M$…
In an earlier paper [6] the author wrote the homothetic equations for vacuum solutions in a first order formalism allowing for arbitrary alignment of the dyad. This paper generalises that method to homothetic equations in non-vacuum spaces…
We discuss contact invariant structures on the space of solutions of a third-order ordinary differential equation. Associated to any third-order differential equation modulo contact transformations, Chern introduced a degenerate conformal…
This paper pursues a twofold goal. First, we introduce and study in detail a new notion of variational analysis called generalized metric subregularity, which is a far-going extension of the conventional metric subregularity conditions. Our…
The modified theories of gravity, especially the f(R) theory, have attracted much attention in recent years. In this context, we explore static plane symmetric vacuum solutions using the metric approach of this theory. The field equations…
The spherically symmetric static solutions are searched for in some f(T) models of gravity theory with a Maxwell term. To do this, we demonstrate that reconstructing the Lagrangian of f(T) theories is sensitive to the choice of frame, and…
Earlier constructed a simple nonlocal de Sitter gravity model has a cosmological solution in a very good agreement with astronomical observations. In this paper, we continue the investigation of the nonlocal de Sitter model of gravity,…
Some examples of three-dimensional metrics of constant curvature defined by solutions of nonlinear integrable differential equations and their generalizations are constructed. The properties of Riemann extensions of the metrics of constant…
We develop a framework for understanding the existence of asymptotically flat solutions to the static vacuum Einstein equations with prescribed boundary data consisting of the induced metric and mean curvature on a 2-sphere. A partial…
We give an update on our derivation of a quantization condition relating the finite-volume spectrum of three particles in a cubic box to infinite-volume scattering quantities. We have discovered and fixed technical problems in the…