相关论文: Perturbative Solutions of the Extended Constraint …

We present a set of dynamical equations based on Ashtekar's extension of the Einstein equation. The system forces the space-time to evolve to the manifold that satisfies the constraint equations or the reality conditions or both as the…

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…

The article proposes an amendment to the relativistic continuum mechanics which introduces the relationship between density tensors and the curvature of spacetime. The resulting formulation of a symmetric stress-energy tensor for a system…

We extend the monumental result of Christodoulou-Klainerman on the global nonlinear stability of the Minkowski spacetime to the global nonlinear stability of a class of large dispersive spacetimes. More precisely, we show that any regular…

This article is dedicated to solving the Einstein constraint equations with apparent horizon boundaries and freely specified mean curvature. The main novelty is that we study the conformal constraint equations assuming only low regularity.

We present a systematic approach to embed $n$-dimensional vacuum general relativity in an $(n + 1)$-dimensional pseudo-Riemannian spacetime whose source is either a (non)zero cosmological constant or a scalar field minimally-coupled to…

General relativistic Gauss equations for osculating elements for bound orbits under the influence of a perturbing force in an underlying Schwarzschild space-time have been derived in terms of Weierstrass elliptic functions. Thereby, the…

The existence of the initial value constraints means that specifying initial data for the Einstein equations is non-trivial. The standard method of constructing initial data in the asymptotically flat case is to choose an asymptotically…

In this paper we are looking for the exponential solutions (i.e. the solutions with the scale factors change exponentially over time) in the Einstein-Gauss-Bonnet gravity. We argue that we found all possible non-constant-volume solutions…

In a nonlinear theory, such as General Relativity, linearized field equations around an exact solution are necessary but not sufficient conditions for linearized solutions. Therefore, the linearized field equations can have some solutions…

Modified gravity theories such as Einstein scalar Gauss Bonnet (EsGB) contain higher derivative terms in the spacetime curvature in their action, which results in modifications to the Hamiltonian and momentum constraints of the theory. In…

In this paper we consider second order perturbations of a flat Friedmann-Lema\^{i}tre universe whose stress-energy content is a single minimally coupled scalar field with an arbitrary potential. We derive the general solution of the…

A new solution of Einstein's vacuum field equations is discovered which appears as a generalization of the well-known Ozsvath-Schucking solution and explains its source of curvature which has otherwise remained hidden. Curiously, the new…

We investigate the vacuum and charged spherically symmetric static solutions of the Einstein equations on cosmological background. The background metric is not flat, but curved, with constant - curvature spatial sections. Both vacuum and…

We consider the metrics of the General Relativity, whose energy-momentum tensor has a bounded support where it is continuous except for a finite step across the corresponding boundary surface. As a consequence, the first derivative of the…

Although the traditional form of the Einstein field equations is intrinsically four-dimensional, the field of numerical general relativity focuses on the reformulation of these equations as a 3 + 1-dimensional Cauchy problem, in which…

In the previous works [I. Rodnianski and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution, arXiv:1912.08478 and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum…

A tensor description of perturbative Einsteinian gravity about an arbitrary background spacetime is developed. By analogy with the covariant laws of electromagnetism in spacetime, gravito-electromagnetic potentials and fields are defined to…

Einstein gravity at $D\rightarrow 2$ limit can be obtained from the Kaluza-Klein procedure by taking the dimensions of the internal space to zero while keeping only the breathing mode. The resulting scalar-tensor theory can be further…

We present a novel homogeneous and geometrically flat exact solution of Einstein's General Relativity equations for an ideal fluid. The solution, which describes an expanding/contracting hypercylinder, fits well with the observational…