相关论文: The causal structure of microlocalized Einstein me…

Recently one and two-parameter deformed Einstein equations have been studied for extremal quantum black holes which have been proposed to obey deformed statistics by Strominger. In this study, we give a deeper insight to the deformed…

This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…

This is the author Master's Thesis and its main purpose is to demonstrate that it is possible to formulate Einstein's field equations as an initial value problem. The first chapter concerns the hyperbolic equations theory. The definition of…

The Cauchy problem of the vacuum Einstein's equations aims to find a semi-metric $g_{\alpha\beta}$ of a spacetime with vanishing Ricci curvature $R_{\alpha,\beta}$ and prescribed initial data. Under the harmonic gauge condition, the…

We analyse the issue of uniqueness of solutions of the static vacuum Einstein equations with prescribed geometric or Bartnik boundary data. Large classes of examples are constructed where uniqueness fails. We then discuss the implications…

We construct new examples of Einstein metrics by perturbing the conformal infinity of geometrically finite hyperbolic metrics and by applying the inverse function theorem in suitable weighted H\"older spaces.

Impulsive gravitational waves are (weak) solutions to the Einstein vacuum equations such that the Riemann curvature tensor admits a delta singularity along a null hypersurface. The interaction of impulsive gravitational waves is then…

A method is presented to construct initial data for Einstein's equations as a superposition of a gravitational wave perturbation on an arbitrary stationary background spacetime. The method combines the conformal thin sandwich formalism with…

We derive, in 3+1 spacetime dimensions, two alternative systems of quasi-linear wave equations, based on Friedrich's conformal field equations. We analyse their equivalence to Einstein's vacuum field equations when appropriate constraint…

The linear Einstein-Boltzmann equations describe the evolution of perturbations in the universe and its numerical solutions play a central role in cosmology. We revisit this system of differential equations and present a detailed…

Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…

In this paper, we present a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can…

We show that certain solutions to the linearized Einstein equation can---by the application of a particular type of linearized gauge transformation---be straightforwardly transformed into solutions of the exact Einstein equation. In cases…

We develop subrepresentation inequalities for infinitely degenerate metrics, and obtain corresponding Poincare and Sobolev inequalities. We then derive conditions on the degenerate metric under which weak solutions to associated infinitely…

Solving Einstein's equations precisely for strong-field gravitational systems is essential to determining the full physics content of gravitational wave detections. Without these solutions it is not possible to infer precise values for…

This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…

This is a survey on the correspondence between asymptotically complex hyperbolic Einstein metrics and CR structures on the boundary at infinity, which is the complex version of that between Poincar\'e-Einstein metrics and conformal…

Given a smooth globally hyperbolic $(3+1)$-dimensional spacetime satisfying the Einstein vacuum equations (possibly with cosmological constant) and an inextendible timelike geodesic, we construct a family of metrics depending on a small…

We consider the Einstein-Boltzmann system for massless particles in the Bianchi I space-time with scattering cross-sections in a certain range of soft potentials. We assume that the space-time has an initial conformal gauge singularity and…

We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative…