相关论文: Characteristic initial value problems for integrab…

We investigate the well-posedness of the characteristic initial-boundary value problem for the Einstein equations in Bondi-like coordinates (including Bondi, double-null and affine). We propose a definition of strong hyperbolicity of a…

We investigate the existence and the global causal structure of plane symmetric spacetimes with weak regularity when the matter consists of an irrotational perfect fluid with pressure equal to its mass-energy density. Our theory encompasses…

Einstein's equations for general relativity, when viewed as a dynamical system for evolving initial data, have a serious flaw: they cannot be proven to be well-posed (except in special coordinates). That is, they do not produce unique…

We formulate an initial boundary value problem (IBVP) for the vacuum Einstein equations by describing the boundary conditions of a spacetime metric in its associated gauge. This gauge is determined, equivariantly with respect to…

In Einstein theory of gravity the initial configuration of metric field and its time derivative are related to matter configuration by four equations called constraints. We use the method of conformal metrics (York Method) to solve…

The physical situation of the collision and subsequent interaction of plane gravitational waves in a Minkowski background gives rise to a well-posed characteristic initial value problem in which initial data are specified on the two null…

We consider the Einstein-Maxwell system as a Cauchy initial value problem taking the electric and magnetic fields as independent variables. Maxwell's equations in curved spacetimes are derived in detail using a 3+1 formalism and their…

A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely…

We prove the well-posedness of the initial boundary value problem for the Einstein equations with sole boundary condition the requirement that the timelike boundary is totally geodesic. This provides the first well-posedness result for this…

Integrable structures arise in general relativity when the spacetime possesses a pair of commuting Killing vectors admitting 2-spaces orthogonal to the group orbits. The physical interpretation of such spacetimes depends on the norm of the…

We consider covariant metric theories of coupled gravity-matter systems satisfying the following two conditions: First, it is assumed that, by a hyperbolic reduction process, a system of first order symmetric hyperbolic partial differential…

We present explicit solutions of the time-symmetric initial value constraints, expressed in terms of freely specfiable harmonic functions for examples of supergravity theories, which emerge as effective theories of compactified string…

For a class of scalar fields including the massless Klein-Gordon field the general relativistic hyperboloidal initial value problems are equivalent in a certain sense. By using this equivalence and conformal techniques it is proven that 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…

In axial symmetry, there is a gauge for Einstein equations such that the total mass of the spacetime can be written as a conserved, positive definite, integral on the spacelike slices. This property is expected to play an important role in…

The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasilinear elliptic--hyperbolic system of evolution…

We consider the initial boundary value problem for the Einstein vacuum equations in the maximal gauge, or more generally, in a gauge where the mean curvature of a timelike foliation is fixed near the boundary. We prove the existence of…

We consider an approach to the hyperboloidal evolution problem based on the Einstein equations written for a rescaled metric. It is shown that a conformal scale factor can be freely prescribed a priori in terms of coordinates in a…

The initial value problem is well-defined on a class of spacetimes broader than the globally hyperbolic geometries for which existence and uniqueness theorems are traditionally proved. Simple examples are the time-nonorientable spacetimes…

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…