相关论文: Cauchy-characteristic extraction in numerical rela…

We construct exact solutions to the Bianchi equations on a flat spacetime background. When the constraints are satisfied, these solutions represent in- and outgoing linearized gravitational radiation. We then consider the Bianchi equations…

We study Cauchy initial data for asymptotically flat, stationary vacuum space-times near space-like infinity. The fall-off behavior of the intrinsic metric and the extrinsic curvature is characterized. We prove that they have an analytic…

We give a local integral formula, valid on general curved space-times, for the characteristic Cauchy problem for the Dirac equation with arbitrary spin using the method developed by Friedlander in his book "the wave equation on a curved…

We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate…

For the isotropic Lam\'e system, we prove in dimensions three or larger that both Lam\'e coefficients are uniquely recovered from partial Cauchy data on an arbitrary open subset of the boundary provided that the coefficient $\mu$ is a…

We present the first proof-of-principle Cauchy evolutions of asymptotically global AdS spacetimes with no imposed symmetries, employing a numerical scheme based on the generalized harmonic form of the Einstein equations. In this scheme, the…

We consider four-dimensional general relativity with a negative cosmological constant in the presence of a finite size boundary, $\Gamma$, for both Euclidean and Lorentzian signature. As our boundary condition, we consider the `conformal'…

Cauchy-characteristic matching (CCM) is a numerical-relativity technique that solves Einstein's equations on an effectively infinite computational domain, thereby eliminating systematic errors associated with artificial boundary conditions.…

This short paper is concerned with the numerical reconstruction of small sources from boundary Cauchy data for a single frequency. We study a sampling method to determine the location of small sources in a very fast and robust way.…

I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…

Inspired by the work of Burq and Tzvetkov (Invent. math. 173(2008), 449-475.), firstly, we construct the local strong solution to the cubic nonlinear wave equation with random data for a large set of initial data in $H^{s}(M)$ with $s\geq…

We solve the problem of expressing the Weyl scalars $\psi $ that describe gravitational perturbations of a Kerr black hole in terms of Cauchy data. To do so we use geometrical identities (like the Gauss-Codazzi relations) as well as…

In this paper we study a numerical implementation for the initial boundary value formulation for the generalized conformal field equations. We propose a formulation which is well suited for the study of the long-time behaviour of perturbed…

A formalism previously introduced by the author using tesselated Cauchy surfaces is applied to define a quantized version of gravitating point particles in 2+1 dimensions. We observe that this is the first model whose quantum version…

We present a new method for treating the inner Cauchy boundary of a black hole spacetime by matching to a characteristic evolution. We discuss the advantages and disadvantages of such a scheme relative to Cauchy-only approaches. A prototype…

We consider the inverse shape and parameter problem for detecting corrosion from partial boundary measurements. This problem models the non-destructive testing for a partially buried object from electrostatic measurements on the accessible…

We devise a new time-stepping algorithm for two-dimensional nonlinear unsteady surface and interfacial waves. The algorithm uses Cauchy's integral formula, which only requires information on the interface, to solve Laplace equation by using…

We analyze the Cauchy problem for the vacuum Einstein equations with data on a complete light-cone in an asymptotically Minkowskian space-time. We provide conditions on the free initial data which guarantee existence of global solutions of…

We study the scalar, conformally invariant wave equation on a four-dimensional Minkowski background in spherical symmetry, using a fully pseudospectral numerical scheme. Thereby, our main interest is in a suitable treatment of spatial…

We describe a numerical method to construct Cauchy data extending to space-like infinity based on Corvino's (2000) gluing method. Adopting the setting of Giulini and Holzegel (2005), we restrict ourselves here to vacuum axisymmetric…