相关论文: Cauchy-characteristic Evolution of Einstein-Klein-…

We analyze the initial value problem for scalar fields obeying the Klein-Gordon equation. The standard Cauchy initial value problem for second order differential equation is to construct a solution function in a neighborhood of space and…

From Einstein's theory we know that besides the electromagnetic spectrum, objects like quasars, active galactic nuclei, pulsars and black holes also generate a physical signal of purely gravitational nature. The actual form of the signal is…

The Cauchy+characteristic matching (CCM) problem for the scalar wave equation is investigated in the background geometry of a Schwarzschild black hole. Previously reported work developed the CCM framework for the coupled…

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D…

We present several improvements to the Cauchy-characteristic evolution procedure that generates high-fidelity gravitational waveforms at $\mathcal{I}^+$ from numerical relativity simulations. Cauchy-characteristic evolution combines an…

In this paper, we consider the initial value problem for the Einstein-Vlasov-Scalar field equations in temporal gauge, where the initial data are prescribed on two characteristic smooth intersecting hypersurfaces. From a suitable choice of…

Computational techniques which establish the stability of an evolution-boundary algorithm for a model wave equation with shift are incorporated into a well-posed version of the initial-boundary value problem for gravitational theory in…

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately…

We study the initial value problem in Einstein-Cartan theory which includes torsion and, therefore, a non-symmetric connection on the spacetime manifold. Generalizing the path of a classical theorem by Choquet-Bruhat and York for the…

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to current 3D black codes that simulate…

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…

These lectures are designed to provide a general introduction to the Einstein-Vlasov system and to the global Cauchy problem for these equations. To start with some general facts are collected and a local existence theorem for the Cauchy…

We study the evolution of a self-gravitating compressible fluid in spherical symmetry and we prove the existence of weak solutions with bounded variation for the Einstein-Euler equations of general relativity. We formulate the initial value…

We investigate the Cauchy problem for the Einstein - scalar field equations in asymptotically flat spherically symmetric spacetimes, in the standard 1+3 formulation. We prove the local existence and uniqueness of solutions for initial data…

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…

We investigate the interior of a dynamical black hole as described by the Einstein-Maxwell-charged-Klein-Gordon system of equations with a cosmological constant, under spherical symmetry. In particular, we consider a characteristic initial…

This paper establishes novel bounds for Gowdy-symmetric Einstein-Euler spacetimes and completes the analysis, initiated by LeFloch and Rendall, of the global areal foliation for these spacetimes. We thus consider the initial value problem…

In this paper, we initiate the study of the asymptotically AdS initial-boundary value problem for the Einstein-massless Vlasov system with $\Lambda<0$ in spherical symmetry. We will establish the existence and uniqueness of a maximal future…

This paper gives a detailed pedagogic presentation of the central concepts underlying a new algorithm for the numerical solution of Einstein's equations for gravitation. This approach incorporates the best features of the two leading…

We analyze the initial value problem for spinor fields obeying the Dirac equation, with particular attention to the characteristic surfaces. The standard Cauchy initial value problem for first order differential equations is to construct a…