Well-posed first-order reduction of the characteristic problem of the linearized Einstein equations

Abstract

A choice of first-order variables for the characteristic problem of the linearized Einstein equations is found which casts the system into manifestly well-posed form. The concept of well-posedness for characteristic problems invoked is that there exists an \textit{a priori} estimate of the solution of the characteristic problem in terms of the data. The notion of manifest well-posedness consists of an algebraic criterion sufficient for the existence of the estimates, and is to characteristic problems as symmetric hyperbolicity is to Cauchy problems. Both notions have been made precise elsewere.

arXiv comment6 pages

References in corpus (7)

• Stable characteristic evolution of generic 3-dimensional single-black-hole spacetimes
• Null cone evolution of axisymmetric vacuum spacetimes
• Moving Black Holes in 3D
• Gravitational waveforms with controlled accuracy
• Characteristic Evolution and Matching
• First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations
• Estimates for the characteristic problem of the first-order reduction of the wave equation

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• Simulations of gravitational collapse in null coordinates: III. Hyperbolicity
• Exact boundary conditions in numerical relativity using multiple grids: scalar field tests
• Estimates for first-order homogeneous linear characteristic problems
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• On the Linear Regime of the Characteristic formulation of General relativity in the Minkowski and Schwarzschild's Backgrounds