Numerical solution of the wave equation on particular space-times using CMC slices and scri-fixing conformal compactification

A. Cruz-Osorio, A. González-Juárez, F.S. Guzmán, F.D. Lora-Clavijo


In this paper we present the numerical solution of the conformally invariant wave equation on top of a fixed background space-time corresponding to two different cases: i) 1+1 Minkowski space-time in Cartesian coordinates and ii) Schwarzschild space-time. In both cases we use hyperboloidal constant mean curvature slices and scri-fixing conformal compactification, and solve the wave equation on the conformal space-time. In the case of the Schwarzschild space-time we study the quasinormal mode oscillations and the late-time polynomial tail decay exponents corresponding to a mass-less scalar field. We also present general formulas to construct hyperboloidal constant mean curvature slicings of spherically symmetric, static, space-times in spherical coordinates.


Relativistic wave equations; numerical relativity; black holes

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Revista Mexicana de Física

ISSN: 2683-2224 (on line), 0035-001X (print)

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