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Free keywords:
General Relativity and Quantum Cosmology, gr-qc, Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
Abstract:
On the basis of a recently proposed strategy of finite element integration in
time domain for partial differential equations with a singular source term, we
present a fourth order algorithm for non-rotating black hole perturbations in
the Regge-Wheeler gauge. Herein, we address even perturbations induced by a
particle plunging in. The forward time value at the upper node of the $(r^*,t)$
grid cell is obtained by an algebraic sum of i) the preceding node values of
the same cell, ii) analytic expressions, related to the jump conditions on the
wave function and its derivatives, iii) the values of the wave function at
adjacent cells. In this approach, the numerical integration does not deal with
the source and potential terms directly, for cells crossed by the particle
world line. This scheme has also been applied to circular and eccentric orbits
and it will be object of a forthcoming publication.
