科研之友
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摘要
Double-null coordinates are highly useful in numerical simulations of dynamical spherically symmetric black holes (BHs). However, they become problematic in long-time simulations: Along the event horizon, the truncation error grows exponentially in the outgoing Eddington null coordinate-which we denote v(e)-and runs out of control for a sufficiently long interval of v(e). This problem, if not properly addressed, would destroy the numerics both inside and outside the black hole at late times (i.e. large ve). In this paper we explore the origin of this problem, and propose a resolution based on adaptive gauge for the ingoing null coordinate u. This resolves the problem outside the BH-and also inside the BH, if the latter is uncharged. However, in the case of a charged BH, an analogous large-v(e) numerical problem occurs at the inner horizon. We thus generalize our adaptive gauge method in order to overcome the inner-horizon problem as well. This improved adaptive gauge, to which we refer as the maximal-sigma gauge, allows long-v double-null numerical simulation across both the event horizon and the (outgoing) inner horizon, and up to the vicinity of the spacelike r = 0 singularity. We conclude by presenting a few numerical results deep inside a perturbed charged BH, in the vicinity of the contracting Cauchy horizon.
- 出版日期2016-1-12
