2015/10/28 by Ehud Eilon, Amos Ori · 1 citation
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Classical mechanics #Cosmology and Gravitation Theories #Event horizon #Gauge (firearms) #Horizon #Mathematical analysis #Mathematical physics #Mathematics #Naked singularity #Null (SQL) #Physics #Quantum mechanics #Singularity #Spacetime #Truncation error #gr-qc
paper · pdf · doi:10.1103/physrevd.93.024016
published as Phys. Rev. D 93, 024016 (2016) · 38 pages, 18 figures. Added References
arxiv created 2015/10/28 · openalex publication_date 2016/01/12 · arxiv updated 2016/01/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 ve---and runs out of control for a sufficiently long interval of ve. 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-ve 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-\ensuremathσ 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.