Adaptive gauge method for long-time double-null simulations of spherical black-hole spacetimes

Understand

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 $v_e$).