Properties of Slicing Conditions for Charged Black Holes

We consider an earlier analysis by Baumgarte and de Oliveira (2022) of static Bona-Massó slices of stationary, nonrotating, uncharged black holes, represented by Schwarzschild spacetimes, and generalize that approach to Reissner-Nordström (RN) spacetimes, representing stationary, nonrotating black holes that carry a nonzero charge. This charge is parametrized by the charge-to-mass ratio λ ≡ Q/M, where M is the black-hole mass and the charge Q may represent electrical charge or act as a placeholder for extensions of general relativity. We use a height-function approach to construct time-independent, spherically symmetric slices that satisfy a so-called Bona-Massó slicing condition. We compute quantities such as critical points and profiles of geometric quantities for several different versions of the Bona-Massó slicing condition. In some cases we do this analytically, while in others we use numerical root-finding to solve quartic equations. We conclude that in the extremal limit as λ → 1, all slices that we consider approach a unique slice that is independent of the chosen Bona-Massó condition. We then study dynamical, i.e. time-dependent, Bona-Massó slices by analytically predicting the qualitative behavior of the central lapse, i.e. the lapse at the black-hole puncture, for a particular slice that Alcubierre (1997) proposed to mitigate gauge shocks. These shock-avoiding slices are a viable alternative to the very common so-called 1 + log slices but exhibit different behavior in dynamical simulations. We use a perturbation of the radial coordinate at the location of the puncture to recover approximately harmonic late-time oscillations of the central lapse that Baumgarte and Hilditch (2022) observed in numerical simulations.