Bona-Masso slicing conditions and the lapse close to black-hole punctures

Abstract

We consider several families of functions $f(\alpha )$ that appear in the Bona-Masso slicing condition for the lapse function $\alpha$. Focusing on spherically symmetric and time-independent slices we apply these conditions to the Schwarzschild spacetime in order to construct analytical expressions for the lapse $\alpha$ in terms of the areal radius $R$. We then transform to isotropic coordinates and determine the dependence of $\alpha$ on the isotropic radius $r$ in the vicinity of the black-hole puncture. We propose generalizations of previously considered functions $f(\alpha )$ for which, to leading order, the lapse is proportional to $r$ rather than a non-integer power of $r$. We also perform dynamical simulations in spherical symmetry and demonstrate advantages of the above choices in numerical simulations employing spectral methods.

arXiv comment8 pages, 4 figures

References in corpus (21)

• Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
• Gravitational wave extraction from an inspiraling configuration of merging black holes
• On the Numerical Integration of Einstein's Field Equations
• Gauge conditions for long-term numerical black hole evolutions without excision
• New Formalism for Numerical Relativity
• Geometry and Regularity of Moving Punctures
• Simple excision of a black hole in 3+1 numerical relativity
• Wormholes and trumpets: the Schwarzschild spacetime for the moving-puncture generation
• Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks
• The appearance of coordinate shocks in hyperbolic formalisms of General Realtivity
• Where do moving punctures go?
• BSSN equations in spherical coordinates without regularization: vacuum and non-vacuum spherically symmetric spacetimes
• Analytical Representation of a Black Hole Puncture Solution
• Late time behaviour of the maximal slicing of the Schwarzschild black hole
• Constant mean curvature slices in the extended Schwarzschild solution and collapse of the lapse: Part I
• Puncture Initial Data for Black-Hole Binaries with High Spins and High Boosts
• Schwarzschild black hole as moving puncture in isotropic coordinates
• Improved Moving Puncture Gauge Conditions for Compact Binary Evolutions
• A Simple Family of Analytical Trumpet Slices of the Schwarzschild Spacetime
• Multidomain Galerkin-Collocation method: characteristic spherical collapse of scalar fields
• Puncture black hole initial data in the conformal thin-sandwich formalism

Cited by in corpus (7)

• Gauge preheating with full general relativity
• Shock-avoiding slicing conditions: tests and calibrations
• Spherically symmetric black hole spacetimes on hyperboloidal slices
• Critical phenomena in the collapse of quadrupolar and hexadecapolar gravitational waves
• Bona-Massó slices of Reissner-Nordström spacetimes
• Dynamical perturbations of black-hole punctures: effects of slicing conditions
• Numerical solutions for the $f(R)$-Klein-Gordon system