Constructing a boosted, spinning black hole in the damped harmonic gauge

Abstract

The damped harmonic gauge is important for numerical relativity computations based on the generalized harmonic formulation of Einstein's equations, and is used to reduce coordinate distortions near binary black hole mergers. However, currently there is no prescription to construct quasiequilibrium binary black hole initial data in this gauge. Instead, initial data are typically constructed using a superposition of two boosted analytic single black hole solutions as free data in the solution of the constraint equations. Then, a smooth time-dependent gauge transformation is done early in the evolution to move into the damped harmonic gauge. Using this strategy to produce initial data in damped harmonic gauge would require the solution of a single black hole in this gauge, which is not known analytically. In this work we construct a single boosted, spinning, equilibrium BH in damped harmonic coordinates as a regular time-independent coordinate transformation from Kerr-Schild coordinates. To do this, we derive and solve a set of 4 coupled, nonlinear, elliptic equations for this transformation, with appropriate boundary conditions. This solution can now be used in the construction of damped harmonic initial data for binary black holes.

Matches PRD version. 8 pages, 3 figures

References in corpus (5)

• Binary-black-hole initial data with nearly-extremal spins
• An Improved Gauge Driver for the Generalized Harmonic Einstein System
• Key Elements of Robustness in Binary Black Hole Evolutions using Spectral Methods
• Reducing spurious gravitational radiation in binary-black-hole simulations by using conformally curved initial data
• Comparison of binary black hole initial data sets

Cited by in corpus (5)

• The SXS Collaboration's third catalog of binary black hole simulations
• Comparison of binary black hole initial data sets
• Multipole moments on the common horizon in a binary-black-hole simulation
• Quasistationary hair for binary black hole initial data in scalar Gauss-Bonnet gravity
• Gravitational collapse in Quadratic Gravity