Trumpet Initial Data for Boosted Black Holes

We describe a procedure for constructing initial data for boosted black holes in the moving-punctures approach to numerical relativity that endows the initial time slice from the outset with trumpet geometry within the black hole interiors. We then demonstrate the procedure in numerical simulations using an evolution code from the Einstein Toolkit that employs 1+log slicing. The Lorentz boost of a single black hole can be precisely specified and multiple, widely separated black holes can be treated approximately by superposition of single hole data. There is room within the scheme for later improvement to re-solve (iterate) the constraint equations in the multiple black hole case. The approach is shown to yield an initial trumpet slice for one black hole that is close to, and rapidly settles to, a stationary trumpet geometry. Initial data in this new approach is shown to contain initial transient (or "junk") radiation that is suppressed by as much as two orders of magnitude relative to that in comparable Bowen-York initial data.Comment: 18 pages, 18 figure

Trumpet Initial Data for Highly Boosted Black Holes and High Energy Binaries

Initial data for a single boosted black hole is constructed that analytically contains no initial transient (junk) gravitational radiation and is adapted to the moving punctures gauge conditions. The properties of this data are investigated in detail. It is found to be generally superior to canonical Bowen-York data and, when implemented numerically in simulations, yields orders of magnitude less junk gravitational radiation content and more accurate black hole velocities. This allows for modeling of black holes that are boosted faster than previously possible. An approximate superposition of the data is used to demonstrate how a binary black hole system can be constructed to retain the advantages found for the single black hole. Extensions to black holes with spin are considered.Doctor of Philosoph