Perturbative evolution of conformally flat initial data for a single boosted black hole

TL;DR

This paper uses second order perturbation theory to analyze the initial data of boosted black holes, revealing complexities in estimating spurious radiation and insights into optimal reference frames for collision studies.

Contribution

It introduces a perturbative approach to study conformally flat initial data for boosted black holes, highlighting new subtleties and limitations compared to spinning black holes.

Findings

Perturbative calculations can estimate radiated energies but with limitations.

Boosted black hole data exhibit additional complexities over spinning cases.

Insights into the most suitable reference frames for collision simulations.

Abstract

The conformally flat families of initial data typically used in numerical relativity to represent boosted black holes are not those of a boosted slice of the Schwarzschild spacetime. If such data are used for each black hole in a collision, the emitted radiation will be partially due to the ``relaxation'' of the individual holes to ``boosted Schwarzschild'' form. We attempt to compute this radiation by treating the geometry for a single boosted conformally flat hole as a perturbation of a Schwarzschild black hole, which requires the use of second order perturbation theory. In this we attempt to mimic a previous calculation we did for the conformally flat initial data for spinning holes. We find that the boosted black hole case presents additional subtleties, and although one can evolve perturbatively and compute radiated energies, it is much less clear than in the spinning case how useful for the study of collisions are the radiation estimates for the ``spurious energy'' in each hole. In addition to this we draw some lessons on which frame of reference appears as more favorable for computing black hole collisions in the close limit approximation.