Improved initial data for black hole collisions

TL;DR

This paper proposes a new simple initial data choice for black hole collision simulations that better represents astrophysical scenarios, especially in the particle limit, improving the realism of numerical relativity models.

Contribution

It introduces a convective initial data method that offers a more accurate representation of astrophysical black hole collisions in numerical relativity.

Findings

Convective initial data yields excellent results in the particle limit.

Standard initial data is less representative of astrophysical scenarios.

Implementation strategies for equal mass black holes are discussed.

Abstract

Numerical relativity codes now being developed will evolve initial data representing colliding black holes at a relatively late stage in the collision. The choice of initial data used for code development has been made on the basis of mathematical definitiveness and usefulness for computational implementation. By using the ``particle limit'' (the limit of an extreme ratio of masses of colliding holes) we recently showed that the standard choice is not a good representation of astrophysically generated initial data. Here we show that, for the particle limit, there is a very simple alternative choice that appears to give excellent results. That choice, ``convective'' initial data is, roughly speaking, equivalent to the start of a time sequence of parameterized solutions of the Hamiltonian constraint; for a particle in circular orbit, it is the initial data of the steady state solution on any hypersurface. The implementation of related schemes for equal mass holes is discussed.