Local and global properties of conformally flat initial data for black hole collisions

TL;DR

This paper analyzes the physical and geometric properties of conformally flat initial data for black hole configurations, focusing on mass dependence, unphysical fields, and tidal forces, using numerical methods and comparisons to analytical solutions.

Contribution

It provides a detailed investigation of how initial data methods influence physical properties and unphysical fields in black hole simulations, with new insights into mass behavior and local invariants.

Findings

Total mass depends on black hole configuration and separation.

Unphysical 'junk' fields are characterized and their effects analyzed.

Spatial invariants reveal local distribution of gravitational fields.

Abstract

We study physical properties of conformal initial value data for single and binary black hole configurations obtained using conformal-imaging and conformal-puncture methods. We investigate how the total mass M_tot of a dataset with two black holes depends on the configuration of linear or angular momentum and separation of the holes. The asymptotic behavior of M_tot with increasing separation allows us to make conclusions about an unphysical ``junk'' gravitation field introduced in the solutions by the conformal approaches. We also calculate the spatial distribution of scalar invariants of the Riemann tensor which determine the gravitational tidal forces. For single black hole configurations, these are compared to known analytical solutions. Spatial distribution of the invariants allows us to make certain conclusions about the local distribution of the additional field in the numerical datasets.