Radiation tails and boundary conditions for black hole evolutions

TL;DR

This paper discusses the impact of boundary conditions on black hole simulations, showing that late-time field decay ('tails') are unlikely with finite boundary approximations, supported by computational evidence.

Contribution

It highlights the non-existence of expected tail behavior in numerical black hole evolutions with finite boundary conditions and provides computational demonstrations.

Findings

Late-time tails are unlikely with finite boundary conditions.

Computational evidence shows deviations from expected tail decay.

Boundary conditions significantly influence black hole evolution simulations.

Abstract

In numerical computations of Einstein's equations for black hole spacetimes, it will be necessary to use approximate boundary conditions at a finite distance from the holes. We point out here that ``tails,'' the inverse power-law decrease of late-time fields, cannot be expected for such computations. We present computational demonstrations and discussions of features of late-time behavior in an evolution with a boundary condition.