Excision without excision: the relativistic turducken

TL;DR

This paper introduces a novel method for simulating black holes by smoothing their interiors and evolving the Einstein equations everywhere, avoiding traditional excision techniques and ensuring constraints propagate causally.

Contribution

The authors develop and validate a new approach to black hole simulation that does not require excision, using smoothing and hyperbolic formulations to maintain causal constraint propagation.

Findings

Numerical evolutions show the method works robustly for generic data.

Constraints propagate causally, preventing interior violations from affecting the exterior.

The approach approaches a stationary end-state regardless of initial data choices.

Abstract

to turducken (turduckens, turduckening, turduckened, turduckened) [math.]: To stuff a black hole. We analyze and apply an alternative to black hole excision based on smoothing the interior of black holes with arbitrary - possibly constraint violating - initial data, and solving the vacuum Einstein evolution equations everywhere. By deriving the constraint propagation system for our hyperbolic formulation of the BSSN evolution system we rigorously prove that the constraints propagate causally and so any constraint violations introduced inside the black holes cannot affect the exterior spacetime. (This does not follow from the causal structure of the spacetime as is often assumed.) We present numerical evolutions of Cook-Pfeiffer binary black hole initial configurations showing that these techniques appear to work robustly for generic data. We also present numerical evidence from spherically symmetric evolutions that for the gauge conditions used the same stationary end-state is approached irrespective of the choice of initial data and smoothing procedure.