Locating boosted Kerr and Schwarzschild apparent horizons

We describe a finite-difference method for locating apparent horizons in generic spacetimes and illustrate its capabilities on boosted Kerr and Schwarzschild black holes. Our model spacetime is given by the Kerr-Schild metric. We apply a Lorentz boost to this spacetime metric and then carry out a $3+1$ decomposition. The result is a slicing of Kerr-Schwarzschild spacetime in which the black hole is propagated and Lorentz contracted. We show that our method can locate distorted apparent horizons efficiently and accurately.