Formulating the complete initial boundary value problem in numerical relativity to model black hole echoes

Understand

In an attempt to simulate black hole echoes (generated by potential quantum-gravitational structure) in numerical relativity, we recently described how to implement a reflecting boundary outside of the horizon of a black hole in spherical symmetry.

• Here, we generalize this approach to spacetimes with no symmetries and implement it numerically using the generalized harmonic formulation.
• We cast the evolution equations and the numerical implementation into a Summation By Parts (SBP) scheme, which seats our method closer to a class of provably numerically stable systems.
• We implement an embedded boundary numerical framework that allows for arbitrarily shaped domains on a rectangular grid and even boundaries that evolve and move across the grid.