Inner boundary conditions for black hole Initial Data derived from Isolated Horizons

TL;DR

This paper introduces boundary conditions for black hole initial data that ensure horizons are in equilibrium, facilitating more accurate simulations of black hole spacetimes, especially in binary systems.

Contribution

It proposes a new set of boundary conditions based on the Isolated Horizons formalism for constructing initial data with black hole horizons in equilibrium.

Findings

Boundary conditions ensure horizons are in equilibrium.

Application to binary black hole initial data.

Comparison with existing methods.

Abstract

We present a set of boundary conditions for solving the elliptic equations in the Initial Data Problem for space-times containing a black hole, together with a number of constraints to be satisfied by the otherwise freely specifiable standard parameters of the Conformal Thin Sandwich formulation. These conditions altogether are sufficient for the construction of a horizon that is instantaneously in equilibrium in the sense of the Isolated Horizons formalism. We then investigate the application of these conditions to the Initial Data Problem of binary black holes and discuss the relation of our analysis with other proposals that exist in the literature.