Excision boundary conditions for the conformal metric

TL;DR

This paper introduces boundary conditions for the conformal metric in Einstein's equations, derived from boundary geometry and gauge freedom, facilitating black hole applications in initial data construction.

Contribution

It provides a natural derivation of boundary conditions for the conformal metric based on boundary geometry and gauge invariance, extending the formalism to black hole scenarios.

Findings

Boundary conditions derived from conformal geometry.

Applicable to black hole initial data.

Enhances the new Einstein decomposition formalism.

Abstract

Shibata, Ury\=u and Friedman recently suggested a new decomposition of Einstein's equations that is useful for constructing initial data. In contrast to previous decompositions, the conformal metric is no longer treated as a freely-specifiable variable, but rather is determined as a solution to the field equations. The new set of freely-specifiable variables includes only time-derivatives of metric quantities, which makes this decomposition very attractive for the construction of quasiequilibrium solutions. To date, this new formalism has only been used for binary neutron stars. Applications involving black holes require new boundary conditions for the conformal metric on the domain boundaries. In this paper we demonstrate how these boundary conditions follow naturally from the conformal geometry of the boundary surfaces and the inherent gauge freedom of the conformal metric.