Constraint preserving boundary conditions for the linearized BSSN formulation

TL;DR

This paper develops explicit algebraic boundary conditions for the linearized BSSN system that preserve constraints, with potential generalizations and energy-based justification, enhancing stability in numerical relativity.

Contribution

It introduces two sets of constraint-preserving boundary conditions for the linearized BSSN formulation, generalizable to more complex conditions, justified through energy estimates.

Findings

Derived explicit algebraic boundary conditions

Proposed generalizations to inhomogeneous conditions

Validated by energy estimates

Abstract

We derive two sets of explicit algebraic constraint preserving boundary conditions for the linearized BSSN system. The approach can be generalized to inhomogeneous differential and evolution conditions, the examples of which are given. The proposed conditions are justified by an energy estimate on the original BSSN variables.