# Excision and avoiding the use of boundary conditions in numerical relativity

## TL;DR

This paper introduces a boundary-condition-free method for evolving hyperbolic systems in numerical relativity by excising the domain along a spacelike direction, demonstrated through scalar field simulations.

## Contribution

It proposes a novel excision technique that eliminates the need for boundary conditions in numerical relativity simulations, improving stability and simplicity.

## Key findings

- The excision method successfully evolves scalar fields without boundary conditions.
- Comparison shows the excision approach is effective and comparable to existing methods.
- Numerical experiments demonstrate the method's stability and accuracy.

## Abstract

A procedure for evolving hyperbolic systems of equations on compact computational domains with no boundary conditions was recently described in [arXiv:1905.08657]. In that proposal, the computational grid is expanded in spacelike directions with respect to the outermost characteristic and initial data is imposed on the expanded grid boundary. We discuss a related method that removes the need for imposing boundary conditions: the computational domain is excised along a direction spacelike with respect to the innermost going characteristic. We compare the two methods, and provide example evolutions from a code that implements the excision method: evolution of a massless self-gravitating scalar field in spherical symmetry.