On the applicability of constrained symplectic integrators in general relativity

TL;DR

This paper discusses the challenges of applying standard constrained symplectic integrators, like SHAKE or RATTLE, to the numerical solution of Einstein's equations in general relativity, highlighting potential issues.

Contribution

It identifies limitations of naive symplectic integrators when used with constrained Hamiltonian systems in the context of general relativity.

Findings

Naive application of symplectic schemes faces difficulties in general relativity.

Standard constrained integrators may not preserve constraints effectively.

Highlights need for specialized methods in numerical relativity.

Abstract

The purpose of this note is to point out that a naive application of symplectic integration schemes for Hamiltonian systems with constraints such as SHAKE or RATTLE which preserve holonomic constraints encounters difficulties when applied to the numerical treatment of the equations of general relativity.