Consistent discretizations: the Gowdy spacetimes

TL;DR

This paper demonstrates the application of consistent discretization to Gowdy spacetimes in general relativity, showing successful numerical evolution with convergence and approximate constraint preservation.

Contribution

It is the first detailed application of the consistent discretization scheme to a non-linear, generally-covariant gravitational system with local degrees of freedom.

Findings

Numerical evolution of Gowdy spacetimes is successful.

The scheme is convergent.

Constraints are approximately preserved.

Abstract

We apply the consistent discretization scheme to general relativity particularized to the Gowdy space-times. This is the first time the framework has been applied in detail in a non-linear generally-covariant gravitational situation with local degrees of freedom. We show that the scheme can be correctly used to numerically evolve the space-times. We show that the resulting numerical schemes are convergent and preserve approximately the constraints as expected.