Past and future gauge in numerical relativity

TL;DR

This paper proposes a novel approach to solving discretized Einstein equations in numerical relativity by using a future gauge choice and a dynamical past gauge, demonstrated on a polarized Gowdy wave.

Contribution

It introduces a new gauge strategy for discretized Einstein equations, enhancing the flexibility of gauge choices in numerical relativity.

Findings

Successful implementation on a polarized Gowdy wave

Demonstrates the feasibility of future and past gauge separation

Provides a new framework for gauge handling in numerical simulations

Abstract

Numerical relativity describes a discrete initial value problem for general relativity. A choice of gauge involves slicing space-time into space-like hypersurfaces. This introduces past and future gauge relative to the hypersurface of present time. Here, we propose solving the discretized Einstein equations with a choice of gauge in the future and a dynamical gauge in the past. The method is illustrated on a polarized Gowdy wave.