Comparing an analytical spacetime metric for a merging binary to a fully nonlinear numerical evolution using curvature scalars

TL;DR

This paper presents a new invariant method based on geodesic deviation to compare analytical and numerical black-hole binary spacetimes, aiding the improvement of analytical models by assessing deviations locally.

Contribution

It introduces a geometrically invariant prescription for comparing spacetimes, bridging analytical models and numerical solutions using curvature scalars.

Findings

The method effectively measures local deviations between analytical and numerical spacetimes.

It can identify regions where analytical models violate Einstein equations.

The approach enhances the accuracy of analytical spacetime models for inspiraling black-hole binaries.

Abstract

We introduce a new geometrically invariant prescription for comparing two different spacetimes based on geodesic deviation. We use this method to compare a family of recently introduced analytical spacetime representing inspiraling black-hole binaries to fully nonlinear numerical solutions to the Einstein equations. Our method can be used to improve analytical spacetime models by providing a local measure of the effects that violations of the Einstein equations will have on timelike geodesics, and indirectly, gas dynamics. We also discuss the advantages and limitations of this method.