Pseudotensor applied to Numerical Relativity in Calculating Global Quantities

TL;DR

This paper applies the Landau-Lifshitz pseudotensor flux formalism to compute global quantities like mass and angular momentum in binary black hole simulations, highlighting its smoother results and potential for improved accuracy over traditional methods.

Contribution

It demonstrates the effectiveness of the pseudotensor flux formalism in numerical relativity for calculating global quantities with smoother numerical behavior.

Findings

Pseudotensor flux yields smoother global quantity values.

Allows larger surface radii for more accurate integrations.

Convergence similar to traditional methods.

Abstract

In this work we apply the Landau-Lifshitz pseudotensor flux formalism to the calculation of the total mass and the total angular momentum during the evolution of a binary black hole system. We also compare its performance with the traditional integrations for the global quantities. It shows that the advantage of the pseudotensor flux formalism is the smoothness of the numerical value of the global quantities, especially of the total angular momentum. Although the convergence behavior of the global quantities with the pseudotensor flux method is only comparable with the ones with the traditional method, the smoothness of its numerical value allows using a larger radius for surface integration to obtain more accurate result.