Einstein-Klein-Gordon system via Cauchy-characteristic evolution: Computation of memory and ringdown tail

TL;DR

This paper extends the Cauchy-characteristic evolution method in numerical relativity to include scalar fields, enabling the accurate computation of gravitational wave memory effects and scalar field tails at null infinity.

Contribution

The authors incorporate scalar fields into the CCE system within SpECTRE, deriving new equations and demonstrating the method's ability to capture scalar and tensor memory effects and tails.

Findings

Successfully captures scalar and tensor memory effects.

Accurately computes Price's power-law tail in scalar fields.

Extends CCE to beyond-GR theories with scalar fields.

Abstract

Cauchy-characteristic evolution (CCE) is a powerful method for accurately extracting gravitational waves at future null infinity. In this work, we extend the previously implemented CCE system within the numerical relativity code SpECTRE by incorporating a scalar field. This allows the system to capture features of beyond-general-relativity theories. We derive scalar contributions to the equations of motion, Weyl scalar computations, Bianchi identities, and balance laws at future null infinity. Our algorithm, tested across various scenarios, accurately reveals memory effects induced by both scalar and tensor fields and captures Price's power-law tail ($u^{-l-2}$) in scalar fields at future null infinity, in contrast to the $t^{-2l-3}$ tail at future timelike infinity.