English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

To model the radiative evolution of extreme mass-ratio binary inspirals (akey target of the LISA mission), the community needs efficient methods forcomputation of the gravitational self-force (SF) on the Kerr spacetime. Here wefurther develop a practical `$m$-mode regularization' scheme for SFcalculations, and give details of a first implementation. The key steps in themethod are (i) removal of a singular part of the perturbation field with asuitable `puncture' to leave a sufficiently regular residual within a finiteworldtube surrounding the particle's worldline, (ii) decomposition in azimuthal($m$-)modes, (iii) numerical evolution of the $m$-modes in 2+1D with a finitedifference scheme, and (iv) reconstruction of the SF from the mode sum. Themethod relies on a judicious choice of puncture, based on theDetweiler--Whiting decomposition. We give a working definition for the `order'of the puncture, and show how it determines the convergence rate of the$m$-mode sum. The dissipative piece of the SF displays an exponentiallyconvergent mode sum, while the $m$-mode sum for the conservative piececonverges with a power law. In the latter case the individual modalcontributions fall off at large $m$ as $m^{-n}$ for even $n$ and as $m^{-n+1}$for odd $n$, where $n$ is the puncture order. We describe an $m$-modeimplementation with a 4th-order puncture to compute the scalar-field SF alongcircular geodesics on Schwarzschild. In a forthcoming companion paper we extendthe calculation to the Kerr spacetime.

Self force via m-mode regularization and 2+1D evolution: Foundations and a scalar-field implementation on Schwarzschild