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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Recent perturbative self-force computations (Shah, Friedman & Whiting,submitted to Phys. Rev. {\bf D}, arXiv:1312.1952 [gr-qc]), both numerical andanalytical, have determined that half-integral post-Newtonian terms arise inthe conservative dynamics of black-hole binaries moving on exactly circularorbits. We look at the possible origin of these terms within the post-Newtonianapproximation, find that they essentially originate from non-linear"tail-of-tail" integrals and show that, as demonstrated in the previous paper,their first occurrence is at the 5.5PN order. The post-Newtonian method we useis based on a multipolar-post-Minkowskian treatment of the field outside ageneral matter source, which is re-expanded in the near zone and extendedinside the source thanks to a matching argument. Applying the formula obtainedfor generic sources to compact binaries, we obtain the redshift factor ofcircular black hole binaries (without spins) at 5.5PN order in the extreme massratio limit. Our result fully agrees with the determination of the 5.5PNcoefficient by means of perturbative self-force computations reported in thepreviously cited paper.

Half-integral conservative post-Newtonian approximations in the redshift factor of black hole binaries