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

This is the second of two companion papers on computing the self-force in aradiation gauge; more precisely, the method uses a radiation gauge for theradiative part of the metric perturbation, together with an arbitrarily chosengauge for the parts of the perturbation associated with changes in black-holemass and spin and with a shift in the center of mass. We compute theconservative part of the self-force for a particle in circular orbit around aSchwarzschild black hole. The gauge vector relating our radiation gauge to aLorenz gauge is helically symmetric, implying that the quantity h_{\alpha\beta}u^\alpha u^\beta (= h_{uu}) must have the same value for our radiation gauge asfor a Lorenz gauge; and we confirm this numerically to one part in 10^{13}. Asoutlined in the first paper, the perturbed metric is constructed from a Hertzpotential that is in term obtained algebraically from the the retardedperturbed spin-2 Weyl scalar, \psi_0 . We use a mode-sum renormalization andfind the renormalization coefficients by matching a series in L = \ell + 1/2 tothe large-L behavior of the expression for the self-force in terms of theretarded field h_{\alpha\beta}^{ret}; we similarly find the leadingrenormalization coefficients of h_{uu} and the related change in the angularvelocity of the particle due to its self-force. We show numerically that thesingular part of the self-force has the form f_{\alpha} \propto < \nabla_\alpha\rho^{-1}>, the part of \nabla_\alpha \rho^{-1} that is axisymmetric about aradial line through the particle. This differs only by a constant from its formfor a Lorenz gauge. It is because we do not use a radiation gauge to describethe change in black-hole mass that the singular part of the self-force has nosingularity along a radial line through the particle and, at least in thisexample, is spherically symmetric to subleading order in \rho.

Conservative, gravitational self-force for a particle in circular orbit around a Schwarzschild black hole in a Radiation Gauge