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Where the Gauss--Bonnet coupling enters the Bondi--Sachs hierarchy

We integrate the Bondi--Sachs hierarchy of scalar--Gauss--Bonnet gravity with an arbitrary coupling function $f(\Phi)$ and a radiating massless scalar, and determine the first order in $1/r$ at which the coupling $\lambda$ becomes visible in each field equation. We obtain the asymptotic falloff of the effective Gauss--...