From the previous post, "Only If You Started Somewhere" dated 27 Dec 2017,
in the case of,
when \(\Delta T=0\) ie. \(T=T_g\), \(r\) is a measure for \(T_k\) up to \(V=0\). \(r\) need not be at infinity, just
\(\left.V=0\right|_{r=r_o}\)
when ever \(V=0\) at \(r_o\).