Solution
= Solution
For two <black holes> of equal <mass>, $M=20M_\odot$ and $\mu=5M_\odot$. The prescribed instantaneous <orbital decay timescale> gives
$$
\boxed{A_{\max}=1.04\times10^{10}\ \mathrm m,\qquad P_{\max}=35.9\ \mathrm h}.
$$
The integrated ten-billion-year criterion gives $51.9$ h. These large initial periods compared with a neutron-star pair reflect the stronger radiation reaction of the more massive system.