Can common-envelope ejection produce tight merging black-hole binaries?
In plain words
Many merging pairs are thought to have shrunk when one star swelled and engulfed its companion, which spiraled in and blew off the shared envelope; whether the envelope can actually be thrown off and leave a tight enough orbit has not been shown.
Precise statement
In common-envelope evolution the orbital energy released during inspiral must unbind the donor envelope, conventionally parametrized by $\alpha_{\mathrm{CE}}\times\lambda$. Determine from $3D$ hydrodynamics (with recombination energy, jets and post-plunge evolution) whether envelopes of $15\ \text{to}\ 40\ M_{\mathrm{sun}}$ red supergiant donors are fully ejected, and whether final separations of a few $R_{\mathrm{sun}}$, small enough to merge by gravitational waves within $1.4e10\ \mathrm{yr}$, result. Answer: final separation and ejected mass versus donor mass and radius, and the implied share of mergers from this route versus stable mass transfer.
What would settle it
3D simulations followed to full envelope ejection or merger for massive donors, calibrated on observed post-common-envelope binaries.