This is the exact same conceptual issue as the formation of a single black hole (BH).  Consider a spherical shell of matter (i.e. GR dust) collapsing inwards to form a BH.  As the dust particles get closer and closer together, one can roughly say that time slows down for them and that none of the particles ever pass through their mutual horizon.  Rather, the argument goes, the particles just becomes exponentially close to where that horizon would form.  From the outside, this is indistinguishable from a BH for all practical purposes, since the only way to isolate the still-free dust particles is to zoom exponentially close to the horizon and then drag yourself out (which requires an exponential amount of energy).<p>The problem with this argument is that there is no preferred global time coordinate with respect to which you declare that &quot;the BH has formed&quot;.  Rather, the spacetime events corresponding to &quot;each dust particle crosses their mutual horizon&quot; (i.e., &quot;the formation of the BH&quot;), along with the rest of the interior of the BH, comprise an <i>additional</i> spacetime region you can choose to attach to your manifold or not.  This is a free choice because causality flows one-way across the boundary; no experiments outside the BH can be sensitive to whether the region &quot;really&quot; exists.  There are multiple ways to extend the normal time coordinates (at infinity) into the interior of the BH, and a natural choice is the proper time of in-falling particles&#x2F;observers.  In that case, the BH definitely forms at a <i>finite</i> values of that time coordinate.<p>Merging two existing BHs doesn&#x27;t introduce new fundamental issues.  Quantum mechanics <i>does</i> introduce new fundamental issues, but formally the jury is still out on whether it resolves this question.  The majority opinion is that the interior of the BH exists just as much as regions beyond your cosmological horizon (in an expanding cosmology) exist, from which you are likewise causally disconnected