What is the region of space that exists at the center of mass of merging black holes? The title of the question does not allow enough characters for a clear statement of the question. This is the question: 
Imagine that a series of black holes are converging toward a common center of gravity. To simplify the scenario, imagine the black holes are all of equal mass and therefore have identical event horizons. They are approaching from identical distances from the center of mass with identical magnitudes of velocity. 
It seems to me that if two of the black holes were approaching on opposite directions on the arbitrary x-axis and three were approaching on the y-z plane with a mutual angular separation of 120 degrees that eventually the event horizons of the five black holes would begin to overlap (of course other numbers of black holes and geometries could create a similar phenomenon). 
Using Euclidean geometry for analysis, it appears that as the black holes continued to approach the common center of gravity, there would be a period of time where a volume of normal space at the center is completely surrounded by a composite event horizon, then by a shell consisting of the space within this common event horizon and then by a continuous outer event horizon which in turn is surrounded by normal space.
So is there anything remarkable about this inner region of space? Is it still normal space? It appears to be completely cut off from the rest of the universe, to a greater extent than is true even for the space within the event horizon of a black hole. Normal space can communicate one-way with inner event horizon space. but there is no communication in either direction between core space and normal space. Also ,nothing within this core-space or the core-space itself ever actually crossed an event horizon, yet it is completely surrounded by not one but two event horizons. 
Is there any reason to think any of the laws of physics would be different in this region of space? As the black holes continued toward the center of gravity and this core space continues to contract, would Hawking radiation at the surrounding event horizon region increase exponentially and attempt to explode this structure (consisting of a concentric shell of space sandwiched between two event horizons and an inner core of normal space) just as an atomic-scale black hole is predicted to do? 
Could this process progress - at the core space region - to form the equivalent of an event horizon of an atomic scale mini-black hole but with negative curvature?
EDIT 1:
It occurs to me that the event horizons of the approaching black holes may not actually merge. There should be a plane of zero net gravity intersecting at a 90 angle to a line segment with the ends defined by any two centers of two black holes. For equimassive black holes the line segment would be intersected at the midpoint of the line, with increasing net gravity as the distance on either side of the plane increases but remaining below a value that creates a continuum of space with the black hole inner event horizon space. 
This may result in a continuous series of pathways of normal space connecting the inner or core space region with normal space surrounding the composite black hole system. 
One commentator inquired whether the composite system could have rotation. If - rather than 5 approaching black holes - the three y-z plane BHs were in the same orbit around the center of mass with 120 degree angular separation and the two x-axis black holes were in orbit in a perpendicular orbital plane (or alternatively three black hole as in the y-z plane) then the composite system would have 2 rotating elements. 
Of course the masses of the black holes in one orbital plane could be different than those in the other orbital plane such that the resultant two orbits did not intersect. The orbital radii could be quite different - perhaps such that the system could be gravitationally stable or quasi-stable.
If the orbital speeds were high enough, the hypothetical pathways between core space and external normal space could be changing so fast that any potential pathway from the exterior of the composite system would require a speed greater than light for any matter/energy to succeed in travelling through the pathway before it was swept away by an approaching event horizon. 
There could still be continuous normal space connections between core space and external space but the core space region would still be effectively isolated from external normal space since no transfer of matter/energy could occur between the two regions.
The commentator also inquired about what I thought the inside event horizon might look like - I interpret this as "what would be the surface topology of inner event horizon?" I imagine in the simplest case it would be five-sided, three "walls" a floor and a ceiling with each wall and the floor and ceiling having a convexity with radius of curvature equal to that of the black hole event horizons.
Of course this core space regions would be extremely black - perhaps the blackest region of space that is theoretically possible. Interestingly if the orbital model of this system included a black hole as the center of mass of the system, the core region would then be a 3-d shell of space bounded by a single inner event horizon and the two outer event horizons - so this inner shell space would be contained within three event horizons. J.F.  
 A: You have some region of space (lets call it the 'center') that is surrounded by black holes (BH), such that their individual event horizons (as spherical surfaces) completely enclose the center.
The 'overall' event horizon (EH) of the spacetime are not just intersecting spheres.  A spherical event horizon exists for a spherically symmetric blackhole, but as soon as you place two blackholes together, the event horizon is no longer spherical.  That is to say that the geometry gets more complicated.  This video (which could be better rendered...) gives a good example.
Event horizons are defined (see, here or here) based on causal interaction.  Mathematically, when geodesics can bi-directionally connect two regions.  Obviously this 'center' region is no longer connected to the outside universe, so from an outside observer, there is just a single (complicated) EH on the outside of all of the collective BH system.  An observer in the inside region could probably see an EH all around them---with everything in all directions becoming extremely redshifted.  (This is analogous, but clearly distinct, from the horizon of the universe, which we also see in all directions.)
The space in the 'center' would be completely "normal" --- but the same is true with space within event horizons in general.  An observing passing an event horizon to the "inside" of a BH doesn't experience anything wild (except perhaps very strong tidal forces), and they wouldn't in this central region either.
A: A few basic observations:


*

*Black holes, even supermassive ones, are pretty small. The supermassive black hole at the center of the Milky Way has a radius of just 41 light seconds. The size of a stellar black hole is a fraction of a light millisecond. So, in very short order after coming into existence as an isolated region of normal space (less than a millisecond), the "center" will receive no light from the outside the "center".

*While tidal forces near a supermassive black hole are modest, tidal forces near stellar sized black holes in the process of merging are huge. And, while it isn't theoretically impossible for enough supermassive black holes to converge in the manner needed to create a "center", I suspect that the probability of that happening more than once or twice anywhere in the entire history of the universe has got to be pretty much negligible.

*Unless the shell black holes are absolutely perfectly balanced in mass, everything in the "center" will be pulled strongly towards the most massive part of the shell. All the mass-energy in the "center" would be sucked up before the last bits of vacuum were absorbed into the event horizon. While Birchoff's theorem theoretically applies to "shell"-"center" systems, there is no physically possible system that could really exist that would be so perfectly balanced. Moving black holes aren't amenable to that degree of precision engineering.

*I can't imagine any way that the "center" can be stable. Any set of dynamics that would lead to the formation of a "shell" as the black holes converged towards a common center of gravity would moments later expand to absorb the "center", which absent a wildly improbable number of simultaneously and perfectly converging black holes, is going to have a maximal dimension on the same order of magnitude as one of the pre-convergence black holes (i.e. a fraction of a light millisecond). Given the duration of the black hole merger event measured by LIGO, it is hard to imagine a "center" existing for more than a matter of few seconds (if that).

*While the "center" is "normal" space in a technical sense, it is still a highly remarkable and short lived unstable environment, that is certainly not an "ordinary" part of space even if it is technically not exotic.

*It is theoretically impossible for anyone outside the "shell" to observe in any way what is going on in the "center". There is no way to empirically test the predictions of GR in this domain that I can imagine.

*In the time leading up to the formation of the "shell", anyone in the soon to be "center" region is going to experience truly intense and weird gravitational lensing as black holes converge on the observer from all directions. This would tip off any observer in the "center" region who understands GR as to what is about to happen, so no sufficiently knowledgable observer could fail to know that they are in an "center" rather than a larger universe.
