Is there a binary black hole system in the middle of the galaxy? We have observed gravity effects from black holes in the center of galaxies, but galactic centers are dusty so we can’t tell if it’s one black hole or two black holes in a binary system in there. A new paper is about the recent discovery of a binary black hole system, they zoomed in on a black hole with a radio telescope, and observed that it actually where two black holes in a binary system. The black holes were 250 light years away and had an orbital period of 4 million years,source. Binary black holes are then no longer just a hypothetical idea.  Binary black holes are then no longer just a hypothetical idea.
The stars in the galactic disk have almost the same speed the center about 200-250 km/s.
 
This does not fit with Newtonian physics and Kepler’s third law. The most accepted theory why this doesn’t fit is the presence of dark matter. The dark matter has to be distributed in such a way that it pulls the stars so they get the same orbital speed, and most of it has to be placed at the outskirts of the galactic disk. Dark matter is currently quite mysterious and there are many proposals to what it can be, we don’t know what it is, but we know it is heavy and weighs more than the galaxy. We currently think the universe consists of about 23 % dark matter, 73 % dark energy, 3,6 % intergalactic gas and only 0,4 % stars: 

We neither know why dark matter would be distributed in the way we think it is, and we might wonder if this almost constant orbital speed of stars is just a coincidence.
Could there be alternative solutions to the dark matter problem? Is there another solution that would explain that the stars have almost the same speed around the center of the galaxy? If there were some sort of engine in the galactic center that pulled all the stars with equal force around the middle, we could do without dark matter. But such an engine might be an absurd thought, as we don’t know any wave or force that could transfer energy in such a way on this scale. 
According to Einstein accelerated mass creates gravitational waves, and a binary black hole system has great acceleration of mass and is a huge gravitational wave source. The binary black hole system creates a gravity wave that travels radially outwards with the speed of light, and the rotation of the binary black hole system creates a spiral of gravitational waves:

Put together with our spiral galaxy the gravitational wave spiral will look something like this:

The binary black hole system probably has slow rotation, thousands or maybe even millions of years, while the gravitational wave goes radially outwards with the speed of light. This creates a pretty steep gravitational spiral that will almost perpendicularly intersect the spiral arms of the galaxy.
I pictured the gravitational wave spiral as moving gravity well ripples, that sweeps the galactic disk. And as stars that interact with the ripples, they get accelerated for a while.
But I found no scientific confirmation that gravitational waves can accelerate mass, only how gravitational waves squeeze mass and set it into some kind of vibration. I started to wonder if I had pictured it all wrong. Then I found some information on how Einstein looked at gravity waves:
“Gravity, according to Einstein's general theory of relativity, is how mass deforms the shape of space: near any massive body, the fabric of space becomes curved. But this curving does not always stay near the massive body. In particular, Einstein realized that the deformation can propagate throughout the Universe, just as seismic waves propagate in Earth's crust. Unlike seismic waves, however, gravitational waves can travel in empty space — and they do so at the speed of light." source.
From the slingshot effect we know that one moving gravity well can accelerate another. Like when Voyager 1 was accelerated by the moving gravity-wells of Jupiter and Saturn. So could a binary black hole in the middle of the galaxy create moving gravity well ripples in spacetime that can accelerate stars? So far gravitational radiation has not been observed and we can’t even be sure it exists, and its interaction with matter is on a theoretical basis. But if there is an engine in the middle of the galaxy that can replace dark matter, and accelerate the stars to the same velocity, gravitational radiation might be a part of the solution. The black hole also accelerate mass to relativistic speeds and have huge relativistic mass, which have relativistic moving gravitational fields, and as gravitation act at the speed of light, this might give different gravitational effects than ordinary mass, especially in a binary black hole system. Steven Hawking has proposed Hawking radiation from black holes due to quantum effects. We also have the black hole information paradox, if information is lost in a black hole it violates the principle of quantum mechanics  “–that complete information about a physical system at one point in time should determine it state at any other time.”
So there might be some unknown radiation or force that may accelerate the stars in the galactic disk, at least we should hold this possibility open, as it might give a more elegant solution, without the use of the mysterious dark matter.
 A: I think the following image sums up why your model, at least for our galaxy, is wrong rather nicely:

These are the orbits for 6 stars in the inner region of the galaxy. The orbital period for S2, for instance, is 15 years for an orbit that is roughly twice the size of Sedna's orbit--which takes it 12 thousand years to complete its orbit. Using Kepler's 3rd Law for many more stars than the 6 shown here shows that the total mass contained around (0,0) is about 4.3 million solar masses ($8.35422 \times 10^{39}$ g), all of it within a volume of about $8.3\times10^{39}$ cubic cm.
If there were two black holes orbiting each other at the center of the galaxy, the dynamics of these interior stars would be different than are actually observed.
As another proof, if you want your binary black holes to have an orbital period of a million years, then Kepler's third law would suggest a distance of
$$
r\simeq\left[T^2_{\rm yr}\,(M+m)_{M_\odot}\right]^{1/3}=1.6\times10^{6}\,{\rm AU}
$$
(using the same total mass from above) which would be discernible in observations. It also does not fit the data, given that the image above is about 5,000 AU in height.
A: There are many problems with this line of reasoning.

The most common galaxy types are elliptical galaxies and spiral galaxies, and there might be a parallel with star systems, where the most common types are systems with a single star, and binary systems with two stars in the middle.

There is simply no justification for this. The dynamics of stellar systems are nothing like the dynamics of galaxies.

The black hole, or binary black hole system, in the center of galaxies keeps the galaxies together, by their great mass and gravity pull.

No, galaxies are held together by the mass of stars and gas and dust -- all normal stuff. The mass of even a supermassive black hole is negligible compared to the mass of stars even in just the central bulge of a galaxy.

The other proposed mechanism that holds the galaxy together, and give stars the same orbital period around the galactic center, is the mysterious dark matter, calculated by mathematicians, but yet not found.

Dark matter has to do with the orbits of very far-out things, like globular clusters well outside the disk of the galaxy. Also, mathematicians have nothing to do with this -- people who study astrophysics are called astrophysicists.

The dark matter has to be distributed in such a way that it looks like there is an engine in the galactic center turning the galactic disk as one solid object.

No, simply the presence of extra matter will alter orbital velocities. Consider Kepler's Third Law, which, thanks to Newton, we can write as
$$ \frac{T^2}{r^3} = \frac{4\pi^2}{GM} $$
for a test object circularly orbiting a spherical mass distribution of mass $M$. Since velocity is $v = 2\pi r/T$, this means
$$ v = \sqrt{\frac{GM}{r}}. $$
Larger $M$ implies larger $v$, no engine or rigid body mechanics necessary.

And I would like to have Einstein’s exact words on the topic, but I haven’t managed to find them.

Making too many references to Einstein is usually a bad sign. Referencing Famous People is no stand-in for science. In fact the equations for black holes weren't interpreted correctly until 1958, and the equations for rotating black holes (i.e. all real black holes) weren't even written down until 1963. Einstein was dead by 1955.

As for binary black holes, they may be in some galaxies, sure. In fact, we believe many supermassive black holes underwent mergers with comparably-sized objects in their past, so at some point there must have been a binary system. But certainly there are plenty of examples where the black holes are isolated. If you want binary black holes to explain galactic rotation curves and spiral arms, you'll need to explain why some galaxies have these features without having binary black holes.
Actually, spiral arms are well understood, and it only relies on Newtonian dynamics. Unfortunately the topic is very complicated. See these three questions for more information. Note that the supermassive black hole has nothing to do with it.

On the topic of gravitational waves, it is conceptually possible for them to induce collapse in gas clouds, but in practice they are far, far, far too weak.
As a gravitational wave passes, it distorts spacetime. Yes, this may be only temporary, but the material through which the wave is passing can respond nonetheless. Suppose a wave temporarily brought two particles closer together. Than these particles can attract each other more strongly than before, either through electromagnetic forces or through their own gravity (which is very well approximated as Newtonian gravitational force on top of the metric of general relativity). They move closer to each other. After the wave passes, restoring the metric to what it used to be, these particles can still be closer to each other than they were before this whole process started.
The thing is, even the gravitational waves from inspiraling supermassive black holes are tiny. We've been trying to detect them for decades, but the largest gravitational wave signature we expect to exist in the universe would change the separation between two atoms initially two miles apart by something like a thousandth the width of a proton. Particles that started out even closer would be perturbed proportionally less.
