We know that there exists no such thing as a "rigid" substance in relativity. Now suppose we had a disc of uniform density the size of the Milky Way. When the "core" of the galaxy starts to rotate, the effects (tidal and gravitational) of this rotation propagate at the speed of light, which is VERY slow compared to the size of entire galaxy. It takes 40,000 years for the effects of the core to be felt by the extremities of the arms! Thus, even the most rigid solid possible, neutronium or quark/strange matter, would experience a "bending", resulting in the disc deforming in a spiral fashion. However, this alone doesn't account for the observed spiral structure, but it provides for the "first half" of the theory. We still haven't accounted for the diminishing effect of gravity/tidal forces from the core to the surface via distance. Now, if we consider the galaxy as it actually was, a disc of gas, gas is very far from being rigid, the only "container" of the gas is the gravity of the entire mass as whole. When the core of this disc starts to rotate, and the effects of the core also DIMINISH with distance by the inverse square, we don't result with a continuous set co-centric rings orbiting the core at different speeds, whose speeds decrease linearly with the radius, but we end up with co-centric rings whose orbiting speeds decrease with the inverse square of the radius. As the co-centric rings merge and separate from their neighboring co-centric rings, they will form into "arms" whose segments will be orbiting at different speeds about the core, becoming more and more spiral, with each revolution widening the total spiral arc of each arm. Initially, there should be MANY arms. After enough revolutions (old galaxies), different arms will come in close proximity, causing a local gravitational effect, causing arms to collide and merge, decreasing the number of observed arms, and creating VERY WIDE ARCS. These would be BARRED SPIRAL GALAXIES. Eventually you should be left with two "parallel" arms. What's nice is that we don't need this fictional dark matter to explain these structures, just stir a cup of coffee from the center, and observe its spiral structure. This is where I got the idea. The liquid of the coffee was from from being rigid, sot he kinetic transfer between the cylindrical axis of the cup to the cylindrical surface area of the cup took quite some time. Now replace Kinetic energy with gravity/tidal forces and you can see how it would effect entire galaxies in a similar way.