I've been doing some writing about warp drive physics, and what the hardware will look like. It all starts with having opto-electronics that can induce acceleration fields. I don't think it will be possible to curve space-time because the energy requirements are unreasonably large (e.g., the Alcubierre drive requires the energy content equivalent to the planet Jupiter). Instead, I believe that transmitting redshift, rapidly and repeatedly (<1 millisecond), will cause hyper-space to curve. If hyperspace curves, it will produce an acceleration field. This will lead to warp drive technology.https://sites.google.com/site/superluminaldrivephysics/
Acceleration field generator technology, which I call Blueshift technology, is all about emitting "shift photons". I expect there to be mathematics with df/dt terms. For example, a frequency shift from 400THz to 800THz, every millisecond, will have a df/dt = 4x10^17.
There will be a frequency analogue to the Newtonian force equation, F = ma, that will look like F = (h/c)(df/dt), where h is the Planck constant and c is the speed of light.
It will take a long time before the physics community discovers the connection between df/dt, and acceleration field generation with opto-electronics.