FTL -Faster than light travel. I can't make it work. I thought I had an idea, but the math doesn't work out. Walk with me. The thought structure went like this.
Outside a black hole, space-time uses real number for the proximity of one bit of space-time to another. This is limited by the speed of light (C, defined in units equating it to 1) to being a number between C (theoretical, requires the complete absence of all gravity) and 0. 0 is what you get at the event horizon of a black hole - space and time appear to come to a halt. Inside a black hole, the proximity is measured using imaginary numbers. As the gravity increases, the imaginary number gets larger arbitrarily, eventually making the inside of a black hole larger than the outside.
Review - The controlling equation is gravity squared plus space-time proximity equals C.
As G exceeds 1, t drops below zero and takes on imaginary values. As G surpasses the square root of two, t must surpass 1i to balance the equation. The speed of light remains constant, but the nature of space-time constantly changes. What does this really look like? No way to tell without experimentation - and I'm not planning on volunteering.
So, I pondered, if we can use imaginary numbers to represent space-time inside a black hole, might there be some way to use that principle outside the black hole? You can't exceed the speed of light, but could you, just possibly, change the apparent speed of light by altering the properties of local space-time?
I started down this road of thought, imagining how time would accelerate for the traveler in relation to those left behind, and how this could be carefully compensated for by increasing the traveler's speed to slow down their rate of time to match. That's when I started reviewing the math, and encountered the error in the system.
Complex numbers would be required. That doesn't seem to work in normal space. And anyways, when you square a complex number, you get another complex number. It doesn't simplify into a real like an imaginary number does.
Even if you could balance the equation by using complex gravity (I'm not certain this is mathematically possible), what the heck would that even look like? Where would it come from? It's entirely too much handwavium. Even inside a supermassive black hole, gravity is still measured in real numbers, not imaginary, much less complex.
This realization burst the bubble of my glorious dream of fast interstellar travel. Stupid, unforgiving math.