Continuing E's discussion on Space-time, Let's dive deep into the actual physics equations involved in constructing a gravity engine, utilizing the Alcubierre drive theory.
According to the Alcubierre drive theory, a spacecraft could effectively move through space-time at faster-than-light speeds by creating a stable "warp bubble" around itself. The idea is simple in and of itself, you warp gravity in a contained way around the front and back of a craft in polarized ways in order to create propulsion.
This, however, would require the manipulation of the curvature of space-time utilizing the Einstein Field Equations, which describe the relationship between matter and energy distribution and curvature in the fabric of space.
In physics you would write that out like this:
Rmunu - (1/2)gmunuR = (8πG/c^4)Tmunu
Where "Rmunu" represents the Riemann tensor (a way to measure the volume and shape of the curvature) , "gmunu" represents the metric tensor (a way to define distance and angles), R represents the Ricci scalar(this measures the curvature of the riemann manifold), Tmunu represents the stress-energy tensor(this measures the density/flux of energy/ momentum in space time, it comes from Newtonian physics ie. gravity), G represents the gravitational constant, and c represents the speed of light.
To create the stable warp bubble, negative mass-energy would have to be created and manipulated. The stress-energy tensor for negative mass is represented as:
Tmunu = -ρc^2uμuν
where ρ represents the mass density of the negative mass-energy (think theoretical antimatter, and black holes), and uμ and uν represent the 4-velocity components (4 velocity is a 4 vector way of describing the rate of change or the relativistic counterpart to velocity in a four dimensional space [velocity works in three dimensions*]).
Finally, the Alcubierre metric equation, which describes the metric tensor associated with a subluminal Alcubierre drive, can be written as:
ds^2 = -(a^2 - [(x - vt)^2 + y^2 + z^2])/c^2 dt^2 + 2[(x - vt)dx/c^2]dt + dx^2 + dy^2 + dz^2
where "a" represents the amplitude of the warp bubble, "v" represents the velocity of the bubble, and "x, y, and z" represent the spatial coordinates.
To create stable warp bubbles the relationship between negative mass-energy and the manipulation of gravitational forces must be understood, and modern physicists don't quite have a proper grasp on that, particularly in regards to antimatter.
Space-Time is a curious thing.