Metric Engineering

We live in a geometry that our best theories of reality describe as a combined space-time. The intrinsic curvature of that geometry is what creates the gravity that we experience. This curvature in turn is made by energy (including mass), the movement of energy (including mass), and stress.

Terminology: A given place and time together define an event. The separation of two events is described by an interval s that is a function of the coordinates (usually represented by a vector x indexed by xμ; μ = 0 … 3 with x0 representing the time coordinate and xi; i = 1 … 3 a spatial coordinate vector) ds2 = Σμν gμν dxμ dxν. Here, gμν are the coordinates of the metric tensor. Knowledge of the metric tensor suffices for a full description of the intrinsic curvature of any space-time. Hence, manipulation of space-time is often described as "metric engineering." Example: The interval between two events at the same time is the distance r: s = r. If x is measured in Cartesian coordinates x = (x, y, z, then we can get the distance from the Pythagorean theorem r =   √  x2 + y2 + z2 We immediately get that g11 = g22 = g33 = 1 and gij = 0 for i ≠ j. In matrix form g =   1     0     0 0     1 0 0     0 1 In flat space-time, we need to account for the differences in the time coordinate to prperly take relativity into account. In this case s =   √  x2 + y2 + z2 - c2 t2 and g =   -c2     0     0     0 0 1 0 0 0 0 1 0 0 0 0 1

Engineering the curvature of space-time is currently (2026) far beyond our reach; requiring energies, stresses, or mass flows far beyond anything we have managed to create. However, our theories of how space-time bends allows us to make predictions about how we could manipulate it if we were able to command such extreme conditions.

Black holes are an extreme form of object defined by their intense space-time curvature. The page on black hole engineering describes some of the things we might do if we could make or otherwise get our hands on one of these objects.

Wormholes are shortcuts between to locations in space-time. They are entirely hypothetical, but if they did exist the page on wormholes describes what we know about their properties.