The Spacetime Metric

The spacetime metric (Or just metric) is a tool used in differential geometry and General Relativity to convert coordinate lengths to "true" or proper lengths and times.

In G.R.M, it is implemented as a 2-D array of numbers with several prepackaged functions to determine certain quantities from input vectors of the coordinate system and curved space such as:

• The inner product (also known as the dot-product)
• The line element dS² (the "true" length of a vector locally)
• The absolute length (returns sqrt(||dS²||))

struct Metric: [4,4] components float sqLength(Vector4 4-vector) float absLength(Vector4 4-vector) float Dot(Vector4 4-vector-a, Vector4 4-vector-b)