The Spacetime Metric

In General Relativity:

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.

It determines the structure of spacetime locally with respect to the chosen coordinate system.

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||))

Metric struct:

• float[4,4] components => Metric components (<dXμ, dXν>).
• float sqLength(Vector4 4-vector) => Returns the square of the "true length" of a vector with components dXμ.
• float absLength(Vector4 4-vector) => Returns the absolute magnitude of the "true length" of a vector with components dXμ.
• float Dot(Vector4 4-vector-a, Vector4 4-vector-b) => Returns the inner product of 2 vectors.