Metric tensor
Lorentzian metrics from relativity

In flat Minkowski space (special relativity), with coordinates

the metric is, depending on choice of metric signature,

For a curve with—for example—constant time coordinate, the length formula with this metric reduces to the usual length formula. For a timelike curve, the length formula gives the proper time along the curve.

In this case, the spacetime interval is written as

The Schwarzschild metric describes the spacetime around a spherically symmetric body, such as a planet, or a black hole. With coordinates

we can write the metric as

where G (inside the matrix) is the gravitational constant and M represents the total mass–energy content of the central object.
keywords:letter_frequency