Notation and conventions[edit]
This article works with a metric signature that is mostly positive (− + + +); see sign convention. The gravitation constant will be kept explicit. This article employs the Einstein summation convention, where repeated indices are automatically summed over.
Examples[edit]
Flat spacetime[edit]
The simplest example of a Lorentzian manifold is flat spacetime, which can be given as R4 with coordinates and the metric
