Conformally flat metric

A metric is conformally flat when it is locally a positive scalar multiple of a flat metric. Multiplication by the conformal factor preserves null cones and unparametrized null geodesics.

A conformal factor is the positive scalar field multiplying a metric under a conformal rescaling. In numerical relativity one often writes a spatial metric as ${\gamma }_{ij}={\psi }^4{\tilde{\gamma }}_{ij}$.