### 6.1 Expanding direction

The starting point is the metric (2). For metrics of this form, Einstein’s vacuum equations are equivalent
to
and
Since the equations for and do not depend on , it is possible to solve Equations (11) – (12) first
and then to calculate using Equation (14). In order for this procedure to be meaningful, it is necessary
to choose the initial data for and in such a way that the integral of the right-hand side of
Equation (14) vanishes. However, assuming that has been done, is determined up to a constant given a
solution to Equations (11) – (12).