The direction towards the singularity

6.2 The direction towards the singularity

In the study of the direction towards the singularity, it is convenient to change the time coordinate to $t = e−τ$ , so that the singularity corresponds to $τ → ∞$ . The metric then becomes

Here, $τ ∈ ℝ$ and $(𝜃,σ,δ )$ are coordinates on T³. Einstein’s vacuum equations take the form

and