From the post "\(\tau_o\) Or No \(\tau_o\)",
\(\tau_o\ne\cfrac{c^4}{4\pi G}\)
but we can have,
\(\tau_o=-A\cfrac{c^4}{4\pi G}\)
since \(\tau_o\) is already unit dimensionally consistent, \(A\) is a dimensionless constant. And if we are really cheeky,
\(\tau_o=-\Lambda \cfrac{c^4}{8\pi G}\)
where \(A=\cfrac{\Lambda }{2}\).
Hello Albert Einstein! Unfortunately, Einstein's \(\Lambda\) has unit m-2, it is likely that he moved from radial formulation to volumetric enclosure and needed \(\Lambda\) to scale from m-1 to m-3.
