It's a perfectly fine limiting case of G + Λg = 8πT.
A minor point: it's "the Newton equation" or "Newton's equation", but not "the Newton's equation" (in the same way that one could write "the Eisenhower presidency" or "Eisenhower's presidency", but not "the Eisenhower's presidency").
A minor point: it's "the Newton equation" or "Newton's equation", but not "the Newton's equation" (in the same way that one could write "the Eisenhower presidency" or "Eisenhower's presidency", but not "the Eisenhower's presidency").