Question

If kappa (Einstein's constant) depends on Lambda (cosmological constant), then why does kappa stay the same when Lambda is not null?

Answer 1

lambda on the left side of the equations means cosmological constant. And the \kappa on the right side of Einstein equations means gravitational constant 6.67408(31)×10−11 m3⋅kg−1⋅s−2.

But often it is in General theory of relativity as G. You can solve Einstein equation without cosmological constant. But with right side with energy-impulse tensor.

Answer 2

$<marquee><b><i>The objection to this solution is that one has to introduce a negative pressure, for which there exists no physical justification. In order to make that solution possible I originally introduced a new member into the equation instead of the above-mentioned pressure, which is permissible from the point of view of relativity...The introduction of this second member constitutes a complication of the theory, which seriously reduces its logical simplicity. Its introduction can only be justified by the difficulty produced by the almost unavoidable introduction of a finite average density of matter .$