Is Empty Space Stable in General Relativity?

In general relativity, there's what is called a positive energy theorem. Under reasonable circumstances, you can't get negative masses just by curving spacetime in weird ways. So when I say that empty space is stable, what I mean is that if there's nothing in the universe but empty space, it can't decay into a positive energy part and a negative energy part, right? Anything you do, anytime you poke empty space to make it ripple or gravitational waves or whatever, you're increasing the total energy. You're never decreasing it. When you're at that minimum of energy, empty space, perfectly flat, there's nowhere to go down and therefore everything is perfectly stable.