R.C. Sproul has recently written against the notion that "God died on the cross". Big topic. Not gonna jump in with both feet here. But allow me to dip a toe...
Just listen to this key paragraph in his argument:
If the being of God ceased for one second, the universe would disappear. It would pass out of existence, because nothing can exist apart from the sustaining power of God. If God dies, everything dies with Him. Obviously, then, God could not have perished on the cross.
Now ask yourself - what definition of death is being used by Sproul? The bible's? Or Bertrand Russell's?
In the bible, death is a realm over to which the Father has handed humanity in its rebellion. It's a realm the Son enters so as to be firstborn from among it.
Where on earth do we get the idea that death = non-existence?
Who knows where Great Aunty Beatrice is, but she's not nowhere. Sproul knows that the dead do not cease to be. But, like so many other theologians who discuss this issue, they use the theist's definition of God and the atheist's defintion of death.