I Can a black hole decrease in spacetime curvature?

For a simple 2-sphere in Euclidean 3-space, yes. But for a spherically symmetric gravitating mass in 4-dimensional spacetime, it's more complicated than that. The simplistic reasoning you are trying to use will not work for this case.

First, as pervect pointed out, spacetime curvature in 4-d spacetime is not a single number. It's a rank 4 tensor, the Riemann tensor. In 4-d spacetime this tensor has twenty independent components, so it takes twenty numbers to describe spacetime curvature in the general case.

Furthermore, each of those twenty numbers applies at a single point of spacetime; the numbers can change from point to point. So you have to specify where in spacetime you want to measure the curvature.

In the case of a black hole, or more generally a spherically symmetric gravitating mass, the spacetime is highly symmetric, so, for example, the curvature of spacetime anywhere on a given 2-sphere will be the same. But it will change from one 2-sphere to another. So you have to specify which 2-sphere (or, equivalently, which radial coordinate ##r##) you want to know the spacetime curvature on. And that curvature will still not be just a single number--it is not the same as the spatial curvature of the 2-sphere (which is a single number).

 

Not really, no. I've reclassified the thread as "I".

If you mean, to report a thread that you think is not correctly classified (should not be "A", for example), yes, you can use the report button for that.