[lutusp]

> What is an example of this positive evidence?

Are you asking what observational evidence exists for black holes? There are very massive, very dense objects at the center of most galaxies, objects that by their mass and density fall well inside the theoretical limits for black holes. At the center of our galaxy, there is a very massive, compact object, around which many stars are orbiting, in orbits that reveal the object's mass and approximate size:

http://astro.uchicago.edu/cosmus/projects/UCLA_GCG/

This is pretty good evidence -- if the object weren't within the mass/density realm that allows for black holes, the orbiting stars couldn't approach it as closely as they do without colliding.

Again, this doesn't prove anything, it only supports the idea that black holes are possible, and that our observations agree with that idea.

[guscost]

I don't disagree with any of that, but the evidence in question still depends on several big assumptions.

[lutusp]

It's the other way around. The evidence doesn't depend on the assumptions, the assumptions depend on the evidence.

The observations are very good and offer little latitude for interpretation -- there is a very massive, very dense object at the focus of multiple stellar orbits near the center of our galaxy, and both the mass and the density of the object are easily and unambiguously derived from the orbits.

It's the same with other galaxies -- a massive, dense central object dominates the orbital dynamics of the galaxy near its center. We're obviously not free to say that means black holes exist, it's just another piece of evidence. But it's a way to exclude certain alternatives.

[guscost]

Maybe it could be worded better. In order to say that gathering this evidence is the same as directly observing a black hole, we have to make several big assumptions.