For those who have a thirst for something physics-y to follow the tomato chutney post, here’s a decorated physics diagram I made in Matlab this morning. Click for a larger view. It’s the phase diagram of interesting black hole transitions* (that I co-discovered 14 years ago) associated with part of the story I mentioned last month. On the right of the line you have small black holes favoured (of a given charge, so move horizontally), and on the left side of the line the system favours large black holes and so when you cross the line you have a sudden jump from one type to the other. That second order critical point I talked about there is the end of the line of first order points. The blue dot. Above there, you cross over smoothly from small to large holes. The blue dot is the border between the two cases.
It is a bit like having steam (or water vapour) on the left and liquid water on the right, and crossing the line is what you call boiling. The second order point is the place where, at high enough pressure and the right temperature, they are indistinguishable. (You don’t usually have those conditions in the kitchen, and so you might not have noticed that point.) The thermodynamic analogy is approximate here, but can be made more precise if you compute in the right thermodynamic ensemble. Have a look here and here.
-cvj
*These are black holes in Anti de Sitter (AdS) spacetime.
