The relationship between extremal and non-extremal black holes was recently studied by Balbinot et al. in
hep-th: 0710.0388. As readers of this blog know, extremal black holes have been all the rage in the string theory community. This is because using D-brane techniques, it is possible to construct an extremal black hole and calculate its entropy. That such D-brane approaches yield an entropy that agrees with the Bekenstein-Hawking formula was hailed as a major triumph for string theory. More recently, Gunaydin and Ferrara have shown that the entropy of black holes in magic supergravities can be calculated using cubic and quartic invariants of the so-called U-duality groups.
Given such success in finding the entropy of extremal black holes, one might wonder why there wasn't more buzz in the popular media. A likely reason is that extremal black holes are rather exotic types of black holes. They have a mass that equals their charge, and are very much unlike the large black holes that astrophysicists rave about. What Balbinot et al. show in their paper is how to
continuously transform a non-extremal black hole to an extremal black hole in the limit that mass approaches charge. This was thought to be impossible, as there were
arguments that the non-extremal and extremal black holes are distinct quantum mechanical objects.
The arguments in the Balbinot paper are based on a two-dimensional analytical treatment, but the authors argue that their techniques generalize to the four-dimensional case.