Universality classes for horizon instabilities

We introduce a notion of universality classes for the Gregory-Laflamme instability and determine, in the supergravity approximation, the stability of a variety of solutions, including the non-extremal D3-brane, M2-brane, and M5-brane. These three non-dilatonic branes cross over from instability to stability at a certain non-extremal mass. Numerical analysis suggests that the wavelength of the shortest unstable mode diverges as one approaches the cross-over point from above, with a simple critical exponent which is the same in all three cases.