Discreteness of Black Hole Microstates

It is explained that, for black holes much heavier than the Planck mass, black hole microstates can be well understood without string theory. It is essential to understand the antipodal identification at the horizon. We show why the microstates exhibit a discrete spectrum, and how they relate to the particles outside the hole. Version 2 has some minor typos corrected and a few sentences added for clarity.