Microscopic origin of non-extremal black hole entropy

4 problems

• Is there a holographic dual for non-extremal Kerr black holes?

  Contested

  Rapidly spinning black holes show a hidden symmetry that lets their entropy be computed with a formula from two-dimensional quantum field theories. Whether such a theory really exists for ordinary spinning black holes, like those seen by gravitational-wave detectors, is unknown.

• Match the logarithmic entropy correction of non-extremal black holes microscopically

  Open

  Beyond the area law, quantum effects add a small correction proportional to the logarithm of the area, with a coefficient that gravity alone determines. Any correct microscopic count must reproduce this number.

• Count the microstates of a four-dimensional Schwarzschild black hole

  Open

  For a black hole with no charge and no spin, like those formed from dead stars, nobody has derived its number of internal states from a microscopic theory. All exact counts so far need extra charges and supersymmetry (a symmetry between matter and force particles).

• Is the string to black hole transition smooth for Schwarzschild black holes?

  Partially resolved

  If a black hole shrinks until its horizon is as small as a fundamental string, it should turn into a single highly excited string, and the two entropy formulas roughly agree there. Whether this crossover is smooth, with an exact match of states, is not established.