Count the microstates of a four-dimensional Schwarzschild black hole
In plain words
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).
Precise statement
Within a UV-complete theory, identify the sector of the Hilbert space that describes a 4D Schwarzschild black hole of mass $M$ and compute the logarithm of its dimension, reproducing $S = 4 \pi G M^2/(\hbar c)$ (entropy in units of $k_B$). An answer is a controlled microscopic count valid away from supersymmetry and extremality.
What would settle it
A microscopic state count, in a defined UV-complete theory, that matches $4 \pi G M^{2}/(\hbar c)$ and its logarithmic correction.
Status in the literature
Unverified note
Exact counts exist only for supersymmetric or near-supersymmetric black holes; none for Schwarzschild as of 2026.
Related problems
- More general than Match the logarithmic entropy correction of non-extremal black holes microscopically
- More general than Is the string to black hole transition smooth for Schwarzschild black holes?