Black Holes, Complex Curves, and Graph Theory: Revising a Conjecture by Kasner

Understand

The ratios $\sqrt{8/9}=2\sqrt{2}/3\approx 0.9428$ and $\sqrt{3}/2 \approx 0.866$ appear in various contexts of black hole physics, as values of the charge-to-mass ratio $Q/M$ or the rotation parameter $a/M$ for Reissner-Nordstr\"om and Kerr black holes, respectively.

• In this work, in the Reissner-Nordstr\"om case, I relate these ratios with the quantization of the horizon area, or equivalently of the entropy.
• Furthermore, these ratios are related to a century-old work of Kasner, in which he conjectured that certain sequences arising from complex analysis may have a quantum interpretation.
• These numbers also appear in the case of Kerr black holes, but the explanation is not as straightforward.