Physical realization for Riemann zeros from black hole physics

TL;DR

This paper proposes a physical model linking black hole near-horizon dynamics to the nontrivial zeros of the Riemann zeta function, suggesting a novel connection between quantum gravity and number theory.

Contribution

It demonstrates that the eigenfrequencies of a scalar field near a Schwarzschild black hole horizon match the Riemann zeros, using black hole area quantization to explain this correspondence.

Findings

Eigenfrequencies coincide with Riemann zeros

Black hole area quantization breaks scale symmetry

Near-horizon dynamics encode number-theoretic properties

Abstract

According to a conjecture attributed to Polya and Hilbert, there is a self-adjoint operator whose eigenvalues are the the nontrivial zeros of the Riemann zeta function. We show that the near-horizon dynamics of a massive scalar field in the Schwarzscild black hole spacetime, under a reasonable boundary condition, gives rise to normal mode frequencies that coincide with the nontrivial Riemann zeros. In achieving this result, we exploit the Bekenstein conjecture of black hole area quantization, and argue that it is responsible for the breaking of the continuous scale symmetry of the near horizon dynamics into a discrete one.