Black Hole Probes of Automorphic Space

TL;DR

This paper explores how automorphic forms and Langlands' reciprocity could connect black hole entropy to the geometry of extra dimensions in string theory, offering a novel theoretical framework for probing spacetime.

Contribution

It proposes a new theoretical approach linking automorphic black hole entropy with the geometry of extra dimensions via Langlands' conjecture and motives.

Findings

Automorphic entropy could serve as a probe of compactified dimensions.

The framework suggests a deep connection between number theory and spacetime geometry.

Potential experimental implications for black hole production and evaporation in laboratories.

Abstract

Over the past few years the arithmetic Langlands program has proven useful in addressing physical problems. In this paper it is shown how Langlands' reciprocity conjecture for automorphic forms, in combination with a representation theoretic notion of motives, suggests a framework in which the entropy of automorphic black holes can be viewed as a probe of spacetime that is sensitive to the geometry of the extra dimensions predicted by string theory. If it were possible to produce black holes with automorphic entropy in the laboratory their evaporation would provide us with information about the precise shape of the compact geometry.