Lorentzian Spectral Geometry for Globally Hyperbolic Surfaces

TL;DR

This paper investigates the spectral properties of the fermionic signature operator on globally hyperbolic Lorentzian surfaces, revealing links between its spectrum and the surface's geometry through examples and counterexamples.

Contribution

It introduces a novel analysis of the fermionic signature operator's spectrum in relation to the geometry of Lorentzian surfaces.

Findings

Spectrum of the fermionic signature operator encodes geometric information.

Examples demonstrate the spectrum's sensitivity to surface geometry.

Counterexamples highlight limitations of spectral characterization.

Abstract

The fermionic signature operator is analyzed on globally hyperbolic Lorentzian surfaces. The connection between the spectrum of the fermionic signature operator and geometric properties of the surface is studied. The findings are illustrated by simple examples and counterexamples.