Spectral Geometry of Cosmological and Event Horizons for Kerr-Newman de Sitter metrics

TL;DR

This paper investigates the spectral properties of horizons in Kerr-Newman de Sitter space-times and demonstrates that their spectral data uniquely determine the entire space-time, providing explicit formulas including for the cosmological constant.

Contribution

It introduces a method to recover the full space-time from spectral data of horizon Laplacians, including explicit formulas for key parameters.

Findings

Spectral data uniquely determine the Kerr-Newman de Sitter space-time.

Explicit formulas relate space-time parameters to spectral invariants.

Derived a new formula for the cosmological constant.

Abstract

We study the Laplace spectra of the intrinsic instantaneous metrics on the event and cosmological horizons of a Kerr-Newman de Sitter space-time and prove that the spectral data from these horizons uniquely determine the space-time. This is accomplished by exhibiting formulae relating the parameters of the space-time metric to the traces of invariant and equivariant Green's operators associated with these Laplacians. In particular, an interesting explicit formula for the cosmological constant is found.