Intrinsic Spectral Geometry of the Kerr-Newman Event Horizon

TL;DR

This paper demonstrates that the intrinsic geometry and key physical parameters of the Kerr-Newman black hole's event horizon can be uniquely reconstructed from its spectral data, effectively allowing one to 'hear' the shape of such black holes.

Contribution

It provides an explicit method to determine the black hole's metric and parameters solely from the spectrum of the horizon's Laplacian, extending the 'hearing the shape' concept to black hole horizons.

Findings

The intrinsic metric of the Kerr-Newman horizon can be reconstructed from spectral data.

The black hole's parameters like angular momentum, radius, and area are expressible in terms of Laplacian eigenvalues.

In the uncharged case, the Kerr metric is explicitly determined by the horizon's spectrum.

Abstract

We uniquely and explicitly reconstruct the instantaneous intrinsic metric of the Kerr-Newman Event Horizon from the spectrum of its Laplacian. In the process we find that the angular momentum parameter, radius, area; and in the uncharged case, mass, can be written in terms of these eigenvalues. In the uncharged case this immediately leads to the unique and explicit determination of the Kerr metric in terms of the spectrum of the event horizon. Robinson's ``no hair" theorem now yields the corollary: One can ``hear the shape" of noncharged stationary axially symmetric black hole space-times by listening to the vibrational frequencies of its event horizon only.