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

Understand

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.