The bimetric spectral Einstein-Hilbert action and the Kastler-Kalau-Walze type theorem for Lorentz warped products

TL;DR

This paper introduces a generalized bimetric spectral Einstein-Hilbert action, computes it for Lorentz warped products, and establishes a Kastler-Kalau-Walze type theorem in this context.

Contribution

It extends the spectral Einstein-Hilbert action to a bimetric setting and applies it to Lorentz warped products, deriving a related Kastler-Kalau-Walze theorem.

Findings

Derived the bimetric spectral Einstein-Hilbert action for Lorentz warped products

Established a Kastler-Kalau-Walze type theorem in this setting

Provided explicit computations and theoretical generalizations

Abstract

In this paper, we define the bimetric spectral Einstein-Hilbert action which generalizes the spectral Einstein-Hilbert action. We compute the bimetric spectral Einstein-Hilbert action for the Lorentz warped product. Thus, we get the Kastler-Kalau-Walze type theorem for the Lorentz warped product.