The Einstein-Hilbert action for perturbed second-order spectral triples

TL;DR

This paper extends the Einstein-Hilbert action to higher-order spectral triples, introducing new examples and explicit computations to demonstrate the framework's applicability in noncommutative geometry.

Contribution

It proposes a novel extension of the Einstein-Hilbert action within higher-order spectral triples and provides explicit examples and calculations.

Findings

Explicit Einstein-Hilbert actions for two second-order spectral triples

Demonstration of the framework's applicability to noncommutative geometry

Extension of the Kastler-Kalau-Walze theorem context

Abstract

In [6], the higher-order spectral triple and its relative K-homology were studied. Motivated by the Kastler-Kalau-Walze theorem, we propose an extension of the Einstein-Hilbert action to the framework of higher-order spectral triples. To illustrate this construction, we introduce two second-order spectral triples and explicitly compute their respective Einstein-Hilbert action, demonstrating the applicability of our theoretical framework.