Alternative actions for quantum gravity and the intrinsic rigidity of the spacetime

TL;DR

This paper explores alternative discrete actions for quantum gravity using geometric invariants, introducing generalized deficit angles related to higher curvature and rigidity in simplicial models.

Contribution

It develops a broad class of discrete integral invariants, including new actions linear in manifold size and generalized deficit angles, advancing simplicial quantum gravity models.

Findings

Discrete invariants include the Regge Hilbert-Einstein action

Introduction of generalized deficit angles related to higher curvature

Potential to model rigidity in quantum gravity simulations

Abstract

Using the Steiner-Weyl expansion formula for parallel manifolds and the so called gonihedric principle we find a large class of discrete integral invariants which are defined on simplicial manifolds of various dimensions. These integral invariants include the discrete version of the Hilbert-Einstein action found by Regge and alternative actions which are linear with respect to the size of the manifold. In addition the concept of generalized deficit angles appear in a natural way and is related to higher order curvature terms. These angles may be used to introduce various aspects of rigidity in simplicial quantum gravity.