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

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.

21 pages, Latex (uses psfig.sty and pictex.sty), five figures

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• Spikes in Quantum Regge Calculus
• Gonihedric (and Fuki-Nuke) Order
• Covariant perturbations in the gonihedric string model
• The Dual Gonihedric 3D Ising Model
• The Gonihedric Paradigm Extensions of the Ising Model
• (Four) Dual Plaquette 3D Ising Models
• Lecture on Quantum Gravity with Perimeter Action and Gravitational Singularities
• Gravity with Perimeter Action and Gravitational Singularities