Wormholes and Spacetime Foam: an approach to the cosmological constant and entropy

This paper summarizes the contribution presented at the IX Marcel Grossmann Meeting (Rome, July 2000). A simple model of spacetime foam, made by N Schwarzschild wormholes in a semiclassical approximation, is here proposed. The Casimir-like energy of the quantum fluctuation of such a model and its probability of being realized are computed. Implications on the Bekenstein-Hawking entropy and the cosmological constant are considered. A proposal for an alternative foamy model formed by N Schwarzschild-Antide Sitter wormholes is here considered. ∗Contributed paper to the IX Marcel Grossmann Meeting (Rome, July 2000) To appear in the Proceedings (World Scientific, Singapore) 1 The term Spacetime Foam was used for the first time by J.A. Wheeler to indicate that spacetime may be subjected to quantum fluctuations in topology and metric at the Planck scale [1]. Since then a lot of work has been done, especially in the direction of string theory and of Euclidean Quantum Gravity, to see if a nontrivial vacuum can be considered for a quantum theory of gravitation. In this paper we will consider a different approach based on a proposed model of spacetime foam, made by N coherent Schwarzschild wormholes [2]. The main reason which has led to consider such a model is based on a Casimir energy computation described by the following Hamiltonian ∆E (M) = E (M)− E (0) = 〈