arXiv subjects
Publications and source records attributed to Remo Garattini.
A simple model of spacetime foam, made by two different types of wormholes in a semiclassical approximation, is taken under examination: one type is a collection of $N_{w}$ Schwarzschild wormholes, while the other one is made by Schwarzschild-Anti-de Sitter wormholes. The area quantization related to the entropy via the Bekenstein-Hawking formula hints a possible selection between the two configurations. Application to the charged black hole are discussed.
A simple model of spacetime foam, made by $N$ wormholes in a semiclassical approximation, is taken under examination. 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 simple model of spacetime foam, made by $N$ Reissner-Nordström wormholes with a magnetic and electric charge in a semiclassical approximation, is taken under examination. The Casimir-like energy of the quantum fluctuation of such a model is computed and compared with that one obtained with a foamy space modeled by $N$ Schwarzschild wormholes. The comparison leads to the conclusion that a foamy spacetime cannot be considered as a collection of $N$ Reissner-Nordström wormholes but that such a collection can be taken as an excited state of the foam.
In the context of a model of space-time foam, made by $N$ wormholes we discuss the possibility of having a foam formed by different configurations. An equivalence between Schwarzschild and Schwarzschild-Anti-de Sitter wormholes in terms of Casimir energy is shown. An argument to discriminate which configuration could represent a foamy vacuum coming from Schwarzschild black hole transition frequencies is used. The case of a positive cosmological constant is also discussed. Finally, a discussion involving charged wormholes leads to the conclusion that they cannot be used to represent a ground state of the foamy type.
A model of space-time foam, made by $N$ wormholes is considered. The Casimir energy leading to such a model is computed by means of the phase shift method which is in agreement with the variational approach used in Refs.[9-14]. The collection of Schwarzschild and Reissner-Nordström wormholes are separately considered to represent the foam. The Casimir energy shows that the Reissner-Nordström wormholes cannot be used to represent the foam.
Following the subtraction procedure for manifolds with boundaries, we calculate by variational methods, the Schwarzschild-de Sitter and the de Sitter space energy difference. By computing the one loop approximation for TT tensors we discover the existence of an unstable mode even for the non-degenerate case. This result seems to be in agreement with the sub-maximal black hole pair creation of Bousso-Hawking. The instability can be eliminated by the boundary reduction method. Implications on a foam-like space are discussed.
A coherent superposition of N Schwarzschild wormholes is proposed as a model for spacetime foam. Following the subtraction procedure for manifolds with boundaries, we calculate by variational methods the Casimir energy. A proposal for an alternative foamy model formed by N Schwarzschild-Anti-de Sitter wormholes is here considered. Finally, a conjecture about the foam evolution is proposed.
We consider a homogeneous space X=(X,d,m) of dimension $ν\geq 1$ and a local regular Dirichlet form in L^{2}(X,m). We prove that if a Poincaré inequality holds on every pseudo-ball B(x,R) of X, with local characteristic constant c_{0}(x) and c_{1}(r), then a Green's function estimate from above and below is obtained. A Saint-Venant-like principle is recovered in terms of the Energy's decay.
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-Anti-de Sitter wormholes is here considered.
We prove the existence of a non-trivial solution for a nonlinear equation related to a measure-valued Lagrangian. The result is based on a compact embedding theorem of the Lagrangian domain and on the application of the Mountain Pass Theorem joined to a Palais-Smale condition.
We consider a homogeneous space $X=(X,d,m) $ of dimension $ν\geq1$ and a local regular Dirichlet form in $L^{2}(X,m) .$ We prove that if a Poincaré inequality holds on every pseudo-ball $B(x,R) $ of $X$, then an Harnack's inequality can be proved on the same ball with local characteristic constant $c_{0}$ and $c_{1}$
Following the subtraction procedure for manifolds with boundaries, we calculate by variational methods, the Schwarzschild-Anti-de Sitter and the Anti-de Sitter space energy difference. By computing the one loop approximation for TT tensors we discover the existence of an unstable mode at zero temperature, which can be stabilized by the boundary reduction method. Implications on a foam-like space are discussed.
We conjecture that the neutral black hole pair production is related to the vacuum fluctuation of pure gravity via the Casimir-like energy. A generalization of this process to a multi-black hole pair is considered. Implications on the foam-like structure of spacetime and on the cosmological constant are discussed.
The entropy for a black hole in a de Sitter space is approached within the framework of spacetime foam. A simple model, made by $N$ wormholes in a semiclassical approximation, is taken under examination to compute the entropy for such a case. An extension to the extreme case when the black hole and cosmological horizons are equal is discussed.
A simple model of spacetime foam, made by N wormholes in a semiclassical approximation, is taken under examination. 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 simple model of spacetime foam, made by N wormholes in a semiclassical approximation, is taken under examination. We show that the Bekenstein-Hawking entropy is here ``quantized'' in agreement with the heuristic calculation of Bekenstein.
Following the subtraction procedure for manifolds with boundaries, we calculate by variational methods, the Schwarzschild and Flat space energy difference. The one loop approximation for TT tensors is considered here. An analogy between the computed energy difference in momentum space and the Casimir effect is illustrated. We find a singular behaviour in the UV-limit, due to the presence of the horizon when $r=2m.$ When $r>2m$ this singular behaviour disappears, which is in agreement with various other models previously presented.
A simple model of spacetime foam, made by $N$ wormholes in a semiclassical approximation, is taken under examination. We show that the qualitative behaviour of the fluctuation of the metric conjectured by Wheeler is here reproduced.