In this work, we consider a Yukawa modification of the Casimir wormhole. With the help of an Equa... more In this work, we consider a Yukawa modification of the Casimir wormhole. With the help of an Equation of State, we impose Zero Tidal Forces. We will examine two different approaches: in a first approach, we will fix the form of the shape function of the Casimir wormholes modified by a Yukawa term in three different ways and finally a superposition of different profiles. In the second approach, we will consider the original Casimir source modified by a Yukawa term in three different ways and we will deduce the form of the shape function In both the approaches the reference energy density will be that of the Casimir source. Connection with the Absurdly Benign Traversable Wormhole are also discussed.
In this work, we explore the connection between Casimir energy and an Absurdly Benign Traversable... more In this work, we explore the connection between Casimir energy and an Absurdly Benign Traversable Wormhole, which in the literature has been considered only in the pioneering paper of Morris and Thorne. To have consistency with the Casimir source, we need to generalize the idea of an Absurdly Benign Traversable Wormhole into a Generalized Absurdly Benign Traversable Wormhole. With this generalization, we have found that the wormhole throat is not more Planckian, but huge. Three profiles have been studied: one of them is directly connected with the Casimir source, while the other two have been obtained approximating the first one close to the throat. In all profiles the wormhole throat size is predicted to be of the order of $$10^{17}~\text {m}$$ 10 17 m . This huge size can be fine tuned by modulating the original Casimir energy source size. We have also found that the traceless and divergenceless property of the original Casimir stress energy tensor is here partially reproduced.
Casimir energy is always indicated as a potential source to generate a traversable wormhole. It i... more Casimir energy is always indicated as a potential source to generate a traversable wormhole. It is also used to prove the existence of negative energy which can be built in the laboratory. However, in the scientific literature there is no trace of the consequences on the traversable wormhole itself. In this work, we would like to consider such a source to see if and which kind of traversable wormhole can be produced. In a further analysis, we examine also the consequences of quantum weak energy conditions on the traversability of the wormhole. We find agreement with the original Casimir traversable wormhole. Nevertheless, despite the traversability result, one finds once again that the traversability is only in principle but not in practice.
We consider the effects of Gravity's Rainbow on the computation of black hole entropy using a dyn... more We consider the effects of Gravity's Rainbow on the computation of black hole entropy using a dynamical brick wall model. An explicit dependence of the radial coordinate approaching the horizon is proposed to analyze the behavior of the divergence. We find that, due to the modification of the density of states, the brick wall can be eliminated. The calculation is extended to include rotations and in particular to a Kerr black hole in a comoving frame.
We compute Zero Point Energy in a spherically symmetric background with the help of the Wheeler-D... more We compute Zero Point Energy in a spherically symmetric background with the help of the Wheeler-DeWitt equation. This last one is regarded as a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The graviton contribution, at one loop is extracted with the help of a variational approach together with Gaussian trial functionals. The divergences handled with a zeta function regularization are compared with the results obtained using a Noncommutative Geometry (NCG) and Modified Dispersion Relations (MDR). In both NCG and MDR no renormalization scheme is necessary to remove infinities in contrast to what happens in conventional approaches. Effects on photon propagation are briefly discussed.
We consider the effects of Gravity's Rainbow on the self-sustained equation which is responsible ... more We consider the effects of Gravity's Rainbow on the self-sustained equation which is responsible to find new traversable wormholes configurations which are sustained by their own gravitational quantum fluctuations. The same selfsustained equation is also used to discover if topology change is possible. In this contribution, we will show that in both uses, the self-sustained equation will produce a Wheeler wormhole, namely a wormhole of Planckian size. This means that, from the point of view of traversability, the wormhole will be traversable in principle, but not in practice. From the topology change point of view, the background metric will be fixed to be Minkowskian in the equation governing the quantum fluctuations, which behaves essentially as a backreaction equation, and the quantum fluctuations are let to evolve. Analyzing this procedure, we will show that the self-sustained equation, endowed with a Gravity's Rainbow distortion, will be responsible of a topology change with the appearance of a Planckian wormhole.
The one loop effective action in a Schwarzschild background is here used to compute the Zero Poin... more The one loop effective action in a Schwarzschild background is here used to compute the Zero Point Energy (ZPE) which is compared to the same one generated by a gravastar. We find that only when we set up a difference between ZPE in these different background we can have an indication on which configuration is favored. Such a ZPE difference represents the Casimir energy. It is shown that the expression of the ZPE is equivalent to the one computed by means of a variational approach. To handle with ZPE divergences, we use the zeta function regularization. A renormalization procedure to remove the infinities together with a renormalization group equation is introduced. We find that the final configuration is dependent on the ratio between the radius of the wormhole augmented by the "brick wall" and the radius of the gravastar.
The cosmological constant induced by quantum fluctuation of the graviton on a given background is... more The cosmological constant induced by quantum fluctuation of the graviton on a given background is considered as a tool for building a spectrum of different geometries. In particular, we apply the method to the Schwarzschild background with positive and negative mass parameter. In this way, we put on the same level of comparison the related naked singularity (−M) and the positive mass wormhole. We discuss how to extract information in the context of a f (R) theory. We use the Wheeler-De Witt equation as a basic equation to perform such an analysis regarded as a Sturm-Liouville problem. The application of the same procedure used for the ordinary theory, namely f (R) = R, reveals that to this approximation level, it is not possible to classify the Schwarzschild and its naked partner into a geometry spectrum.
We consider a homogeneous space X = (X, d, m) of dimension ν ≥ 1 and a local regular Dirichlet fo... more We consider a homogeneous space X = (X, d, m) of dimension ν ≥ 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, then an Harnack's inequality can be proved on the same ball with local characteristic constant c 0 and c 1
In the Wheeler-DeWitt framework, by a gauge fixing procedure, we set up a scheme to recover a Sch... more In the Wheeler-DeWitt framework, by a gauge fixing procedure, we set up a scheme to recover a Schrödinger type equation, living in the orbits space with the lapse function as evolution parameter. By means of the associated stationary equation, we have the possibility of calculating quantum corrections to classical quantities. The Schwarzschild wormhole case is discussed as an example of application.
We use variational methods to calculate quasilocal energy quantum corrections. A comparison with ... more We use variational methods to calculate quasilocal energy quantum corrections. A comparison with the effective potential calculated at quadratic order is made by means of gaussian wave functionals. The method is a particular case of the effective action for composite operators used in quantum field theory. In pure gravity the method is applied for the first time. Implications on the foam-like scenario are discussed.
A simple model of spacetime foam, made by spherically symmetric wormholes, with or without a cosm... more A simple model of spacetime foam, made by spherically symmetric wormholes, with or without a cosmological term is proposed. The black hole area quantization and its consequences are examined in this context. We open the possibility of probing Lorentz symmetry in this picture.
We regard the Wheeler-De Witt equation as a Sturm-Liouville problem with the cosmological constan... more We regard the Wheeler-De Witt equation as a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The used method to study such a problem is a variational approach with Gaussian trial wave functionals. We approximate the equation to one loop in a Schwarzschild background. A zeta function regularization is involved to handle with divergences. The regularization is closely related to the subtraction procedure appearing in the computation of Casimir energy in a curved background. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation.
The cosmological constant appearing in the Wheeler-De Witt equation is considered as an eigenvalu... more The cosmological constant appearing in the Wheeler-De Witt equation is considered as an eigenvalue of the associated Sturm-Liouville problem. A variational approach with Gaussian trial wave functionals is used as a method to study such a problem. We approximate the equation to one loop in a Schwarzschild background and a zeta function regularization is involved to handle with divergences. The regularization is closely related to the subtraction procedure appearing in the computation of Casimir energy in a curved background. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation. The case of massive gravitons is discussed.
The cosmological constant induced by quantum fluctuation of the graviton on a given background is... more The cosmological constant induced by quantum fluctuation of the graviton on a given background is considered as a tool for building a spectrum of different geometries. In particular, we apply the method to the Schwarzschild background with positive and negative mass parameter. In this way, we put on the same level of comparison the related naked singularity (−M) and the positive mass wormhole. We use the Wheeler-De Witt equation as a basic equation to perform such an analysis regarded as a Sturm-Liouville problem. The cosmological constant is considered as the associated eigenvalue. The used method to study such a problem is a variational approach with Gaussian trial wave functionals. We approximate the equation to one loop in a Schwarzschild background. A zeta function regularization is involved to handle with divergences. The regularization is closely related to the subtraction procedure appearing in the computation of Casimir energy in a curved background. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation.
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Papers by Remo Garattini