arXiv subjects
Publications and source records attributed to G. Modanese.
The functional integral of pure Einstein 4D quantum gravity admits abnormally large and long-lasting "dipolar fluctuations", generated by virtual sources with the property Int d^4x Sqrt{g(x)} Tr T(x) = 0. These fluctuations would exist also at macroscopic scales, with paradoxical consequences. We set out their general features and give numerical estimates of possible suppression processes.
In a composite superconductor in uniform rotation, the London field strength at equilibrium is given by the usual expression B_L = 2m Omega/e; here m corresponds to the bare electron mass, although the effective mass m* can be different in different layers. In the presence of strong angular accelerations, however, transient phases and differences in m* can become relevant. In particular, if the layers are orthogonal to the rotation axis and one of them is much thinner than the others, the superconductor may enter metastable states characterized by intense "slide" supercurrents in this layer. We investigate this phenomenon theoretically and with reference to current experiments.
The positive energy theorem precludes the possibility of Minkowski flat space decaying by any mechanism. In certain circumstances, however, large quantum fluctuations of the gravitational field could arise---not only at the Planck scale, but also at larger scales. This is because there exists a set of localised weak field configurations which satisfy the condition int d4x sqrt{g}R = 0 and thus give a null contribution to the Einstein action. Such configurations can be constructed by solving Einstein field equations with unphysical dipolar sources. We discuss this mechanism and its modification in the presence of a cosmological term and/or an external field.
It was recently suggested that the gravitational action could contain a scale-dependent cosmological term, depending on the length or momentum scale characteristic of the processes under consideration. In this work we explore a simple possible consequence of this assumption. We compute the field generated in empty space by a static spherical source (the Schwarzschild metric), using the modified action. The resulting static potential turns out to contain a tiny non-Newtonian component which depends on the size of the test particles. The possible relevance of this small correction for the analysis of the recent Pioneers data [J.D. Anderson et al., Phys. Rev. Lett. 81 (1998) 2858] is briefly discussed.
In this report we summarize in an informal way the main advances made in the last 3 years and give a unified scheme of our theoretical work. This scheme aims at connecting in a consistent physical picture (by the introduction of some working hypotheses when necessary) the technical work published in several single articles. The part of our model concerning the purely gravitational aspects of the weak shielding phenomenon is almost complete; the part concerning the density distribution of the superconducting carriers in the HTC disks is still qualitative, also due to the very non-standard character of the experimental setup. The main points of our analysis are the following: coherent coupling between gravity and a Bose condensate; induced gravitational instability and "runaway" of the field, with modification of the static potential; density distribution of the superconducting charge carriers; energetic balance; effective equations for the field; existence of a threshold density.
We propose a method for the approximate computation of the Green function of a scalar massless field Phi subjected to potential barriers of given size and shape in spacetime. This technique is applied to the case of a 3D gaussian ellipsoid-like barrier, placed on the axis between two pointlike sources of the field. Instead of the Green function we compute its temporal integral, that gives the static potential energy of the interaction of the two sources. Such interaction takes place in part by tunneling of the quanta of Phi across the barrier. We evaluate numerically the correction to the potential in dependence on the size of the barrier and on the barrier-sources distance.
It is known that the action of Euclidean Einstein gravity is not bounded from below and that the metric of flat space does not correspond to a minimum of the action. Nevertheless, perturbation theory about flat space works well. The deep dynamical reasons for this reside in the non perturbative behaviour of the system and have been clarified in part by numerical simulations. Several open issues remain. We treat in particular those zero modes of the action for which R(x) is not identically zero, but the integral of sqrt{g(x)} R(x) vanishes.
We derive the kinematical constraints which characterize the decay of any massless particle in flat spacetime. We show that in perturbation theory the decay probabilities of photons and Yang-Mills bosons vanish to all orders; the decay probability of the graviton vanishes to one-loop order for graviton loops and to all orders for matter loops. A general power counting argument indicates in which conditions a decay of a massless particle could be possible: the lagrangian should contain a self-coupling without derivatives and with a coupling constant of positive mass dimension.
Under special conditions (Meissner-effect levitation in a high frequency magnetic field and rapid rotation) a disk of high-$T_c$ superconducting material has recently been found to produce a weak shielding of the gravitational field. We show that this phenomenon has no explanation in the standard gravity theories, except possibly in the non-perturbative Euclidean quantum theory.
The most recent data about the weak gravitational shielding produced recently through a levitating and rotating HTC superconducting disk show a very weak dependence of the shielding value ($\sim 1 \%$) on the height above the disk. We show that whilst this behaviour is incompatible with an intuitive vectorial picture of the shielding, it is consistently explained by our theoretical model. The expulsive force observed at the border of the shielded zone is due to energy conservation.
In 4D non-perturbative Regge calculus a positive value of the effective cosmological constant characterizes the collapsed phase of the system. If a local term of the form $S'=\sum_{h ε\{h_1,h_2,...\} } λ_h V_h$ is added to the gravitational action, where $\{h_1,h_2,...\}$ is a subset of the hinges and $\{λ_h\}$ are positive constants, one expects that the volumes $V_{h_1}$, $V_{h_2}$, ... tend to collapse and that the excitations of the lattice propagating through the hinges $\{h_1,h_2,...\}$ are damped. We study the continuum analogue of this effect. The additional term $S'$ may represent the coupling of the gravitational field to an external Bose condensate.
By means of general kinematical arguments, the lifetime $τ$ of a graviton of energy $E$ for decay into gravitons is found to have the form $τ^{-1} = \frac{1}{EG} \sum_{j=1,2,...} c_j (ΛG)^j$. Some recent, preliminary results of non perturbative simplicial quantum gravity are then employed to estimate the effective values of $G$ and $ΛG$. It turns out that a short lifetime of the graviton cannot be excluded.
The vacuum correlations of the gravitational field are highly non-trivial to be defined and computed, as soon as their arguments and indices do not belong to a background but become dynamical quantities. Their knowledge is essential however in order to understand some physical properties of quantum gravity, like virtual excitations and the possibility of a continuum limit for lattice theory. In this review the most recent perturbative and non-perturbative advances in this field are presented. (To appear on Riv. Nuovo Cim.)
We give a general procedure for extracting the propagators in gauge theories in presence of a sharp gauge fixing and we apply it to derive the propagators in quantum gravity in the radial gauge, both in the first and in the second order formalism in any space-time dimension. In the three dimensional case such propagators vanish except for singular collinear contributions, in agreement with the absence of propagating gravitons.