Francesco Sorge

Casimir effect in a weak gravitational field

We study the Casimir vacuum energy density for a massless scalar field confined between two nearby parallel plates (a cavity) in a slightly curved, static spacetime background, employing the weak-field approximation. Following an order-by-order perturbative approach, we evaluate the gravity-induced correction to Casimir energy. We find evidence for a small shift in the (negative) vacuum energy. As a consequence, the (attractive) force between the cavity walls is expected to weaken. Although derived in the weak-field approximation, and too small to be detected with the current technology, such gravitationally induced shift in vacuum energy seems nevertheless interesting from a theoretical point of view, since it might play a role in a cosmological scenario (e.g., gravitational influence on the Λ-term) as well as at a microscopic level (quark confinement) in strong gravitational fields. Finally, the analysis of the possible gravitational effects on Casimir cavities faces the open issue concerning the limits of validity of general relativity at small distances.

Magnetized orbits around a Schwarzschild black hole

We study the motion of a magnetized particle orbiting around a supermassive Schwarzschild black hole, surrounded by a strong (asymptotically uniform) magnetic field. Using the Hamilton–Jacobi formalism, we solve in a fully analytical way the problem of finding the innermost circular orbits. We show that, for suitable values of the parameters controlling the magnetic interaction, these orbits may become stable near r = 3M, hence giving rise to a possible mechanism for particle confinement and energy storage. We argue that any sudden change in the above parameters could allow for abrupt release of large amounts of energy from such innermost orbits.

Magnetized orbits around a Kerr black hole

We study the motion of magnetized particles near a rotating black hole. The main result is that the spacetime curvature and electromagnetic field conspire to allow for the existence, inside the ergosphere, of stable circular orbits occupied by particles with negative total energy and angular momentum. Since these particles would never populate stable orbits were they not magnetized, a large binding energy is required to let them exist. A simple model of a magnetized belt in the ergosphere of a massive black hole with a strong magnetic field, shows that it can store a binding energy as high as 1054 erg, an amount comparable with the energy detected in gamma ray bursts. Besides the above astrophysical considerations, this paper contains a formal deduction, from an appropriate Hamiltonian, of the equations of motion of a neutral and magnetized fluid made of spinless dust particles interacting with a magnetic field. This analysis does not appear to have been done before.

Local and Global Anisotropy in the Speed of Light

We briefly review Lorentz invariance and the locality principle, which are the grounds of the theory of Relativity. Subsequently we discuss some recent claims about local anisotropy in the speed of light, as observed in a non inertial frame, and especially in a rotating frame. We show that a standard analysis of a typical physical measurement of the speed of light performed in a rotating frame leads to global anisotropic effects which vanish as the size of the experimental apparatus becomes negligible with respect to the typical lengthscales involved in the non inertial motion of the observer. The expected effects seem too small to be detected with the actual sensitivities at our disposal.

Do gravitational waves create particles

Solving the Klein-Gordon equation for a free scalar field in a curved spacetime in the weak-field approximation we rederive the results of Gibbons et?al: no particle creation from the interaction between scalar fields and gravitational waves. We show, however, that particle creation would really occur when the matter field is constrained in space by some boundaries. Such an effect is likely to be related to the uncertainty principle, in connection with a sort of dimensional reduction (as in the Kaluza-Klein theory) that causes the field to acquire a mass term, also responsible for conformal symmetry breaking in a spatially flat FRW spacetime. Although derived in the weak-field approximation, the results seem also to be reasonably valid in the presence of exact gravitational waves.

Quantum fluids, Josephson tunneling and gravitational waves

In this paper we study the Josephson tunneling for a quantum fluid (a Bose–Einstein condensate) in the presence of a weak gravitational wave. Starting from a Lagrangian formulation in the framework of linearized gravity, we deduce the Gross–Pitaevskii equation for the fluid in a weak gravitational background. We use such an equation to investigate the influence of a gravitational wave on the Josephson effect. Considering a double-well trap, made of two identical boxes placed orthogonally to each other and weakly coupled through a small junction, we show how the trap geometry influences the coupling between the gravitational wave and the quantum field modes in the two sides of the trap. Namely, the macroscopic wavefunction of the condensate acquires a different phase shift on the two sides, hence giving rise to a gravitationally induced ac-Josephson effect through the trap junction. Although small, such an effect is theoretically interesting, since it represents the influence of a gravitational wave on a mesoscopic quantum system. Also the effect exhibits polarimetric properties. Possible experimental detection of such an effect is briefly discussed at the end of the paper.

Casimir energy and gravitomagnetism

In this paper, we discuss the influence of a gravitomagnetic field on the vacuum energy of a scalar quantum field confined in a Casimir cavity. To avoid complications which could obscure the pure gravitomagnetic effects on vacuum flucuations inside the cavity, we consider a somewhat idealized scenario, namely a Casimir cavity lying between two parallel massive walls, moving in opposite directions to each other. This motion provides the required gravitomagnetic field experienced by the quantum field in the cavity. Following Schwingers proper-time approach, we evaluate the corrections to the Casimir energy in the framework of linearized gravity. At variance with what is expected in the presence of a pure magnetic or a gravitoelectric field, we did not find a first-order effect in the vacuum energy shift for the confined quantum field. We discuss and compare our results with those presented in other papers, also suggesting a physical explanation of such null effect.

On the gravitational scattering of quantum fields

Working in the weak-field approximation, we study the scattering of quantum fields from a gravitational source. For definiteness, we consider the electromagnetic radiation field as well as a massive scalar field, both propagating in a slightly curved spacetime and employ the first-order Born approximation to deduce the scattering cross-sections of the process. We find that the (unpolarized) cross-section for the electromagnetic field coincides (at the tree level) with the classical value, predicted by general relativity; also our results fairly agree with those obtained by other authors in some previous works. On the other hand, our analysis of the massive scalar field leads to results which are quite different when compared with those presented, e.g., in the papers by Golowich et al (1990 Am. J. Phys. 58 688) and by Uno et al (1996 Phys. Lett. A 223 137). Actually, we find that the quantum behavior deviates from its classical counterpart, showing an enhancement in the cross-section as the massive field approaches the non-relativistic regime. We critically discuss and compare our results and those of the above references, attempting to give a possible physical justification of such a puzzling issue in terms of quantum non-locality.

Neutrino spin flip around a Schwarzschild black hole

We propose a new approach to the study of spin-flip probability for massive Dirac neutrinos orbiting around a Schwarzschild black hole, recently considered by Dvornikov (2006 Int. J. Mod. Phys. 15 1017). Inspired by the paper by Papini and Lambiase (2002 Phys. Lett.A 294 175), we employ a reference frame comoving with the particle in the curved spacetime background. Using a suitable tetrad adapted to a comoving observer, we discuss the gravito-inertial effects (curvature plus spin rotation or Mashhoon effect) on the massive neutrino spin-flip probability. At variance with some recent claims, we find non-null results, in very good agreement with those obtained in [19], although through quite a different approach. Such results suggest a sort of competition between gravity and inertia. Taking into account the possible anomalous magnetic moment μν of a massive Dirac neutrino, we also briefly consider the interplay between gravito-inertial and magnetic effects, in the presence of some external strong magnetic field in the Schwarzschild geometry (which is believed to be a typical scenario in the case of Active Galactic Nuclei (AGN) or neutron stars). We find some evidence that the actual poor knowledge about the bounds on μν cannot rule out the possibility of some relevant competition between the two effects.

On the gravitational scattering of gravitational waves

We discuss the scattering of weak gravitational waves from a slowly rotating gravitational source, having mass M and angular momentum . We start considering the dynamics of a massless spin-2 field propagating in the weak gravitational field of the source, writing down the Fierz?Pauli in the presence of a slightly curved background. We adopt a semiclassical framework, where the gravitational background is described as a classical external field; meanwhile, the spin-2 field is treated quantum mechanically. In the weak-coupling limit, in which the typical wavelength of satisfies (where Rs is the Schwarzschild radius of the source), we obtain the cross-section for the scattering process in the Born approximation. We also discuss helicity asymmetry, showing its relationship with the spin-2 field coupling to the derivatives of the background metric. We finally consider the transition to the case of gravitational wave scattering, showing that?under reasonable assumptions?gravitational waves are expected to follow the same behavior. Our results partly agree with those presented through the years by various authors. The present analysis suggests that the scattering of weak gravitational waves in the field of a macroscopic gravitational source still represents an interesting open issue for further careful investigation.