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In this paper we discuss the Casimir effect in a small cavity at rest in the weak gravitational field of a massive, non-rotating source. We propose a new approach, based upon Schwinger’s effective action method, showing that the gravitational interaction induces a small correction in the vacuum energy density, in full agreement with the result we obtained in a previous work (Sorge 2005 Class. Quantum Grav. 22 5109), following a standard field mode decomposition technique. The present result reinforces the belief that gravity can indeed be effective in modifying the vacuum energy of a quantum field confined to the cavity, against the recent claim appeared in Lima et al (2019 J. Cosmol. Astropart. Phys. JCAP07(2019)11) that a weak gravitational field has no influence on the Casimir energy.

The three main requirements of a vehicle-trailer connection system are: en route stability, over- or under-steering restraint, minimum off-tracking along curved path. Linking the two units by four-bar trapeziums, wider stability margins may be attained in comparison with the conventional pintle-hitch for both instability types, divergent or oscillating. The stability maps are traced applying the Hurwitz method or the direct analysis of the characteristic equation at the instability threshold. Several types of four-bar linkages may be quickly tested, with the drawbars converging towards the trailer or the towing unit. The latter configuration appears preferable in terms of self-stability and may yield high critical speeds by optimising the geometrical and physical properties. Nevertheless, the system stability may be improved in general by additional vibration dampers in parallel with the connection linkage. Moreover, the four-bar connection may produce significant corrections of the under-steering or over-steering behaviour of the vehicle-train after a steering command from the driver. The off- tracking along the curved paths may be also optimized or kept inside prefixed margins of acceptableness. Activating electronic stability systems if necessary, fair results are obtainable for both the steering conduct and the off-tracking.

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.

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.

In this paper, we consider the effects of a magnetic field on the dynamics of the early universe. As predicted by Matravers and Tsagas (2000 Phys. Rev. D 62 103519) we find that the coupling between spatial curvature and primordial magnetic field permeating a perfectly conducting barotropic fluid can inhibit the accelerated expansion but may also induce acceleration in a variety of cases not considered in the above paper.

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.

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.

We study the behaviour of a small gyroscope moving on a circular trajectory in the field of a weak gravitational plane wave. In order to monitor the precessional velocity we introduce an observer comoving with the gyroscope and an observer-adapted frame optically defined by means of light rays and not Fermi-Walker transported. From such a frame we infer some physical information about the gravitational-wave-induced frame dragging, which the observer will detect looking at the small perturbations on the gyroscopic precession. We find evidence of gyroscope sensitivity to the polarization state of the gravitational wave. As expected, the general relativistic precession of the compass of inertia and the `memory effect' which are discussed in this paper are very small and hardly detectable with modern technology; however, they are operationally well defined and therefore not ignorable for future considerations.

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.

Horizontal rotor systems on lubricated journal bearings may incur instability risks depending on the load and the angular speed. The instability is associated with the asymmetry of the stiffness matrix of the bearings around the equilibrium position, in like manner as the internal hysteretic instability somehow, where some beneficial effect is indeed obtainable by an anisotropic configuration of the support stiffness. Hence, the idea of the present analysis is to check if similar advantages are also obtainable towards the oil film instability. The instability thresholds are calculated by usual methods, such as the Routh criterion or the direct search for the system eigenvalues. The results indicate that the rotor performances may be improved in the range of low Sommerfeld numbers by softening the support stiffness in the vertical plane, and hardening it on the horizontal one, up to the complete locking, though this advantage has to be paid by rather lower instability thresholds for large Sommerfeld numbers. Nevertheless, a "two-mode" arrangement is conceivable, with some vertical flexibility of the supports for large journal eccentricity, and complete locking for small eccentricity. As another alternative, the support anisotropy may be associated with the use of step bearings, whose particular characteristic is to improve the stability for small eccentricities.

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.

In this paper, we discuss the gravitational scattering of fermions in the gravitational field of a massive, slowly rotating source characterized by an arbitrary spin orientation. We derive the gravito-electromagnetic field of the source using the weak-field approximation of Einstein’s equations, which holds true when dealing with sources having a weak gravitational field and non-relativistic rotation. In such a gravitational background, we obtain the linearized fermion interaction Lagrangian. We then evaluate at the tree level the transition amplitude and the cross-section of the fermion scattering process in the ultra-relativistic limit (m ≪ E). We examine the dependence of the cross-section on the relative orientation between the source spin and the direction of the fermion flux and discuss the contributions deriving from the gravitoelectric and the gravitomagnetic parts of the background field of the source. Further insight into the underlying physics is gained by comparing the results with those obtained in the case of gravitational scattering of a massless scalar field. We also find evidence of non-null backscattering in the case of orthogonality between the direction of propagation of the fermion flux and the source spin.

International audience; In this paper we study the Josephson tunneling for a quantum fluid (a Bose-Einstein condensate) in 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 equation to investigate the influence of a gravitational wave on Josephson effect. Considering a double-well trap, made of two identical boxes placed orthogonally 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 in the two sides, hence giving rise to a gravitationally-induced ac-Josephson effect through the trap junction. Although small, such 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 effect is briefly discussed at the end of the paper.

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 Schwinger's 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.

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.