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.

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 investigate the vacuum energy of a scalar massless field confined in a Casimir cavity moving in a circular equatorial orbit in the exact Kerr space-time geometry. We find that both the orbital motion of the cavity and the underlying space-time geometry conspire in lowering the absolute value of the (renormalized) Casimir energy hϵ vac i ren , as measured by a comoving observer, with respect to whom the cavity is at rest. This, in turn, causes a weakening in the attractive force between the Casimir plates. In particular, we show that the vacuum energy density hϵ vac i ren → 0 when the orbital path of the Casimir cavity comes close to the corotating or counter-rotating circular null orbits (possibly geodesic) allowed by the Kerr geometry. Such an effect could be of some astrophysical interest on relevant orbits, such as the Kerr innermost stable circular orbits, being potentially related to particle confinement (as in some interquark models). The present work generalizes previous results obtained by several authors in the weak field approximation.

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 10 54 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.