We consider a hydrogen atom in the background spacetimes generated by an infinitely thin cosmic string and by a pointlike global monopole. In both cases, we find the solutions of the corresponding Dirac equations and we determine the energy levels of the atom. We investigate how the geometric and topological features of these spacetimes lead to shifts in the energy levels as compared with the flat Minkowski spacetime.

This work deals with the influence of the gravitational field produced by a charged and rotating black hole (Kerr–Newman spacetime) on massive scalar fields. We obtain an exact solution of the Klein–Gordon equation in this spacetime, which is given in terms of the confluent Heun functions. In the particular case corresponding to an extreme Kerr–Newman black hole the solution is given by the double confluent Heun functions. We also investigate the solutions in the regions near the event horizon and far from the black hole.

The Lovelock gravity is a natural extension of the Theory of General Relativity (TGR) to higher dimensions, which presents the criteria of general covariance and whose field equations are of second...

We evaluate the Hadamard function and the vacuum expectation value of the current density for a massive complex scalar field in the generalized geometry of a straight cosmic string with a finite core enclosing an arbitrary distributed magnetic flux along the string axis. For the interior geometry, a general cylindrically symmetric static metric tensor is used with finite support. In the region outside the core, both the Hadamard function and the current density are decomposed into the idealized zero-thickness cosmic string and core-induced contributions. The only nonzero component corresponds to the azimuthal current. The zero-thickness part of the latter is a periodic function of the magnetic flux inside the core, with the period equal to the quantum flux. As a consequence of the direct interaction of the quantum field with the magnetic field inside the penetrable core, the core-induced contribution, in general, is not a periodic function of the flux. In addition, the vacuum current, in general, is not a monotonic function of the distance from the string and may change the sign. For a general model of the core interior, we also evaluate the magnetic fields generated by the vacuum current. As applications of the general results, we have considered an impenetrable core modeled by Robin boundary condition, a core with the Minkowski-like interior and a core with a constant positive curvature space. Various exactly solvable distributions of the magnetic flux are discussed.

We investigate the vacuum expectation value of the fermionic current induced by a magnetic flux in a (2+1)-dimensional conical spacetime in the presence of a circular boundary. On the boundary the fermionic field obeys the MIT bag boundary condition. For irregular modes, a special case of boundary conditions at the cone apex is considered, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. We observe that the vacuum expectation values for both the charge density and azimuthal current are periodic functions of the magnetic flux with the period equal to the flux quantum whereas the expectation value of the radial component vanishes. For both exterior and interior regions, the expectation values of the current are decomposed into boundary-free and boundary-induced parts. For a massless field the boundary-free part in the vacuum expectation value of the charge density vanishes, whereas the presence of the boundary induces nonzero charge density. Two integral representations are given for the boundary-free part in the case of a massive fermionic field for arbitrary values of the opening angle of the cone and magnetic flux. The behavior of the induced fermionic current is investigated in various asymptotic regions of the parameters. At distances from the boundary larger than the Compton wavelength of the fermion particle, the vacuum expectation values decay exponentially with the decay rate depending on the opening angle of the cone. We make a comparison with the results already known from the literature for some particular cases.

In this paper we investigate the Wightman function, the renormalized vacuum expectation values of the field square, and the energy-momentum tensor for a massive scalar field with general curvature coupling inside and outside of a cylindrical shell in the generalized spacetime of straight cosmic string. For the general case of Robin boundary condition, by using the generalized Abel-Plana formula, the vacuum expectation values are presented in the form of the sum of boundary-free and boundary-induced parts. The asymptotic behavior of the vacuum expectation values of the field square, energy density, and stresses are investigated in various limiting cases. The generalization of the results to the exterior region is given for a general cylindrically symmetric static model of the string core with finite support.