In this paper we study the vacuum quantum fluctuations of the stationary modes of an uncharged scalar field with mass m around a Schwarzschild black hole with mass M, at zero and non-zero temperatures. The procedure consists of calculating the energy eigenvalues starting from the exact solutions found for the dynamics of the scalar field, considering a frequency cutoff in which the particle is not absorbed by the black hole. From this result, we obtain the exterior contributions for the vacuum energy associated to the stationary states of the scalar field, by considering the half-summing of the levels of energy and taking into account the respective degeneracies, in order to better capture the nontrivial topology of the black hole spacetime. Then we use the Riemann's zeta function to regularize the vacuum energy thus found. Such a regularized quantity is the Casimir energy, whose analytic computation we show to yield a convergent series. The Casimir energy obtained does not take into account any boundaries artificially imposed on the system, just the nontrivial spacetime topology associated to the source and its singularity. We suggest that this latter manifests itself through the vacuum tension calculated on the event horizon. We also investigate the problem by considering the thermal corrections via Helmholtz free energy calculation, computing the Casimir internal energy, the corresponding tension on the event horizon, the Casimir entropy, and the thermal capacity of the regularized quantum vacuum, analyzing their behavior at low and high temperatures, pointing out the thermodynamic instability of the system in the considered regime, i.e. mM << 1.

In this paper we study the polarized vacuum energy on the conducting surface of a topological insulator characterized by both $Z_2$ topological index and time reversal symmetry. This boundary is subject to the action of a static and spatially homogeneous magnetic field perpendicular to it as well as of an electric field that is uniform near the considered surface and produced by a biased voltage, at zero temperature. To do this, we consider modifications in the Gauss law that arise due to the nonzero gradient of the axionlike pseudoscalar factor coupled to the applied magnetic field, which accounts for the topological properties of the system. Such a term allows us to find a correction to the induced charges which modifies the quantum vacuum of the spinor field regarding an ordinary surface. The polarized vacuum energy is calculated in both the weak-field approximation and in the general case, and since the found energy depends on a length defined on the boundary, we show that there is a radial density of force or a surface shear stress that tends to shrink it.

Starting from an analytical expression for the Helmholtz free energy we calculate the thermal corrections to the Casimir energy density and entropy within nearby ideal parallel plates in the vacuum of

In this paper, we investigate how the fine-structure constant, α, locally varies in the presence of a static and spherically symmetric gravitational source. The procedure consists in calculating the solution and the energy eigenvalues of a massive scalar field around that source, considering the weak-field regime. From this result, we obtain expressions for a spatially variable fine-structure constant by considering suitable modifications in the involved parameters admitting some scenarios of semi-classical and quantum gravities. Constraints on free parameters of the approached theories are calculated from astrophysical observations of the emission spectra of a white dwarf. Such constraints are finally compared with those obtained in the literature.

In this paper, we investigate how the fine structure constant, $\alpha$, locally varies in the presence of a static and spherically symmetric gravitational source. The procedure consists in calculating the solution and the energy eigenvalues of a massive scalar field around that source, considering the weak-field regimen. From this result, we obtain expressions for an spatially variable fine structure constant by considering suitable modifications in the involved parameters admitting some scenarios of semi-classical and quantum gravities. Constraints on free parameters of the approached theories are calculated from astrophysical observations of the emission spectra of a white dwarf. Such constraints are finally compared with those ones obtained in the literature.