# V. B. Bezerra - UFPB

## Contact Details

NameV. B. Bezerra |
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AffiliationUFPB |
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Location |
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## Pubs By Year |
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## Pub CategoriesGeneral Relativity and Quantum Cosmology (30) High Energy Physics - Theory (24) Quantum Physics (13) High Energy Physics - Phenomenology (7) Physics - Mesoscopic Systems and Quantum Hall Effect (4) Mathematics - Mathematical Physics (4) Mathematical Physics (4) Physics - Other (3) Cosmology and Nongalactic Astrophysics (2) Physics - General Physics (2) Physics - Superconductivity (1) Solar and Stellar Astrophysics (1) Physics - History of Physics (1) |

## Publications Authored By V. B. Bezerra

Massive scalar fields are considered in the gravitational field produced by a Schwarzschild black hole with a global monopole in $f(R)$ gravity. Exact solution of the radial part of the Klein-Gordon equation in this background is obtained and is given in terms of the general Heun functions. We apply the properties of the general Heun functions to study the Hawking radiation and the resonant frequencies of scalar particles. Read More

We obtain the exact (Heun type) solutions to the massive scalar field in a Gravity's Rainbow Schwarzschild metric. With these solutions at hand, we study the Hawking radiation resulting from the tunneling rate through the event horizon. We show that the emission spectrum obeys non-extensive statistics and is halted when a certain mass remnant is reached. Read More

In this paper we study the effects of quantum scalar field vacuum fluctuations on scalar test particles in an analog model for the Friedmann-Robertson-Walker spatially flat geometry. In this scenario, the cases with one and two perfectly reflecting plane boundaries are considered as well the case without boundary. We find that the particles can undergo Brownian motion with a nonzero mean squared velocity induced by the quantum vacuum fluctuations due to the time dependent background and the presence of the boundaries. Read More

The existence of the Higgs particle necessarily implies in the inclusion of Einstein's gravitational field in the standard model of interactions. It also implies in the existence of a new massive, spin-2, weakly interacting field of geometrical nature, acting as a short range carrier of Einstein's gravitation. Read More

We find analytic asymptotic expressions at low temperature for the Casimir free energy, entropy and pressure of two parallel graphene sheets in the framework of the Lifshitz theory. The reflection coefficients of electromagnetic waves on graphene are described on the basis of first principles of quantum electrodynamics at nonzero temperature using the polarization tensor in (2+1)-dimensional space-time. The leading contributions to the Casimir entropy and to the thermal corrections to the Casimir energy and pressure are given by the thermal correction to the polarization tensor at nonzero Matsubara frequencies. Read More

We calculate the Casimir energy of a massless scalar field in a cavity formed by nearby parallel plates orbiting a rotating spherical body surrounded by quintessence, investigating the influence of the gravitational field on that energy, at zero temperature. This influence includes the effects due to the spacetime dragging caused by the source rotation as well as those ones due to the quintessence. We show that the energy depends on all the involved parameters, as source mass, angular momentum and quintessence state parameter, for any radial coordinate and polar angle. Read More

We propose an experiment for measuring the effective Casimir pressure between two parallel SiC plates with aligned nuclear spins. The prospective constraints on an axion-neutron coupling constant for both hadronic and GUT axions are calculated using the process of one-axion exchange. For this purpose, a general expression for the additional pressure arising between two polarized plates due to the exchange of one axion between their constituent fermions is derived. Read More

In the spacetime induced by a rotating cosmic string we compute the energy levels of a massive spinless particle coupled covariantly to a homogeneous magnetic field parallel to the string. Afterwards, we consider the addition of a scalar potential with a Coulomb-type and a linear confining term and completely solve the Klein-Gordon equations for each configuration. Finally, assuming rigid-wall boundary conditions, we find the Landau levels when the linear defect is itself magnetized. Read More

In this paper we consider light-cone fluctuations arising as a consequence of the nontrivial topology of the locally flat cosmic string spacetime. By setting the light-cone along the z-direction we are able to develop a full analysis to calculate the renormalized graviton two-point function, as well as the mean square fluctuation in the geodesic interval function and the time delay (or advance) in the propagation of a light-pulse. We found that all these expressions depend upon the parameter characterizing the conical topology of the cosmic string spacetime and vanish in the absence of it. Read More

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. Read More

The quasinormal modes for a scalar field in the background spacetime corresponding to a black hole, with a cloud of strings, in Einstein-Gauss-Bonnet gravity, and the tensor quasinormal modes corresponding to perturbations in such spacetime, were both calculated using the WKB approximation. In the obtained results we emphasize the role played by the parameter associated with the string cloud, comparing them with the results already obtained for the Boulware-Deser metric. We also study how the Gauss-Bonnet correction to general relativity affects the results for the quasinormal modes, comparing them with the same background in general relativity. Read More

In this paper we compute the regularized vacuum energy associated with vectorial perturbations of the SU(2) Yang-Mills field. We regard Dirichlet and twisted boundary conditions in a chromomagnetic background, at zero temperature. Then, we analyse the behavior of the Casimir energy in the weak and strong coupling regimens, comparing with similar results obtained for the scalar and spinorial fields in an ordinary magnetic field background. Read More

We apply the confluent Heun functions to study the resonant frequencies (quasispectrum), the Hawking radiation and the scattering process of scalar waves, in a class of spacetimes, namely, the ones generated by a Kerr-Newman-Kasuya spacetime (dyon black hole) and a Reissner-Nordstr\"{o}m black hole surrounded by a magnetic field (Ernst spacetime). In both spacetimes, the solutions for the angular and radial parts of the corresponding Klein-Gordon equations are obtained exactly, for massive and massless fields, respectively. The special cases of Kerr and Schwarzschild black holes are analyzed and the solutions obtained, as well as in the case of a Schwarzschild black hole surrounded by a magnetic field. Read More

We show that the solutions of the Wheeler-DeWitt equation in a homogeneous and isotropic universe are given by triconfluent Heun functions for the spatially closed, flat, and open geometries of the Friedmann-Robertson-Walker universe filled with different forms of energy. In a matter-dominated universe, we find the polynomial solution and the energy density spectrum. In the cases of radiation-dominated and vacuum universes, there are no polynomial solutions as shown. Read More

We apply the confluent Heun functions to study the resonant frequencies (quasispectrum), the Hawking radiation and the scattering process of scalar waves, in a class of spacetimes, namely, the ones generated by a Kerr-Newman-Kasuya spacetime (dyon black hole) and a Reissner-Nordstr\"{o}m black hole surrounded by a magnetic field (Ernst spacetime). In both spacetimes, the solutions for the angular and radial parts of the corresponding Klein-Gordon equations are obtained exactly, for massive and massless fields, respectively. The special cases of Kerr and Schwarzschild black holes are analyzed and the solutions obtained, as well as in the case of a Schwarzschild black hole surrounded by a magnetic field. Read More

We analyze numerically the behaviour of the solutions corresponding to an Abelian cosmic string taking into account an extension of the Starobinsky model, where the action of general relativity is replaced by $f(R) = R - 2\Lambda + \eta R^2 + \rho R^m$, with $m > 2$. As an interesting result, we find that the angular deficit which characterizes the cosmic string decreases as the parameters $\eta$ and $\rho$ increase. We also find that the cosmic horizon due to the presence of a cosmological constant is affected in such a way that it can grows or shrinks, depending on the vacuum expectation value of the scalar field and on the value of the cosmological constant Read More

The quasinormal modes for scalar and spinor fields in the background spacetime corresponding to an $f(R)$ global monopole are calculated using the WKB approximation. In the obtained results we emphasize the role played by the parameter $\psi_{0}$, associated with the $f(R)$ gravity. We discuss the appropriate limit $\psi_{0} \rightarrow 0$, in which case the results concerning to the Schwarzschild black hole are obtained, as it should be expected. Read More

In this paper we apply the usual perturbative methodology to evaluate the one-loop effective potential in a nonlocal scalar field theory. We find that the effect induced by the nonlocaliity of the theory is always very small and we discuss the consequences of this result. In particular we argue that, looking at one-loop corrections for matter fields, it is not possible to find signals of the nonlocality of the theory in cosmological observables since, even during inflation when energies are very high, nonlocality-induced corrections are expected to be very small. Read More

In this manuscript we explicitly compute the effective dimension of spacetime in some backgrounds of Ho\v{r}ava-Lifshitz (H-L) gravity. For all the cases considered, the results are compatible with a dimensional reduction of the spacetime to $d+1=2$, at high energies (ultraviolet limit), which is confirmed by other quantum gravity approaches, as well as to $d+1=4$, at low energies (infrared limit). This is obtained by computing the free energy of massless scalar and gauge fields. Read More

We obtain the exact solution of the Schr\"odinger equation for a particle (galaxy) moving in a Newtonian universe with a cosmological constant, which is given in terms of the biconfluent Heun functions. The first six Heun polynomials of the biconfluent function are written explicitly. The energy spectrum which resembles the one corresponding to the isotropic harmonic oscillator is also obtained. Read More

Charged massive scalar fields are considered in the gravitational and electromagnetic field produced by a dyonic black hole with a cosmic string along its axis of symmetry. Exact solutions of both angular and radial parts of the covariant Klein-Gordon equation in this background are obtained, and are given in terms of the confluent Heun functions. The role of the presence of the cosmic string in these solutions is showed up. Read More

The spectral dimension $d_s$ for high energies is calculated using the Relativistic Schr\"{o}dinger Equation Analytically Continued (RSEAC) instead of the so-called Telegraph's Equation (TE), in both ultraviolet (UV) and infrared (IR) regimens. Regarding the TE, the recent literature presents difficulties related to its stochastic derivation and interpretation, advocating the use of the RSEAC to properly describe the relativistic diffusion phenomena. Taking into account that the Lorentz symmetry is broken in UV regime at Lifshitz point, we show that there exists a degeneracy in very high energies, meaning that both the RSEAC and the TE correctly describe the diffusion processes at these energy scales, at least under the spectral dimension criterion. Read More

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. Read More

We obtain stronger laboratory constraints on the coupling constants of axion-like particles to nucleons from measurements of the normal and lateral Casimir forces between sinusoidally corrugated surfaces of a sphere and a plate. For this purpose, the normal and lateral additional force arising in the experimental configurations due to two-axion exchange between protons and neutrons are calculated. Our constraints following from measurements of the normal and lateral Casimir forces are stronger than the laboratory constraints reported so far for masses of axion-like particles larger than 11eV and 8eV, respectively. Read More

We obtain the analytic solutions of the radial part of the massless Klein-Gordon equation in the spacetime of both three dimensional rotating and four dimensional canonical acoustic black holes, which are given in terms of the confluent Heun functions. From these solutions, we obtain the scalar waves near the acoustic horizon. We discuss the analogue Hawking radiation of massless scalar particles and the features of the spectrum associated with the radiation emitted by these acoustic black holes. Read More

We analyze the influence of the gravitational field produced by a slowly rotating black hole with a cosmic string along the axis of symmetry on a massive scalar field. Exact solutions of both angular and radial parts of the Klein-Gordon equation in this spacetime are obtained, and are given in terms of the confluent Heun functions. We emphasize the role of the presence of the cosmic string in these solutions. Read More

We calculate the Casimir energy of a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed tangentially to the surface of a sphere with mass M and radius R. To this end, we take into account a static and spherically symmetric solution of Ho\v{r}ava-Lifshitz (HL) gravity, with a cosmological constant term, in lower orders of approximation, considering both weak-field and infrared limits. We show that the Casimir energy, just in the second order weak-field approximation, is modified due to the parameter of the HL gravity as well as to the cosmological constant. Read More

We analyze the quantum phenomenon arising from the interaction of a spinless charged particle with a rotating cosmic string, under the action of a static and uniform magnetic field parallel to the string. We calculate the energy levels of the particle in the non-relativistic approach, showing how these energies depend on the parameters involved in the problem. In order to do this, we solve the time independent Schroedinger equation in the geometry of the spinning cosmic string, taking into account that the coupling between the rotation of the spacetime and the angular momentum of the particle is very weak, such that makes sense to apply the Schr\"odinger equation in a curved background whose metric has an off diagonal term which involves time and space. Read More

Stronger constraints on the pseudoscalar coupling constants of an axion to a proton and a neutron are obtained from an indirect measurement of the effective Casimir pressure between two Au-coated plates by means of micromechanical torsional oscillator. For this purpose, the additional effective pressure due to two-axion exchange is calculated. The role of boundary effects and the validity region of the proximity force approximation in application to forces of axion origin are determined. Read More

We calculate the additional force due to two-axion exchange acting in a sphere-disc geometry, used in experiments on measuring the gradient of the Casimir force. With this result, stronger constraints on the pseudoscalar coupling constants of an axion and axion-like particles to a proton and a neutron are obtained over the wide range of axion masses from 0.03mV to 1eV. Read More

In this paper, we use the Lagrangian formalism of classical mechanics and some assumptions to obtain cosmological differential equations analogous to Friedmann and Einstein equations, obtained from the theory of general relativity. This method can be used to a universe constituted of incoherent matter, that is, the cosmologic substratum is comprised of dust. Read More

Stronger constraints on the pseudoscalar coupling constants of an axion and axion-like particles with a proton and a neutron are obtained from measurements of the thermal Casimir-Polder force between a Bose-Einstein condensate of $^{87}$Rb atoms and a SiO$_2$ plate. For this purpose the additional force acting between a condensate cloud and a plate due to two-axion exchange is calculated. The obtained constraints refer to the axion masses from 0. Read More

This work considers the influence of the gravitational field produced by a charged and rotating black hole (Kerr-Newman spacetime) on a charged massive scalar field. We obtain exact solutions of both angular and radial parts of the Klein-Gordon equation in this spacetime, which are given in terms of the confluent Heun functions. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation of charged massive scalar particles. Read More

We calculate the renormalized vacuum energy density for a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed very close to the surface of a rotating spherical gravitational source with mass $M$, radius $R$ and momentum angular $J$, at the equatorial region. We consider that the source rotates slowly and that the gravitational field is weak. Corrections to the Casimir energy density induced by the gravitational field generated by this source are calculated up to $M/R^2$ order. Read More

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. Read More

We discuss the correspondence between metric $f(R)$ gravity and $\omega=0$ Brans-Dicke theory with a potential, by working out an example that reconfirms this equivalence. Read More

We calculate the renormalized vacuum energy of a massless scalar field confined between two nearby parallel plates formed by ideal uncharged conductors, placed tangentially to the surface of a sphere with mass M and radius R. This study will take into account the static and spherically symmetric solution of Horava-Lifshitz gravity found by Kehagias-Sfetsos (KS), in both weak field and infrared limits. A slight amplification of the Casimir force between the conducting plates is found. Read More

We discuss the BCS theory for electrons in graphene with a superimposed electrical unidirectional superlattice potential (SL). New Dirac points emerge together with van Hove singularities (VHS) linking them. We obtain a superconducting transition temperature $ T_c $ for chemical potentials close to the VHS assuming that acoustic phonon coupling should be the dominant mechanism. Read More

We calculate the electrostatic self-force on an electric dipole in the spacetime generated by a static, thin, infinite and straight cosmic string. The electric dipole is held fixed in different configurations, namely, parallel, perpendicular to the cosmic string and oriented along the azimuthal direction around this topological defect, which is stretched along the z axis. We show that the self-force is equivalent to an interaction of the electric dipole with an effective dipole moment which depends on the linear mass density of the cosmic string and on the configuration. Read More

The Casimir-Polder interaction potential is evaluated for a polarizable microparticle and a conducting wall in the geometry of a cosmic string perpendicular to the wall. The general case of the anisotropic polarizability tensor for the microparticle is considered. The corresponding force is a function of the wall-microparticle and cosmic string-microparticle distances. Read More

Measurements of the Casimir force are used to obtain stronger constraints on the parameters of hypothetical interactions predicted in different unification schemes beyond the Standard Model. We review new strong constraints on the Yukawa-type interactions derived during the last two years from recent experiments on measuring the lateral Casimir force, Casimir force in configurations with corrugated boundaries and the Casimir-Polder force. Specifically, from measurements of the lateral Casimir force compared with the exact theory the strengthening of constraints up to a factor of 24 millions was achieved. Read More

We calculate the total internal energy, total energy density and pressure, and the free energy for the neutrino and electromagnetic fields in Einstein and closed Friedmann cosmological models. The Casimir contributions to all these quantities are separated. The asymptotic expressions for both the total internal energy and free energy, and for the Casimir contributions to them are found in the limiting cases of low and high temperatures. Read More

We derive the exact Casimir-Polder potential for a polarizable microparticle inside an ideal metal cylindrical shell using the Green function method. The exact Casimir-Polder potential for a particle outside a shell, obtained recently by using the Hamiltonian approach, is rederived and confirmed. The exact quantum field theoretical result is compared with that obtained using the proximity force approximation and a very good agreement is demonstrated at separations below 0. Read More

We report constraints on the parameters of Yukawa-type corrections to Newtonian gravity from measurements of the gradient of the Casimir force in the configuration of an Au-coated sphere above a Si plate covered with corrugations of trapezoidal shape. For this purpose, the exact expression for the gradient of Yukawa force in the experimental configuration is derived and compared with that obtained using the proximity force approximation. The reported constraints are of almost the same strength as those found previously from several different experiments on the Casimir force and extend over a wide interaction range from 30 to 1260\,nm. Read More

The impact of imperfections, which are always present on surfaces of lenses with centimeter-size curvature radii, on the Casimir force in the lens-plate geometry is investigated. It is shown that the commonly used formulation of the proximity force approximation is inapplicable for spherical lenses with surface imperfections, such as bubbles and pits. More general expressions for the Casimir force are derived that take surface imperfections into account. Read More

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 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. Read More

We calculate the vacuum average value of the field square and the stress-energy tensor of a massive scalar field, with non-minimal coupling $\xi$ to the curvature in the short-throat flat-space wormhole background. The obtained results are not suitable for an analytical analysis and for this reason we provide a numerical analysis for different values of the coupling constant, $\xi$. It was shown that the vacuum polarization cannot self-consistently support the wormhole. Read More

We report stronger constraints on the parameters of Yukawa-type corrections to Newtonian gravity from measurements of the lateral Casimir force between sinusoidally corrugated surfaces of a sphere and a plate. In the interaction range from 1.6 to 14 nm the strengthening of previously known high confidence constraints up to a factor of $2. Read More

The Dicke spin-boson model is composed by a single bosonic mode and an ensemble of $N$ identical two-level atoms. Assuming thermal equilibrium with a reservoir at temperature $\beta^{-1}$, we consider the situation where the coupling between the bosonic mode and the atoms generates resonant and non-resonant processes. The thermodynamic of the model is investigated. Read More

**Affiliations:**

^{1}UFPB,

^{2}IF Fluminense,

^{3}UFCG

**Category:**High Energy Physics - Theory

We consider a scalar field interaction with a cosmic string configuration in a flat 3-brane. The origin of this field is given by a compactification mechanism in the context of a 5-dimensional Brans-Dicke theory. We use the Cosmic Microwave Background Radiation constraint to analyse a possibility of optical activity effect in connection with the Brans-Dicke parameter w and obtain relations between the compactification modes. Read More