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We obtain a class of solutions corresponding to a generalization of the Hayward black hole by solving the Einstein equations coupled to a particular nonlinear electromagnetic field. The generalization is realized by considering, additionally, the presence of the cosmological constant and a source corresponding to an anisotropic fluid, namely, a fluid of strings, that surrounds the black hole. We show that the obtained class of solutions preserves or does not the regularity of the original Hayward black hole solution, depending on the values of the parameter $\beta$ which labels the different solutions. We discuss the characteristics of the solutions, from the point of view of the singularities of spacetime, by examining the behavior of the Kretschmann scalar as well as of the geodesics concerning their completeness. We analyze some aspects of thermodynamics, particularizing one of the solutions obtained, namely, for $\beta =-1/2$, in which case the regularity of the Hayward black hole is preserved. Some thermodynamic quantities are obtained and analyzed, for example, pressure, heat capacity, and the critical points, and we show how these quantities change for different values of the parameter $q$ associated with the original Hayward solution, as well as with the parameter $b$ associated with the presence of the fluid of strings. The phase transitions are also analyzed by using the equation of state and the Gibbs free energy.

In this work, we investigate some extensions of the Kiselev black hole solutions in the context of $f(\mathbb{T},\CMcal{T})$ gravity. By mapping the components of the Kiselev energy-momentum tensor into the anisotropic energy-momentum tensor and assuming a particular form of $f(\mathbb{T},\CMcal{T})$, we obtain exact solutions for the field equation in this theory that carries dependence on the coupling constant and on the parameter of the equation of state of the fluid. We show that in this scenario of modified gravity some new structure is added to the geometry of spacetime as compared to the Kiselev black hole. We analyse the energy conditions, mass, horizons and the Hawking temperature considering particular values for the parameter of the equation of state.

We obtain the metric corresponding to the Hayward black hole spacetime surrounded by a cloud of strings and investigate the role played by this cloud on the horizons, geodesics, effective potential and thermodynamics. We compare the obtained results with the ones of the literature, corresponding to the Hayward black hole, when the cloud of strings is absent. Also, the question related to its nature, with respect to regularity, in this scenario, is examined.

We obtain new exact solutions for the gravitational field equations in the context of $f(R,T)$ gravity, thereby obtaining different classes of black holes surrounded by fluids, taking into account some specific values of the parameter of the equations of state, $w$. In order to obtain these solutions in the context of $f(R,T)$ gravity, we consider viable particular choices of the $f(R,T)$. Considering an anisotropic energy-momentum tensor, we write the field equations with the required symmetries for this type of solution. Then, we analyze the conditions of energy in a general way and also for particular values of the parameter $w$ of the equation of state. In addition, thermodynamic quantities, such as Hawking temperature and mass associated to the horizons of solutions, are taken into account in our analysis.

In this paper, we study quantum relativistic features of a scalar field around the Rindler-Schwarzschild wormhole. First, we introduce this new class of spacetime, investigating some energy conditions and verifying their violation in a region nearby the wormhole throat, which means that the object has to have an exotic energy in order to prevent its collapse. Then, we study the behavior of the massless scalar field in this spacetime and compute the effective potential by means of tortoise coordinates. We show that such a potential is attractive nearby the wormhole throat and that is traversable via quantum tunneling by massive particles with sufficiently low energies. The solution of the Klein-Gordon equation is obtained subsequently, showing that the energy spectrum of the field is subject to a constraint which induces a decreasing oscillatory behavior. On imposing Dirichlet boundary conditions on a spherical shell nearby the throat we then determine the particle energy levels, and we use this spectrum to calculate the quantum revival of the eigenstates. Finally, we compute the Casimir energy associated with the massless scalar field at zero temperature. We perform this calculation by means of the sum of modes method. The zero-point energy is regularized using the Epstein-Hurwitz zeta-function. We also obtain an analytical expression for the Casimir force acting on the shell., Comment: 14 pages, 6 figures

We investigate non-inertial effects induced by a rotating frame on a non-relativistic quantum harmonic oscillator as well as of the topology associated to a screw dislocation, which corresponds to a distortion of a vertical line into a vertical spiral. To do this, we obtain the analytical solutions of the time-independent Schr\"odinger equation for this harmonic oscillator potential in this background. The expressions for the energy spectrum are obtained and the solutions for four quantum states, namely $n=0,1,2$ and $3$, are analysed. Our results show that the presence of the topological defect (screw dislocation) as well the fact that we are analysing the system from the point of view of a rotating frame, changes the solutions of Schr\"odinger equation and the corresponding spectrum. Now these quantities depend on the angular velocity of the rotating frame, $\Omega$, and also on the parameter $\beta$, which codifies the presence of the screw dislocation. Particularly, with respect to the energy spectrum of the system the changing is such that when $\Omega$ increases, the energy can increase or decrease depending on the values we assign to the eigenvalues of the angular and linear momenta. Additionally, we observe that the values of the parameter $\beta$ that characterizes the screw dislocation causes a shift in the energy spectrum.

We examine the interaction between massless scalar fields and the gravitational field generated by a black hole solution that was recently obtained in the consistent well-defined 4-dimensional Einstein-Gauss-Bonnet gravity with a cosmological constant. In order to do this, we calculate quasibound state frequencies of scalar fields for the spherically symmetric black hole in the consistent 4-dimensional Einstein-Gauss-Bonnet-de Sitter and Anti-de Sitter theories. The expression for the quasibound states is obtained by using the polynomial condition associated to the Heun functions, and their values are overdamped. We also demonstrate the stability of the systems., Comment: 30 pages, 14 figures. arXiv admin note: text overlap with arXiv:2112.08711

Considering exact spacetimes representing rotating black holes and naked singularities, we study the possibility that the Sagnac effect detects $i$) higher dimensions, $ii$) rotation of black holes in higher dimension, and also, $iii$) distinguishes black holes from naked singularities. The results indicate that the Sagnac time delay gets affected by the presence of extra-dimension or its associated angular momentum. This time delay is also different in the spacetime of a naked singularity compared to that of a black hole. Hence, the Sagnac effect may be used as an experiment for better understanding of spacetimes with higher dimensions or those that admit naked singularities., Comment: 6 pages and 6 figures

We analyze the effect of Planck-scale modified radiation equation of state on the Reissner-Nodstr\"om-anti-de Sitter black hole inspired by Kiselev's ansatz. Deformed thermodynamic quantities are found, phase transitions and black holes as heat engines are described for the Carnot and square cycles. Non-trivial differences between linear and quadratic Planck-scale corrections are discussed in detail., Comment: 13 pages, 7 figures. Matches published version

We investigate the quasibound states of charged massive scalar fields in the Kerr-Newman black hole spacetime by using a new approach recently developed, which uses the polynomial conditions of the Heun functions. We calculate the resonant frequencies related to the spectrum of quasibound states, as well as its corresponding angular and radial wave eigenfunctions. We also analyze the instability of the system. These results are particularized to the cases of Schwarzschild and Kerr black holes. Additionally, we compare our analytical results with the numerical ones known in the literature. Finally, we apply the obtained results to compute the characteristic times of growth and decay of bosonic particles around a supermassive black hole situated at the center of the M87 galaxy., Comment: 29 pages, 8 figures

We do a detailed study of the thermodynamics of black holes in Rainbow gravity in the framework of the Kiselev metric, taking into account different cosmic fluids which can mimic several kinds of dark energy scenarios. A discussion related to the appearance of black hole remnants is presented and, unlike other studies on the same topic, we found no evidence of the appearance of remnants in Rainbow gravity, except in peculiar cases.

In this paper, we investigate the simplest wormhole solution - the Ellis-Bronnikov one - in the context of the Asymptotically Safe Gravity (ASG) at the Planck scale. We work with three models, which employ Ricci scalar, Kretschmann scalar, and squared Ricci tensor to improve the field equations by turning the Newton constant into a running coupling constant. For all the cases, we check the radial energy conditions of the wormhole solution and compare them with those valid in General Relativity (GR). We verify that asymptotic safety guarantees that the Ellis-Bronnikov wormhole can satisfy the radial energy conditions at the throat radius, $r_0$, within an interval of values of this latter. That is quite different from the result found in GR. Following, we evaluate the effective radial state parameter, $\omega(r)$, at $r_0$, showing that the quantum gravitational effects modify Einstein's field equations in such a way that it is necessary a very exotic source of matter to generate the wormhole spacetime -- phantom or quintessence-like. That occurs within some ranges of throat radii, even though the energy conditions are or not violated there. Finally, we find that, although at $r_0$ we have a quintessence-like matter, on growing of $r$ we necessarily come across phantom-like regions. We speculate if such a phantom fluid must always be present in wormholes in the ASG context or even in more general quantum gravity scenarios., Comment: Minor changes, references added

In this paper we show that wormholes in (2+1) dimensions (3-D) cannot be sourced solely by both Casimir energy and tension, differently from what happens in a 4-D scenario, in which case it has been shown recently, by the direct computation of the exact shape and redshift functions of a wormhole solution, that this is possible. We show that in a 3-D spacetime the same is not true since the arising of at least an event horizon is inevitable. We do the analysis for massive and massless fermions, as well as for scalar fields, considering quasi-periodic boundary conditions and find that a possibility to circumvent such a restriction is to introduce, besides the 3-D Casimir energy density and tension, a cosmological constant, embedding the surface in a 4-D manifold and applying a perpendicular weak magnetic field. This causes an additional tension on it, which contributes to the formation of the wormhole. Finally, we discuss the possibility of producing the condensed matter analogous of this wormhole in a graphene sheet and analyze the electronic transport through it., Comment: two figures, typos fixed

We obtain an exact solution of Einstein's equations for a charged, static and spherically symmetric body, surrounded by a fluid of strings and with a cosmological constant. This corresponds to the Reissner-Nordstr\"om (de Sitter)-Anti de Sitter black hole surrounded by a fluid of strings. Some aspects concerning the horizons and geodesic motion are discussed. We also obtain the metric corresponding to the Kerr-Newman black hole surrounded by a fluid of strings, by using a method to construct the rotating solution from its counterpart static one. The horizons, ergoregions, and geodesic motion are analyzed. In both cases, the role played by the fluid of strings was pointed out.

In this letter, we discuss the Wheeler-DeWitt equation with an ordering parameter in the Friedmann-Robertson-Walker universe. The solutions when the universe was very small and at the end of the expansion are obtained in terms of Bessel and Heun functions, respectively. We also obtain a boundary condition which should be satisfied by the ordering parameter, namely, $0 \leq p \leq 2$. We investigate the minimum value of the scale factor with respect to the maximum value of the probability density., Comment: 6 pages, 9 figures

We analyze the dynamics of scalar particles in gravity's rainbow considering the space-time of a cosmic string in this modified gravity. Thus, we solve the Klein-Gordon equation for two types of potential in which two possible rainbow functions are selected. In all cases studied we obtain exact solutions for the wave equation, derive the energy spectrum, analyze it in detail and discuss the dependence of the results with the choice of the rainbow functions.

Considering corrections produced by modified dispersion relations on the equation of state parameter of radiation, we study the induced black hole metric inspired by Kiselev's ansatz, thus defining a deformed Reissner-Nordstr\"{o}m metric. In particular, we consider thermodynamic properties of such a black hole from the combined viewpoints of the modified equation of state parameter and the phenomenological approach to the quantum gravity problem called rainbow gravity., Comment: 16 pages, 8 figures

We analyze the electrostatic self-energy of a point like electrically charged particle induced by a cosmic string in the context of gravity's rainbow, as well the electrostatic self-force on this particle. The possibility of the solution associated with a charged particle to be altered by modifications in dispersion relations of the space-time is discussed. We show that the self-energy depends on the rainbow functions and that this quantity can either increase or decrease depending on the rainbow function chosen, as compared with analogous result in the framework of general relativity. With respect to the self-force, its dependence with the rainbow functions is also pointed out

In this work we consider the exact solution of the Klein-Gordon equation describing a massless scalar field in the spacetime of a four dimensional canonical acoustic black hole, which is given in terms of the general Heun function, to investigate the interesting phenomena related to the resonant frequencies., Comment: 14 pages, 2 figures

We study some properties of the extended phase space of a quantum-corrected Schwarzschild black hole surrounded by a perfect fluid. In particular we demonstrate that, due to the quantum correction, there exist first and second order phase transitions for a certain range of the state parameter of the perfect fluid, and we explicitly analyze some cases. Besides that, we describe the efficiency of this system as a heat engine and the effect of quantum corrections for different surrounding fluids., Comment: 10 pages, 12 figures. References added

In this work the wave functions associated to the quantum relativistic universe, which is described by the Wheeler-DeWitt equation, are obtained. Taking into account different kinds of energy density, namely, matter, radiation, vacuum, dark energy, and quintessence, we discuss some aspects of the quantum dynamics. In all these cases, the wave functions of the quantum relativistic universe are given in terms of the triconfluent Heun functions. We investigate the expansion of the universe using these solutions and found that the asymptotic behavior for the scale factor is $a(t) \sim \mbox{e}^{t}$ for whatever the form of energy density is. On the other hand, we analyze the behavior at early stages of the universe and found that $a(t) \sim t^{1/2}$. We also calculate and analyze the transmission coefficient through the effective potential barrier., Comment: 17 pages, 7 figures, 1 table

The description of the accelerated phases for the current and primordial cosmos has been obtained in the framework of R\'{e}nyi cosmology. The results show that corrections to the Friedmann equations, originated from differences between R\'{e}nyi and Bekenstein entropies, can describe both the current accelerated and inflationary eras. The effects of these corrections can be appointed to a hypothetical fluid which is classically unstable. Although inflation can be obtained in R\'{e}nyi cosmology as the vacuum solution, the values found for the parameters of the hypothetical fluid which supports the current accelerated and primary inflationary cosmos differ from each other., Comment: 4 pages, 4 figures

In this paper we analyze the energy levels of a charged scalar particle placed in the static cosmic string spacetime, under the action of a uniform magnetic field parallel to the string, in the context of the semi-classical approach of the rainbow gravity. Firstly, we focus on the non-relativistic regime by solving the corresponding Schr\"{o}dinger equation, following by a complete relativistic treatment of the problem in which we considered the Klein-Gordon equation. In both cases we find exact expressions for the Landau levels in terms of the rainbow functions, used to characterize a rainbow gravity model. In order to achieve the results of this paper we considered three different rainbow gravity models mostly used in the literature and compare the resulting modifications in the Landau levels with the standard case, namely without rainbow gravity., Comment: 21 pages, 6 figures. Accepted for publication in Annals of Physics

We obtain the solution corresponding to a static and spherically symmetric black hole with a cloud of strings (Letelier spacetime) immersed in a quintessential fluid. We discuss some aspects of its thermodynamics. We also present a discussion about Hawking radiation of particles, in the background under consideration.

In this study, we consider charged massive scalar fields around a Kerr-Sen spacetime. The radial and angular parts of the covariant Klein-Gordon equation are solved in terms of the confluent Heun function. From the exact radial solution, we obtain the Hawking radiation spectrum and discuss its resonant frequencies. The massless case of the resonant frequencies is also examined., Comment: 13 pages, 11 figures

We obtain the wave functions associated to the quantum Newtonian universe with a cosmological constant which is described by the Schr\"{o}dinger equation and discuss some aspects of its dynamics for all forms of energy density, namely, matter, radiation, vacuum, dark energy, and quintessence. These wave functions of the quantum Newtonian universe are obtained in terms of the Heun's functions and the respective energy levels are shown. We use these solutions to investigate the expansion of the universe and found that the asymptotic behavior for the scale factor is $R \sim \mbox{e}^{t}$ for whatever the form of energy density is. We also analyze the behavior of the universe at early stages., Comment: 15 pages, 4 figures

We use the exact analytical solution of the radial part of the Klein-Gordon equation describing a charged massive scalar field in the electrically charged Garfinkle-Horowitz-Strominger dilaton black hole spacetime, given in terms of the confluent Heun functions, to study the physical phenomena related to resonant frequencies associated to this field, and also to examine some aspects related to its Hawking radiation. The special case of a Schwarzschild spacetime is also considered., Comment: 30 pages, 10 figures

In this paper we study the electronic properties of carbon nanocones with one and two nappes, with pentagonal and heptagonal defects in their lattices. We use the continuum model, which is based on a Dirac-like Hamiltonian with the topological effects described by localized non-Abelian gauge field fluxes. We develop a geometrical approach that can describe the two nappes of the double cone surface simultaneously, by extending the radial coordinate to the complete set of real numbers. We show that, for some combinations of different nanocones, forming the double conical surface, the local density of states near the apex of the cone does not vanish at the Fermi energy and presents a strong dependence on the angular momentum. We also obtain the energy spectrum for finite-sized nanocones and verify that it depends on the choice of topological defect on the surface, which suggests that a double nanocone can be used to control the electronic transport in carbon-based electronic devices.

The quantum fluctuations of the geodesic deviation equation in a flat background spacetime are discussed. We calculate the resulting mean squared fluctuations in the relative velocity and separation of test particles. The effect of these quantum fluctuations of the spacetime geometry is given in terms of the Riemann tensor correlation function. Three different sources of the Riemann tensor fluctuations are considered: a thermal bath of gravitons, gravitons in a squeezed state, and the graviton vacuum state., Comment: 27 pages, 3 figures

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 a massless scalar field. Our framework is the Kerr spacetime in the presence of quintessence and massive gravitons. The high and low temperature regimes are especially analysed in order to distinguish the main contributions. For instance, in the high temperature regime, we show that the force between the plates is repulsive and grows with both the quintessence and the massive gravitons. Regarding the Casimir entropy, our results are in agreement with the Nernst heat theorem and therefore confirm the third law of thermodynamics in the present scenario., Comment: 15 pages, 4 figures

In this paper, we analyze numerically the behaviour of the solutions corresponding to a non-Abelian cosmic string in the framework of the Starobinsky model, i.e. where $f(R)=R + \zeta R^2$. We perform the calculations for both an asymptotically flat and asymptotically (anti)de Sitter spacetimes. We found that the angular deficit generated by the string decreases as the parameter $\zeta$ increases, in the case of a null cosmological constant. For a positive cosmological constant, we found that the cosmic horizon is affected in a non-trivial way by the parameter $\zeta$., Comment: 16 pages, 9 figures, accepted for publication in IJMPD

In the present paper we investigate the effects caused by the modification of the dispersion relation obtained by solving the Klein-Gordon equation in the closed Einstein's universe in the context of rainbow's gravity models. Thus, we analyse how the quantum vacuum fluctuations of the scalar field are modified when compared with the results obtained in the usual General Relativity scenario. The regularization, and consequently the renormalization, of the vacuum energy is performed adopting the Epstein-Hurwitz and Riemann's zeta functions., Comment: 15 pages, 1 figure. To appear in Europhysics Letters

Massive scalar fields are considered in the gravitational field produced by a Schwarzschild black hole with a global monopole in $f(R)$ gravity. The 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., Comment: 12 pages, 8 figures

We obtain the exact (confluent Heun) 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. Next, we infer constraints on the rainbow parameters from recent LHC particle physics experiments and Hubble STIS astrophysics measurements. Finally, we study the low frequency limit in order to find the modified energy spectrum around the source., Comment: Rewritten and enlarged version. 17 pages, 1 figure, 1 table. Some typos corrected. Final version to appear in Phys. Rev. D

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. Typical singularities which appears due to the presence of the boundaries in flat spacetime can be naturally regularized for an asymptotically bounded expanding scale function. Thus, shifts in the velocity could be, at least in principle, detectable experimentally. The possibility to implement this observation in an analog cosmological model by the use of a Bose-Einstein condensate is also discussed., Comment: 26 pages, 7 figures. Accepted for Publication in Phys. Rev. D

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. It is shown that the Casimir entropy for two graphene sheets goes to zero when the temperature vanishes, i.e., the third law of thermodynamics (the Nernst heat theorem) is satisfied. At low temperature, the magnitude of the thermal correction to the Casimir pressure between two graphene sheets is shown to vary inversely proportional to the separation. The Nernst heat theorem for graphene is discussed in the context of problems occurring in Casimir physics for both metallic and dielectric plates., Comment: 29 pages

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. We show that at the north pole the Casimir energy is not influenced by the quintessential matter. At the equatorial plane, when the quintessence is canceled, the result obtained in the literature is recovered. Finally, constraints in the quintessence parameters are obtained from the uncertainty in the current measurements of Casimir effect., Comment: 13 pages. Two figures

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. We demonstrate that only the polarization component perpendicular to the plates contribute to the pressure. The obtained pressure can be both repulsive and attractive depending on whether the polarizations of both plates are unidirectional or directed in opposite directions. It is shown that although the constraints on an axion-electron coupling obtained in the case of magnetized plates are not competitive, the constraints on an axion-neutron coupling found for plates with polarized nuclear spins are of the same order of magnitude of those obtained previously for the GUT axions alone using the process of two-axion exchange. The proposed experiment allows also to strengthen the presently known constraints on the axion-neutron coupling constants of GUT axions by using both processes of one- and two-axion exchange., Comment: 20 pages, 2 figures; to appear in Phes. Rev. D

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. Remarkably, our analysis reveals that the Landau quantization occurs even in the absence of gauge fields provided the string is endowed with spin., Comment: Writing and grammar revised. References added. 14 pages, no figures. To appear in European Phys. J. C

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. We also point out that at large distances from the cosmic string the mean square fluctuation in the geodesic interval function is extremely small while in the opposite limit it logarithmically increases, improving the signal and thus, making possible the detection of such quantity., Comment: 19 pages, 1 figure

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., Comment: Revised version. New title. References added. 16 pages, no figures. To appear in Europhysics Letters. arXiv admin note: text overlap with arXiv:1510.06655

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., Comment: 15 pages, 7 figures; To appear in IJMPD

In this paper we study the effects associated to quantum vacuum fluctuations of vectorial perturbations of the Abelian SU(2) Yang-Mills field in a static and homogeneous chromomagnetic-like background field, at zero temperature. We use periodic and antiperiodic boundary conditions in order to calculate the Casimir energy by means of the frequency sum technique and of the regularization method based on zeta functions, analyzing its behavior in the weak and strong coupling regimes. We compare the obtained results with the similar ones found for scalar and spinor fields placed in an ordinary magnetic field background. We show that only in the weak coupling regime the non-trivial topology of the system encoded in the antiperiodic boundary conditions changes the nature of the Casimir force with respect to the periodic ones. Considering the weak coupling scenario, we show that the introduction of a third polarization state in the perturbations makes manifest the effects on the Casimir energy due to the coupling with the chromomagnetic-like background field, for both the boundary conditions. Finally, in the strong coupling regime, in which the quantum vacuum is not stable due to the Nielsen-Olesen instabilities, we evaluate the effects of a compact extra dimension on its stabilization., Comment: Improved and enlarged text, some references added, 13 pages, 1 figure. To appear in the Brazilian Journal of Physics

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. In all these special situations, the resonant frequencies, Hawking radiation and scattering are studied., Comment: 18 pages. This paper was unified and published with arXiv:1603.02240

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., Comment: 20 pages, 10 figures