Search

In this work we estimate the $N_{\psi(2S)} / N_{J/\psi}$ yield ratio in heavy-ion collisions, considering the interactions of the $\psi (2S) $ and $J/\psi$ states with light mesons in the hadron gas formed at the late stages of these collisions. Starting from the appropriate effective Lagrangians, we first compute the thermally-averaged cross sections for the production and absorption of the mentioned states, and then use them as input in the rate equations to determine the time evolution of $N_{\psi(2S)}$, $N_{J/\psi}$ and $N_{\psi(2S)} / N_{J/\psi}$. The main conclusion of our study is that the $\psi (2S) $ and $J/\psi$ multiplicities do not change much in the hadron gas phase and that the $\psi (2S)$ is more absorbed than the $J/\psi$. The obtained final ratio is in qualitative agreement with experimental data., Comment: 8 pages, 6 figures

In this work we evaluate the $X(3872)$ to $ \psi (2S) $ yield ratio ($N_X/N_{\psi(2S)}$) in Pb Pb collisions, taking into account the interactions of the $\psi (2S) $ and $ X(3872)$ states with light mesons in the hadron gas formed at the late stages of these collisions. We employ an effective Lagrangian approach to estimate the thermally-averaged cross sections for the production and absorption of the $\psi(2S)$ and use them in the rate equation to determine the time evolution of $N_{\psi(2S)}$. The multiplicity of these states at the end of mixed phase is obtained from the coalescence model. The multiplicity of $X(3872)$, treated as a bound state of $(D\bar D^{*} + c.c.)$ and also as a compact tetraquark, was already calculated in previous works. Knowing these yields, we derive predictions for the ratio ($N_X/N_{\psi(2S)}$) as a function of the centrality, of the center-of-mass energy and of the charged hadron multiplicity measured at midrapidity $[dN_{ch}/d\eta \,(\eta<0.5)]$. Finally, we make predictions for this ratio in Pb Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV to be measured by the ALICE Collaboration in the Run 3., Comment: 10 pages, 10 figures

We investigate the interactions of the charged exotic state $Z_c(3900)$ in a hadronic medium composed of light mesons. We study processes such as $Z_c \pi \to D\bar{D}$, $Z_c \pi \to D^*\bar{D}^*$, $Z_c \pi \to D\bar{D}^*$ and the inverse ones. Using effective Lagrangians and form factors calculated with QCD sum rules (treating the $Z_c(3900)$ as a tetraquark) we estimate the vacuum and thermally-averaged cross-sections of these reactions. We find that the $Z_c(3900)$ has relatively large interaction cross sections with the constituent particles of the hadronic medium. After that, we use the production and suppression cross sections in a rate equation to estimate the time evolution of the $Z_c$ multiplicity. We include the $Z_c$ decay and regeneration terms. The coalescence model is employed to compute the initial $Z_c$ multiplicity for the compact tetraquark configuration. Our results indicate that the combined effects of hadronic interactions, hydrodynamical expansion, decay and regeneration affect the final yield, which is bigger than the initial value. Besides, the dependence of the $Z_c$ final yield with the centrality, center-of-mass energy and the charged hadron multiplicity measured at midrapidity $[dN_{ch}/d\eta \,(\eta<0.5)]$ is also investigated., Comment: 9 pages; 8 figures

In this paper, we examine the role played by topology, and some specific boundary conditions as well, on the physics of a higher-dimensional black hole. We analyze the line element of a five-dimensional non-extremal Reissner-Nordstr\"{o}m black hole to obtain a new family of subspaces that are types of strong retractions and deformations, and then we extend these results to higher dimensions in order to deduce the relationship between various types of transformations. We also study the scalar field perturbations in the background under consideration and obtain an analytical expression for the quasibound state frequencies by using the Vieira-Bezerra-Kokkotas approach, which uses the polynomial conditions of the general Heun functions, and then we discuss the stability of the system and present the radial eigenfunctions. Our main goal is to discuss the physical meaning of these mathematical applications in such higher-dimensional effective metric., Comment: 17 pages, 4 figures. Matches published version in Universe

In a previous work we computed the thermally-averaged cross sections for the production and absorption of the $\chi_{c1}(4274)$ state in the hot hadron gas formed in heavy ion collisions. In the present work we estimate the final yield of this exotic state in these collisions. We use the coalescence model to fix the initial multiplicities. The state is is treated as a $P-$wave bound state of $D_s\bar D_{s0}$ and also as a compact tetraquark. The Bjorken picture is used to model the hydrodynamic expansion and cooling. Then, the kinetic equation is solved to evaluate the time evolution of the $\chi_{c1}(4274)$ yield during the hot hadron gas phase. Since the $\chi_{c1}(4274)$ decay width is large it might decay inside the hadron gas. Therefore we also include the $chi_{c1}(4274)$ decay and regeneration terms by means of an effective coupling, estimated from the available data. The combined effects of hadronic interactions and the $\chi_{c1}(4274)$ decay have a strong impact on the final yield. Also, predictions of the $\chi_{c1}(4274)$ multiplicity as a function of centrality and of the charged hadron multiplicity (measured at midrapidity) are presented. Finally, we calculate the yield of a proposed $P-$wave molecular state of $D_s \bar{D_{s0}}$, $Y^{\prime}(4274)$, characterized by a smaller width and smaller coupling constant obtained from the Weinberg compositeness condition., Comment: 7 pages, 5 figures

Using the coalescence model we compute the multiplicity of $Z_{cs} (3985)^-$ (treated as a compact tetraquark) at the end of the quark gluon plasma phase in heavy ion collisions. Then we study the time evolution of this state in the hot hadron gas phase. We calculate the thermal cross sections for the collisions of the $Z_{cs} (3985)^-$ with light mesons using effective Lagrangians and form factors derived from QCD sum rules for the vertices $Z_{cs}\bar{D}_{s }^* D $ and $Z_{cs} \bar{D}_{s} D^{*}$. We solve the kinetic equation and find how the $Z_{cs} (3985)^-$ multiplicity is affected by the considered reactions during the expansion of the hadronic matter. A comparison with the statistical hadronization model predictions is presented. Our results show that the tetraquark yield increases by a factor of about $2-3$ from the hadronization to the kinetic freeze-out. We also make predictions for the dependence of the $Z_{cs} (3985)^-$ yield on the centrality, the center-of-mass energy and the charged hadron multiplicity measured at midrapidity $ \left[ d N_{ch} / d \eta (\eta < 0.5)\right]$., Comment: 9 pages, 8 figures

Analog models of black holes have unequivocally proven to be extremely beneficial in providing critical information regarding black hole spectroscopy, superradiance, quantum phenomena and most importantly Hawking radiation and black hole evaporation; topics that have either recently begun to bloom through gravitational wave observations or have not yet been investigated in astrophysical setups. Black hole analog experiments have made astonishing steps toward the aforementioned directions and are paramount in understanding the quantum nature of the gravitational field. Recently, a tabletop analog Schwarzschild black hole has been proposed by placing Bose-Einstein condensates of photons inside a mirror's cavity, leading to a sink with a radial vortex that represents a velocity singularity. Here, we provide an extensive spectral analysis of both the tabletop acoustic black hole and its higher-dimensional gravitational analog. We find that quasinormal modes and quasibound states share qualitative similarities in both systems and show that the eikonal quasinormal modes of the analog acoustic black hole have a photon-sphere-like interpretation, which points to the existence of a phonon sphere in the analog black hole. Our results, complemented with the recently calculated graybody factors and Hawking radiation of the acoustic analog, can provide a theoretical test bed for future tabletop experiments with condensates of light in a mirror's cavity and provide significant insights regarding classical and quantum phenomena in higher-dimensional black holes., Comment: 13 pages, 5 figures, 1 Appendix, published version

In this work we analyze the sound perturbation of Unruh's acoustic effective geometry in both (2+1) and (3+1) spacetime dimensions and present an exact analytical expression for the quasibound states of these idealized black-hole configurations by using a new approach recently developed, which uses the polynomial conditions of the hypergeometric functions. Our main goal is to discuss the effects of having an event horizon in such effective metrics. We also discuss the stability of the systems and present the radial eigenfunctions related to these quasibound state frequencies. These metrics assume just the form it has for a Schwarzschild black hole near the event horizon, and therefore may, in principle, shed some light into the underlying classical and quantum physics of astrophysical black holes through analog acoustic probes., Comment: 15 pages, 6 figures, 2 tables. Matches published version in PRD

We study the production of heavy multiquark states in the heavy ion collisions performed at the LHC. We assume that they are produced at the end of the quark-gluon plasma phase and then interact with light hadrons during the hadron gas phase. We use the coalescence model to compute the initial multiplicities and effective Lagrangians to describe the interactions. We find that the initial multiplicity of molecules is two orders of magnitude larger than that of tetraquarks. The interactions in the hadron gas reduce the number of molecules and increase the number of tetraquarks by a factor two in each case. At kinetic freeze-out, the difference is still very large., Comment: Talk presented at QCD22 (04-07/07/20222, Montpellier - FR). 4 pages, 3 figures

In this work we study the $D^*$ and $D$ multiplicities and how they change during the hadron gas phase of heavy ion collisions. With the help of an effective Lagrangian formalism, we calculate the production and absorption cross sections of the $D^*$ and $D$ mesons in a hadronic medium. We compute the time evolution of the abundances and the ratio $D^* /D$. They are approximately constant in time. Also, assuming a Bjorken type cooling and using an empirical relation between the freeze-out temperature and the central multiplicity density, we estimate $D^* /D$ as a function of $ dN /d \eta (\eta =0)$, which represents the system size. We find that, while the number of $D^*$'s and $D$'s grows significantly with the system size, their ratio remains approximately constant. This prediction can be compared with future experimental data. Our results suggest that the charm meson interactions in the hadron gas do not change their multiplicities and consequently these mesons are close to chemical equilibrium., Comment: 11 pages, 8 figures

In this work we study the interactions of the multiquark state $Z_{cs} (3985)^-$ with light mesons in a hot hadron gas. Using an Effective Lagrangian framework, we estimate the vacuum cross sections as well as the thermal cross sections of the production processes $ \bar{D}_{s}^{(*)} D_{s}^{(*)} \rightarrow Z_{cs}^- X \, (X=\pi , K, \eta) $ and the corresponding inverse reactions. The results indicate that the considered processes have sizeable cross sections. Most importantly, the thermal cross sections for $Z_{cs}$ annihilation are much larger than those for production. This feature might produce relevant effects on some observables, such as the final $Z_{cs}$ multiplicity, measured in heavy ion collisions., Comment: 8 pages; 6 figures

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

Astrophysical black holes are generally surrounded by accretion disks, galactic matter and the omnipresent cosmic microwave background radiation, thus allowing for the concurrent propagation of both gravitational and sound waves. Recently, acoustic black holes were embedded in Schwarzschild spacetime allowing for the coexistence of event and acoustic horizons. Here, we obtain a class of perturbative solutions to the field equations of the relativistic Gross-Pitaevskii and Yang-Mills theories, which describe sound waves propagating on a curved slowly-rotating acoustic black hole, akin to Lense-Thirring spacetime. We investigate the quasinormal mode frequencies, Hawking-Unruh radiation, and quasibound states. Our novel metric mimics the gravitational field of astrophysical compact objects in the limiting case of slow rotation, and therefore could, in principle, shed more light into the underlying classical and quantum physics of black holes through analog acoustic probes., Comment: 18 pages, 5 figures. Matches published version in PRD

We investigate the absorption and production processes of this new state in a hadronic medium, considering the reactions $T_{cc}^+ \pi, T_{cc}^+ \rho \rightarrow D^{(*)} D^{(*)} $ and the corresponding inverse reactions. We use effective field Lagrangians to account for the couplings between light and heavy mesons, and give special attention to the form factors in the vertices. We calculate here for the first time the $ T_{cc}^+ - D - D^*$ form factor derived from QCD sum rules. The results are also obtained by testing widely utilized empirical form factors. The absorption cross sections are found to be larger than the production ones. We compare our results with the only existing estimate of these quantities, presented in a work of J.~Hong, S.~Cho, T.~Song and S.~H.~Lee, in which the authors employed the quasi-free approximation. We find cross sections which are one order of magnitude smaller., Comment: 10 pages; 6 figures; v2: added a new Section and two Subsections with a comprehensive study of the influence of form factors on the results; empirical formulas have been tested and compared with those derived from QCD sum rules; the $ T_{cc}^+ - D - D^*$ form factor has been calculated with QCD sum rules for the first time

In this work, we follow the recently revisited f(R) theory of gravity for studying the interaction between quantum scalar particles and the gravitational field of a generalized black hole with an f(R) global monopole. This background has a term playing the role of an effective cosmological constant, which permits us to call it as Schwarzschild-Anti-de Sitter (SAdS) black hole with an f(R) global monopole. We examine the separability of the Klein-Gordon equation with a non-minimal coupling and then we discuss both the massless and massive cases for a conformal coupling. We investigate some physical phenomena related to the asymptotic behavior of the radial function, namely, the black hole radiation, the quasibound states, and the wave eigenfunctions., Comment: 13 pages, 7 figures

In this work we explore some mathematical physics aspects of the spherically symmetric Lovelock black hole in high dimensions. Intended for this aim, we thoroughly consider the metric corresponding to the five-dimensional Lovelock black hole spacetime. We construct the strong retractions by the geodesic equations on the background under consideration. As a result, from the topological point of view, we construct the theory of strong homotopy retract, which will allow us, in principle, to better understand some of its suitable applications on astrophysics and cosmology, in particular, in the analysis of the spacetime singularities. We find the solutions of the equation of motion for both radial and angular coordinates, and then we describe the outer ("exterior") and lower ("interior") apparent horizons. Indeed, the outer apparent horizon is the last surface from which the light waves could still escape from the black hole. Thus, it is meaningful to analyze some physical phenomena related to quantum particles propagating outside the exterior apparent horizon, in particular, we discuss the quasistationary levels of scalar fields and their radial wave functions, which are given in terms of the general Heun functions. We also calculate the perihelion precession in this background., Comment: 14 pages, 4 figures

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 examine the interaction between quantum test particles and the gravitational field generated by a black hole solution that was recently obtained in the consistent 4-dimensional Einstein-Gauss-Bonnet gravity. While quasinormal modes of scalar, electromagnetic, and Dirac fields have been recently studied in this theory, there is no such study for the quasibound states. Here, we calculate the spectrum of quasibound states for the test fields in a spherically symmetric and asymptotically flat black hole solution in the consistent 4-dimensional Einstein-Gauss-Bonnet gravity. The quasispectrum of resonant frequencies is obtained by using the polynomial condition associated to the general Heun functions. We also discuss the stability of the systems for some values of the Gauss-Bonnet coupling constant., Comment: 17 pages, 7 figures. Matches published version in Universe

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 study the recently proposed Schwarzschild acoustic black hole spacetime, in which we investigate some physical phenomena related to the effective geometry of this background, including the analogous Hawking radiation and the quasibound states. We calculate the spectrum of quasibound state frequencies and the wave functions on the Schwarzschild acoustic background by using the polynomial condition of the general Heun function, and then we discuss the stability of the system. We also compare the resonant frequencies of the Schwarzschild acoustic black hole with the ones by the standard Schwarzschild black hole. Our results may shed some light on the physics of black holes and their analog models in condensed matter. Moreover, these studies could provide the possibility, in principle, for laboratory testing of effects whose nature is unquestionably associated with purely quantum effects in gravity., Comment: 14 pages, 3 figures. Matches published version in PRD

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 study the interaction between massive scalar fields and the gravitational field produced by a higher dimensional Schwarzschild solution in a string cloud model. Exact analytical solutions of both angular and radial parts of the Klein--Gordon equation are obtained in terms of the three-dimensional spherical harmonics and general Heun functions, respectively. From these solutions, we examine the interesting physical phenomena related to the Hawking radiation and resonant frequencies., Comment: 19 pages, 4 figures, 4 tables

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 investigate the quantum evolution of the universe in the presence of two types of dark energies. First, we consider the phantom class ($\omega<-1$) which would be responsible for a super-accelerated cosmic expansion, and then we apply the procedure to an ordinary $\Lambda>0$ vacuum ($\omega=-1$). This is done by analytically solving the Wheeler-DeWitt equation with ordering term (WdW) in the cosmology of Friedmann-Robertson-Walker. In this paper, we find exact solutions in the scale factor $a$ and the ordering parameter $q$. For $q=1$ it is shown that the universe has a high probability of evolving from a big bang singularity. On the other hand, for $q = 0$ the solution indicates that an initial singularity is unlikely. Instead, the universe has maximal probability of starting with a finite well-defined size which we compute explicitly at primordial times. We also study the time evolution of the scale factor by means of the Hamilton-Jacobi equation and show that an ultimate big rip singularity emerges explicitly from our solutions. The phantom scenario thus predicts a dramatic end in which the universe would reach an infinite scale factor in a finite cosmological time as pointed by Caldwell et al. in a classical setup. Finally, we solve the WdW equation with ordinary constant dark energy and show that in this case the universe does not rip apart in a finite era., Comment: 16 pages, improved figures, some new relevant conclusions, 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

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

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

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 study the sound perturbation of a rotating acoustic black hole in the presence of a disclination. The radial part of the massless Klein-Gordon equation is written into a Heun form, and its analytical solution is obtained. These solutions have an explicit dependence on the parameter of the disclination. We obtain the exact Hawking-Unruh radiation spectrum., Comment: 6 pages

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

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

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: This paper has been withdrawn by the author because was unified and published with arXiv:1603.02233

We study the sound perturbation of the hydrodynamic vortex geometry and present an exact expression for the resonant frequencies (quasispectrum) of this geometry. Exact solution for the radial part of the covariant Klein-Gordon equation in this spacetime is obtained, and is given in terms of the double confluent Heun functions. We found that the resonant frequencies are complex number., Comment: 9 pages, 1 figure

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., Comment: 13 pages, 4 figures

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., $mM\ll 1$., Comment: New version with 15 pages and 3 figures. To appear in JCAP

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. The wave functions as well as the energy levels codify the role played by the cosmological constant., Comment: 15 pages, 2 figures

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. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation spectrum and the energy flux., Comment: 21 pages. arXiv admin note: substantial text overlap with arXiv:1405.7846, arXiv:1401.5397, arXiv:1406.6884

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., Comment: 26 pages, with erratum. arXiv admin note: text overlap with arXiv:1405.7846

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. We also investigate the solutions in regions near and far from the event horizon. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation of massive scalar particles., Comment: 6 pages

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., Comment: 5 pages. accepted for publication in Revista Brasileira de Ensino de F\'{i}sica (RBEF). arXiv admin note: text overlap with arXiv:astro-ph/0309756 by other authors

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., Comment: 25 pages

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 regions near the event horizon and far from the black hole., Comment: 13 pages