Acoustic black holes: massless scalar field analytic solutions and analogue Hawking radiation

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:1405.784

Lagrangian formulation of Newtonian cosmology

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 author

Class of solutions of the Wheeler-DeWitt equation in the Friedmann-Robertson-Walker universe

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 figure

Confluent Heun functions and the physics of black holes: resonant frequencies, Hawking radiation and scattering of scalar waves

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:1603.0224

Quantum Newtonian cosmology and the biconfluent Heun functions

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 figure

Ground State Energy of Massive Scalar Field in the Global Monopole Background

We consider the ground state energy of scalar massive field in the spacetime of a pointlike global monopole. Using zeta function regularization method we obtain the heat kernel coefficients for this system. We show that the coefficient $B_1$ contains additional contribution due to the non-trivial topological structure of the spacetime. Taking into account the heat kernel coefficients we obtain that the ground state energy of the scalar field is zero. We also discuss our result using dimensional considerations.Comment: 8 pages, RevTex, no figure

On the extension of Jackiw's scalar theory to (2+1)- dimensional gravity

We study some aspects of three-dimensional gravity by extending Jackiw's scalar theory to (2+1)-dimensions and find a black hole solution. We show that in in general this teory does not possess a Newtonian limit except for special metric configurations.Comment: 11 pages, LATEX fil

Remarks on some quantum effects in the spacetime of a cosmic string

We study the behaviour of a non-relativistic quantum particle interacting with different potentials, in the background spacetime generated by a cosmic string. We find the energy spectra for the quantum systems under consideration and discuss how they differ from their flat Minkowski spacetime values.Comment: 17 pages, LATEX fil

Analytic solutions in the dyon black hole with a cosmic string: scalar fields, Hawking radiation and energy flux

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:1406.688

Hydrogen atom in the gravitational fields of topological defects

We consider a hydrogen atom in the background spacetimes generated by an infinitely thin cosmic string and by a point-like global monopole. In both cases, we find the solutions of the corresponding Dirac equations and we determine the energy levels of the atom. We investigate how the geometric and topological features of these spacetimes leads to shifts in the energy levels as compared with the flat Minkowski spacetime.Comment: 17 pages, LATEX fil