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

Phonon induced Superconductivity of High Temperatures in Electrical Graphene Superlattices

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. Pairing of two onsite electrons with one electron close to the ${\bf K}$ and the other close to the $-{\bf K}$ point is the most stable pair formation. The resulting order parameter is almost constant over the entire SL.Comment: 10 pages, 2 figure

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

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

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

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

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

Comment on "Does the transverse electric zero mode contribute to the Casimir effect for a metal?"

Recently J.S. Hoye, I.Brevik, J.B. Aarseth, and K.A. Milton [Phys. Rev. E v.67, 056116 (2003); quant-ph/0212125] proposed that if the Lifshitz formula is combined with the Drude model, the transverse electric zero mode does not contribute to the result for real metals and there arises a linear temperature correction to the Casimir force at small temperatures. The authors claim that in spite of the fact that the Casimir entropy in their approach is negative, the Nernst heat theorem is satisfied. In the present Comment we show that the authors' conclusion regarding the Nernst heat theorem is in error. We demonstrate also the resolution of this thermodynamic puzzle based on the use of the surface impedance instead of the Drude dielectric function. The results of numerical computations obtained by the authors are compared with those from use of the surface impedance approach which are thermodynamically consistent.Comment: 6 pages, 3 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