Emil M. Prodanov

Nearly-Hamiltonian Structure for Water Waves with constant vorticity

Abstract.We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.

Pseudo-Newtonian Potential for Charged Particle in Kerr-Newman Geometry

Abstract We consider the equatorial circular motion of a test particle of specific charge q ≪ m in the Kerr–Newman geometry of a rotating charged black hole. We find the particles conserved energy and conserved projection of the angular momentum on the black holes axis of rotation as corrections, in leading order of q / m , to the corresponding energy and angular momentum of a neutral particle. We determine the centripetal force acting on the test particle and, consequently, we find a classical pseudo-Newtonian potential with which one can mimic this general relativistic problem.

Cyclic Universe with an Inflationary Phase from a Cosmological Model with Real Gas Quintessence

Phase-plane stability analysis of a dynamical system describing the Universe as a two-fraction fluid containing baryonic dust and real virial gas quintessence is presented. Existence of a stable periodic solution experiencing inflationary periods is shown. A van der Waals quintessence model is revisited and cyclic Universe solution again found.

Hamiltonian Dynamics of Cosmological Quintessence Models

Abstract The time-evolution dynamics of two nonlinear cosmological real gas models has been reexamined in detail with methods from the theory of Hamiltonian dynamical systems. These examples are FRWL cosmologies, one based on a gas, satisfying the van der Waals equation and another one based on the virial expansion gas equation. The cosmological variables used are the expansion rate, given by the Hubble parameter, and the energy density. The analysis is aided by the existence of global first integral as well as several special (second) integrals in each case. In addition, the global first integral can serve as a Hamiltonian for a canonical Hamiltonian formulation of the evolution equations. The conserved quantities lead to the existence of stable periodic solutions (closed orbits) which are models of a cyclic Universe. The second integrals allow for explicit solutions as functions of time on some special trajectories and thus for a deeper understanding of the underlying physics. In particular, it is shown that any possible static equilibrium is reachable only for infinite time.

Daemon decay and inflation

Abstract Quantum tunneling in Reissner–Nordstrom geometry is studied and the tunneling rate is determined. A possible scenario for cosmic inflation, followed by reheating phases and subsequent radiation-domination expansion, is proposed.

On the Field Equations of Kaluza’s Theory

Abstract The field equations of the original Kaluzas theory are analyzed and it is shown that they lead to modification of Einsteins equations. The appearing extra energy–momentum tensor is studied and an example is given where this extra energy–momentum tensor is shown to allow four-dimensional Schwarzschild geometry to accommodate electrostatics. Such deviation from Reissner–Nordstrom geometry can account for the interpretation of Schwarzschild geometry as resulting not from mass only, but from the combined effects of mass and electric charge, even electric charge alone.

Dynamical analysis of an n−H−T cosmological quintessence real gas model with a general equation of state

The cosmological dynamics of a quintessence model based on real gas with general equation of state is presented within the framework of a three-dimensional dynamical system describing the time evolution of the number density, the Hubble parameter and the temperature. Two global first integrals are found and examples for gas with virial expansion and van der Waals gas are presented. The van der Waals system is completely integrable. In addition to the unbounded trajectories, stemming from the presence of the conserved quantities, stable periodic solutions (closed orbits) also exist under certain conditions and these represent models of a cyclic Universe. The cyclic solutions exhibit regions characterized by inflation and deflation, while the open trajectories are characterized by inflation in a “fly-by” near an unstable critical point.

Haunted Kaluza universe with four-dimensional Lorentzian flat, Kerr, and Taub–NUT slices

Abstract The duality between the original Kaluzas theory and Kleins subsequent modification is duality between slicing and threading decomposition of the five-dimensional spacetime. The field equations of the original Kaluzas theory lead to the interpretation of the four-dimensional Lorentzian Kerr and Taub–NUT solutions as resulting from static electric and magnetic charges and dipoles in the presence of ghost matter and constant dilaton, which models Newtons constant.

Standard cosmology on a self-tuning domain wall

Abstract We investigate the cosmology of (4+1)-dimensional gravity coupled to a scalar field and a bulk anisotropic fluid within the context of the single-brane Randall–Sundrum scenario. Assuming a separable metric, a static fifth radius and the scalar to depend only on the fifth direction, we find that the warp factor is given as in the papers of Kachru, Schulz and Silverstein “Phys. Rev. D 62 (2000) 045021, Phys. Rev. D (2000) 085003” and that the cosmology on a self-tuning brane is standard. In particular, for a radiation-dominated brane the pressure in the fifth direction vanishes.

A Remark on Schwarz's Topological Field Theory

The standard evaluation of the partition function Z of Schwarzs topological field theory results in the Ray–Singer analytic torsion. Here we present an alternative evaluation which results in Z=1. Mathematically, this amounts to a novel perspective on analytic torsion: it can be formally written as a ratio of volumes of spaces of differential forms which is formally equal to 1 by Hodge duality. An analogous result for Reidemeister combinatorial torsion is also obtained.