International Journal of Modern Physics D

Trajectories of the third body in the Restricted Problem of Three Bodies including a Yukawa term to the Newtonian gravitational potential are analyzed. It is shown that this modified gravitational potential changes some important aspects of the Restricted Problem of Three Bodies. Depending of coupling constant α, motions obtained in the pure Newtonian case are qualitatively different when Yukawa term is included. Depending of coupling parameters α, the nature of dynamics change from regular to chaotic (α<0) or from chaotic to regular (α>0) and in both cases using the same length scales λ.

According to the teleparallel equivalent of general relativity, curvature and torsion are two equivalent ways of describing the same gravitational field. Though equivalent, they act differently: curvature yields a geometric description, in which the concept of gravitational force is absent whereas torsion acts as a true gravitational force, quite similar to the Lorentz force of electrodynamics. As a consequence, the right-hand side of a spinless-particle equation of motion (which would represent a gravitational force) is always zero in the geometric description, but not in the teleparallel case. This means that the gravitational coupling prescription can be minimal only in the geometric case. Relying on this property, a new gravitational coupling prescription in the presence of curvature and torsion is proposed. It is constructed in such a way to preserve the equivalence between curvature and torsion, and its basic property is to be equivalent to the usual coupling prescription of general relativity. According to this view, no new physics is connected with torsion, which is just an alternative to curvature in the description of gravitation. An application of this formulation to the equations of motion of both a spinless and a spinning particle is discussed.

In the heterotic superstring theory, the decay constant of the QCD axion lies within the range 3×10¹⁶≲f_aGeV≲10¹⁸, the lower limit referring to the model-independent axion, while the upper limit is due to dimension-five, non-renormalizable effects first calculated by Cvetič. Consequently, the neutralino χ⁰, assumed to be a nearly pure B-ino, decays into the axino ã on the time scale obtained by Covi et al., , which is ≲10^-3 times the age of the Universe t₀≈4×10¹⁷s, but can only be made less than the time t≈1s of the onset of Big-Bang nucleosynthesis by revising m_χ⁰ to an unnaturally high level, m_χ⁰≳500 TeV. Therefore, it is necessary to set the coefficient C_aYY=0, which is possible for the Kim–Shifman–Vainshtein–Zakharov invisible-axion model if the electric charge q_c of the heavy-quark colour representation C vanishes. The neutralino does not then decay and can constitute some fraction of the dark matter of the Universe, depending upon the value of m_χ⁰ (for a gaugino-dominated state, where is the SU(2) singlet slepton). The consequences of an ultra-light axion with f_a≈10¹⁸GeV are also discussed.

We study the distortion of electron neutrino energy spectrum due to oscillations with the sterile neutrino ν_e↔ν_s, for different initial populations of the sterile state δN_s at the onset of oscillations. The influence of this spectrum distortion on Big Bang Nucleosynthesis is analyzed. Only the case of an initially empty sterile state was studied in previous publications.

The primordial abundance of ⁴He is calculated for all possible δN_s:0≤δN_s≤1 in the model of oscillations, effective after electron neutrino decoupling, for which the spectrum distortion effects on the neutron–proton transitions are the strongest.

It is found that the spectrum distortion effect may be dominant, not only in the case of small δN_s, but also in the case of large initial population of ν_s. For example, in the resonant case it may play a considerable role even for very large δN_s~0.8. Cosmological constraints on neutrino mixing for small δN_s are discussed.

A theoretical attempt to identify the physical process responsible for the afterglow emission of Gamma-Ray Bursts (GRBs) is presented, leading to the occurrence of thermal emission in the comoving frame of the shock wave which gives rise to the bursts. The determination of the luminosities and spectra involves integration over an infinite number of Planckian spectra, weighted by appropriate relativistic transformations, each one corresponding to a different viewing angle in the past light cone of the observer. The relativistic transformations have been computed using the equations of motion of GRBs within our theory, giving special attention to the determination of the equitemporal surfaces. The only free parameter of the present theory is the "effective emitting area" in the shock wave front. A self-consistent model for the observed hard-to-soft transition in GRBs is also presented. When applied to GRB 991216 a precise fit (χ²≃1.078) of the observed luminosity in the 2–10 keV band is obtained. Similarly, detailed estimates of the observed luminosity in the 50–300 keV and in the 10–50 keV bands are obtained.

In this paper a new small parameter associated with the density matrix deformation (density pro-matrix) studied in previous works of the author is introduced into the Generalized Quantum Mechanics (GQM), i.e. quantum mechanics involving description of the Early Universe. It is noted that this parameter has its counterpart in the Generalized Statistical Mechanics. Both parameters offer a number of merits: they are dimensionless, varying over the interval from 0 to 1/4, and assuming in this interval a discrete series of values. Besides, their definitions contain all the fundamental constants. These parameters are very small for the conventional scales and temperatures, e.g. the value of the first parameter is on the order of ≈10^-66+2n, where 10^-n is the measuring scale and the Planck scale ~ 10^-33cm is assumed. The second one is also too small for the conventional temperatures, that is those much below the Planck temperature. It is demonstrated that relative to the first of these parameters the Universe may be considered as a nonuniform lattice in the four-dimensional hypercube with dimensionless finite-length (1/4) edges. And the time variable is also described by one of the above-mentioned dimensions due to the second parameter and Generalized Uncertainty Relation in thermodynamics. In this context the lattice is understood as a deformation rather than approximation.

A conventional explanation of the correlation between the linear and the angular accelerations of Pioneer 10/11 spacecraft is given. First, the rotational Doppler shift analysis is improved. Finally, a relation between the radio beam reaction force and the spin-rate change is established. Computations are found in good agreement with observational data. Our analysis leads us to the conclusion that the Pioneer anomaly may not necessarily be due to systematics.

We study a closed model of a universe filled with viscous fluid and quintessence matter components. The dynamical equations imply that the universe might look like an accelerated flat Friedmann–Robertson–Walker (FRW) universe at low redshift. We consider here dissipative processes which obey a causal thermodynamics. Here, we account for the entropy production via causal dissipative inflation.

Bekenstein argues that the horizon area of a black hole has a constant distance spectrum. We investigate the effects of such a discrete spectrum on the thermodynamics of a Schwarzchild black hole (SBH) and a Schwarzchild–de Sitter black hole (SdBH), in terms of the time-energy uncertainty relation and Stefan–Boltzman law. For the massive SBH, a negative and logarithmic correction to the Bekenstein–Hawking entropy is obtained, as well as other authors by using other methods. As to the minimal hole near the Planck scale, its entropy is no longer proportional to the horizon area, but is of order of the mass of the hole. This is similar to an excited stringy state. The vanishing heat capacity of such a minimal black hole implies that it may be a remnant as the ground state of the evaporating hole. The properties of a SdBH are similar to the SBH, except for an additional term of square area associated with the cosmological constant. In order to maintain the validity of the Bekenstein–Hawking formula, the cosmological constant is strongly limited by the size of the biggest black hole in the universe. A relation associated with the cosmological constant, Planck area and the Stefan–Boltzman constant is obtained. The cosmological constant is not only related to the vacuum energy, but is also related to the thermodynamics.

NASA has been considering a solar sail that would accelerate a craft to a high velocity (~14 AU/yr) by the time it reached 5 AU. Then the sail would be dropped and the craft would coast alone to deep space. We propose that the sail be retained longer. Then the density of the interplanetary medium could be determined by measuring the drag force on the huge sail using radiometric navigational data. Such an experiment would yield an independent, new type of measurement of the interplanetary medium and should be pursued.

We study some interesting properties of the de Broglie gravitational waves. In particular, we investigate the properties of the polarization and the energy momentum tensor and the geodesic deviation associated with these waves. We observe that the polarization tensor has both transverse and longitudinal components and depends on the wave number. We find a new effect which does not occur in the standard gravitational waves. Our waves are responsible of a longitudinal shift of test particles placed along the direction of propagation. The amplitude of the shift decreases when the velocity of the source becomes closer to the speed of light; so slow massive particles must be used for an experimental test of the theory.

The condensation of fermion bilinears in the dimensionally-reduced, E₈×E'₈ heterotic superstring theory often refers to the E'₈ hidden-sector gauginos, but in principle condensation may also occur in the compactified internal space, for example of the gravitino and the spin-1/2 Majorana–Weyl field λ of eleven-dimensional supergravity. This possibility, raised by Duff and Orzalesi as a method of spontaneous compactification that maintains vanishing vacuum energy (cosmological constant), was subsequently considered in the context of the heterotic superstring theory by Helayël–Neto and Smith and by the present author, assuming the internal-space gravitinos to condense close to the compactification scale M_c~M_P/10. Here, by including the four-fermion terms in the Lagrangian density ℒ, we point out that the observable-sector gravitinos ψ_i and gauginos g typically have comparable, but not identical, masses m_3/2~m_g~M_c as a result of this process. Hence, such condensation is only permitted either at the much lower scale (as for the hidden-sector gaugino condensation), so that , the upper limit on m_g ensuring that the Higgs doublets are sufficiently light or, more plausibly, by setting 1TeV~m_g≪m_3/2~M_c, which requires a constraint on the condensate parameters. If the three-index field also condenses, then the vacuum expectation value of the dimensionless combination of the dilaton A_r and modulus B_r is fixed at a scale ~1, thus yielding the Kähler potential K and hence m_3/2~M_c Since B_r is determined from supersymmetry, this mechanism determines A_r.

In this paper the massless Duffin–Kemmer–Petiau equation in a nonstationary rotating, causal Gödel-type cosmological background is studied. Exact solutions of the corresponding field equation are obtained and used to calculate the frequency spectrum of photon in nonstationary Gödel-type universe. To compare the results found with the classical field solutions, we also solved Maxwell's equations as given in the appendix.

Dynamics of relativistic outflows along the rotation axis of a Kerr black hole is investigated using a simple model that takes into account the relativistic tidal force of the central source as well as the Lorentz force due to the large-scale electromagnetic field which is assumed to be present in the ambient medium. The evolution of the speed of the flow relative to the ambient medium is studied. In the force-free case, the resulting equation of motion predicts rapid deceleration of the initial flow and an asymptotic relative speed with a Lorentz factor of . In the presence of the Lorentz force, the long-term relative speed of the clump tends to the ambient electrical drift speed.

We study stability, dispersion and dissipation properties of four numerical schemes (Itera-tive Crank–Nicolson, 3rd and 4th order Runge–Kutta and Courant–Fredrichs–Levy Nonlinear). By use of a Von Neumann analysis we study the schemes applied to a scalar linear wave equation as well as a scalar nonlinear wave equation with a type of nonlinearity present in GR-equations. Numerical testing is done to verify analytic results. We find that the method of lines (MOL) schemes are the most dispersive and dissipative schemes. The Courant–Fredrichs–Levy Nonlinear (CFLN) scheme is most accurate and least dispersive and dissipative, but the absence of dissipation at Nyquist frequency, if fact, puts it at a disadvantage in numerical simulation. Overall, the 4th order Runge–Kutta scheme, which has the least amount of dissipation among the MOL schemes, seems to be the most suitable compromise between the overall accuracy and damping at short wavelengths.