Optical Definition of Gravity Under Static Conditions

The experiment of Pound & Repka shows that light undergoes a frequency shift in the gravitational field of the earth in accordance with General Relativity. Conversely, in the static case, we can use only the observed frequency shifts to define the gravitational field, presupposing the (constant) 3-geometry of the 3-space slices is known. The latter can be probed in principle by rigid rods, but more elegantly by the light geometry as developed by Abramowicz, shortly reviewed here. Our optical definition is independent of the theory of relativity. However, in the second part, we show that, in the static case, it coincides with the predictions for the acceleration of test particles in General Relativity. For the non-static case, our definition of gravity is no substitute for that one given in General Relativity. However, the static case is sufficient for certain discussions about the validity of the Principle of Equivalence.     

Nonstationary motion of a shell on the surface of a heavy fluid

A three-dimensional nonstationary problem of vibrations of a flexible shell moving on the surface of an ideal heavy fluid. The forces due to surface tension are ignored. The problem is formulated in the space of the acceleration potential. The potential of the pulsating source is found by solving the Euler equation and the continuity equation taking into account the free-surface conditions (linear theory of small waves) and the conditions at infinity. The density distribution function of the dipole layer is determined from the boundary conditions on the surface of the shell. Formulas for determining the shape of gravity waves on the fluid surface and the natural frequencies of vibrations of the shell are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 66–75, July–August, 2009.     

New Agegraphic Dark Energy in Brans-Dicke Theory

In this paper, we investigate the new agegraphic dark energy model in the framework of Brans-Dicke theory, which is a natural extension of the Einstein's general relativity. In this framework the form of the new agegraphic dark energy density takes as ρ_q =3n² φ(t) η^-2, where η is the conformalage of the universe and φ(t) is the Brans-Dicke scalar field representing the inverse of the time-variable Newton's constant. We derive the equation of state of the new agegraphic dark energy and the deceleration parameter of the universe in the Brans-Dicke theory. It is very interesting to find that in the Brans-Dicke theory the agegraphic dark energy realizes quintom-like behavior,i.e., its equation of state crosses the phantom divide w=-1 duringthe evolution. We also compare the situation of the agegraphic darkenergy model in the Brans-Dicke theory with that in the Einstein'stheory. In addition, we discuss the new agegraphic dark energy modelwith interaction in the framework of the Brans-Dicke theory.     

Condensation and evolution of a space–time network

In this work, we try to propose in a novel way, using the Bose and Fermi quantum network approach, a framework studying condensation and evolution of a space–time network described by the Loop quantum gravity. Considering quantum network connectivity features in Loop quantum gravity, we introduce a link operator, and through extending the dynamical equation for the evolution of the quantum network posed by Ginestra Bianconi to an operator equation, we get the solution of the link operator. This solution is relevant to the Hamiltonian of the network, and then is related to the energy distribution of network nodes. Showing that tremendous energy distribution induces a huge curved space–time network may indicate space time condensation in high-energy nodes. For example, in the case of black holes, quantum energy distribution is related to the area, thus the eigenvalues of the link operator of the nodes can be related to the quantum number of the area, and the eigenvectors are just the spin network states. This reveals that the degree distribution of nodes for the space–time network is quantized, which can form space–time network condensation. The black hole is a sort of result of space–time network condensation, however there may be more extensive space–time network condensations, such as the universe singularity (big bang).     

Internal gravity waves in critical generation modes and in the vicinity of trajectories of motion of perturbation sources

The field of internal gravity waves in a layer of an arbitrary stratified fluid is studied for critical generation modes and in the vicinity of trajectories of motion of the perturbation sources. The exact solutions describing the structure of a separate mode of the wave field in the vicinity of the perturbation source in the critical generation modes are investigated, and expressions for the total field representing the sum of all wave modes are obtained. In the vicinity of the trajectories of the perturbation sources, asymptotic representations of the eigenfunctions and eigenvalues of the basic vertical spectral problem of internal waves are constructed in the approximation of large wave numbers and asymptotic expressions for a separate mode of the wave field are obtained that describe the spatial structure and features of the fields of internal gravity waves. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 70–79, September–October, 2008.     

Numerical simulation of plane and spatial nonlinear stationary waves in a two-layer fluid of arbitrary depth

The solution of a model differential equation for the three-dimensional perturbations of the interface between two immiscible fluids of different densities lying between a stationary nondeformable bottom and cover is presented. It is assumed that the waves have an arbitrary length and small, though finite, amplitude. The shapes of stationary traveling internal waves, both periodic in the two horizontal coordinates and soliton-like, are presented. These shapes depend on different parameters of the problem: the direction of the perturbation wave vector and the fluid layer depth and density ratios.     

Spin-Spin Interactions in Gauge Theory of Gravity, Violation of Weak Equivalence Principle and New Classical Test of General Relativity

For a long time, it has been generally believed that spin-spin interactions can only exist in a theory where Lorentz symmetry is gauged, and a theory with spin-spin interactions is not perturbatively renormalizable. But this is not true. By studying the motion of a spinning particle in gravitational field, it is found that there exist spin-spin interactions in gauge theory of gravity. Its mechanism is that a spinning particle will generate gravitomagnetic field in space-time, and this gravitomagnetic field will interact with the spin of another particle, which will cause spin-spin interactions. So, spin-spin interactions are transmitted by gravitational field. The form of spin-spin interactions in post Newtonian approximations is deduced. This result can also be deduced from the Papapetrou equation. This kind of interaction will not affect the renormalizability of the theory. The spin-spin interactions will violate the weak equivalence principle, and the violation effects are detectable. An experiment is proposed to detect the effects of the violation of the weak equivalence principle.     

Matter Loops Corrected Modified Gravity in Palatini Formulation

Recently, corrections to the standard Einstein-Hilbert action were proposed to explain the current cosmic acceleration in stead of introducing dark energy. In the Palatini formulation of those modified gravity models, there is an important observation due to Arkani-Hamed: matter loops will give rise to a correction to the modified gravity action proportional to the Ricci scalar of the metric. In the presence of such a term, we show that the current forms of modified gravity models in Palatini formulation, specifically, the 1/R gravity and ln R gravity, will have phantoms. Then we study the possible instabilities due to the presence of phantom fields. We show that the strong instability in the metric formulation of 1/R gravity indicated by Dolgov and Kawasaki will not appear and the decay timescales for the phantom fields may be long enough for the theories to make sense as effective field theory . On the other hand, if we change the sign of the modification terms to eliminate the phantoms, some other inconsistencies will arise for the various versions of the modified gravity models. Finally, we comment on the universal property of the Palatini formulation of the matter loops corrected modified gravity models and its implications.     

Logarithmic Entropy Corrected Holographic Dark Energy with F(R,T) Gravity

In this paper, we consider F(R,T) gravity as a linear function of the curvature and torsion scalars and interact it with logarithmic entropy corrected holographic dark energy to evaluate cosmology solutions. The model is investigated by FRW metric, and then the energy density and the pressure of dark energy are calculated. Also we obtain equation of state (EoS) parameter of dark energy and plot it with respect to both variable of redshift and e-folding number. Finally, we describe the scenario in three status: early, late and future time by e-folding number.     

Throughflow and g-jitter effects on binary fluid saturated porous medium

A non-autonomous complex Ginzburg-Landau equation (CGLE) for the finite amplitude of convection is derived, and a method is presented here to determine the amplitude of this convection with a weakly nonlinear thermal instability for an oscillatory mode under throughflow and gravity modulation. Only infinitesimal disturbances are considered. The disturbances in velocity, temperature, and solutal fields are treated by a perturbation expansion in powers of the amplitude of the applied gravity field. Throughflow can stabilize or destabilize the system for stress free and isothermal boundary conditions. The Nusselt and Sherwood numbers are obtained numerically to present the results of heat and mass transfer. It is found that throughflow and gravity modulation can be used alternately to heat and mass transfer. Further, oscillatory flow, rather than stationary flow, enhances heat and mass transfer.