Presence Of Gravitation Research Articles

Conservation laws and invariant solutions of the wave equation on Bianchi I space–time: A comprehensive analysis

In accordance with Einstein’s theory of general relativity, gravity is a phenomenon attributed to the curvature of spacetime. This notion has allowed physicists to investigate behaviour of physical processes, with respect to different curved spacetime, occurring in the presence of gravitation. One of the most basic of these processes is wave propagation whose various behaviours due to curvature effects have been investigated in the literature. This present study exhaustively explores the invariant solutions of the wave equation on Bianchi I space–time using Lie symmetry method. Under the isotropic Bianchi I universe, we showed how the aforementioned wave equation is connected to one of the most important equations encountered in the heat and mass transfer theory. Furthermore, we completely classify its conservation laws when the potentials are O(tω) for any parameter ω.

On the Semiclassical Approach of the Heisenberg Uncertainty Relation in the Strong Gravitational Field of Static Blackhole

Heisenberg Uncertainty and Equivalence Principle are the fundamental aspect respectively in Quantum Mechanic and General Relativity. Combination of these principles can be stated in the expression of Heisenberg uncertainty relation near the strong gravitational field i.e. pr and Et . While for the weak gravitational field, both relations revert to pr and Et. It means that globally, uncertanty principle does not invariant. This work also shows local stationary observation between two nearby points along the radial direction of blackhole. The result shows that the lower point has larger uncertainty limit than that of the upper point, i.e. . Hence locally, uncertainty principle does not invariant also. Through Equivalence Principle, we can see that gravitation can affect Heisenberg Uncertainty relation. This gives the impact to our’s viewpoint about quantum phenomena in the presence of gravitation. Key words: Heisenberg Uncertainty Principle , Equivalence Principle, and gravitational field

Relativistic potential of Weyl: a gateway to quantum physics in the presence of gravitation?

The well-noted correspondence between gravitation and electrodynamics emphasizes the importance of the Lanczos tensor—the potential of the Weyl tensor—which is an inherent structural element of any metric theory of gravity formulated in a 4-dimensional pseudo Riemannian spacetime. However, this ingenious discovery has gone largely unnoticed. We elucidate this important quantity by deriving its expressions in some particularly chosen spacetimes and try to find out what it represents actually. We find out that the Lanczos potential tensor does not represent the potential of the gravitational field, as is ascertained by various evidences. Rather, it is enriched with various signatures of quantum character, which provides a novel insight into the heart of a geometric embodiment of gravity.

On Derivation and Classification of Vlasov Type Equations and Equations of Magnetohydrodynamics. The Lagrange Identity, the Godunov Form, and Critical Mass

The derivation of the Vlasov–Maxwell and the Vlasov–Poisson–Poisson equations from Lagrangians of classical electrodynamics is described. The equations of electromagnetohydrodynamics (EMHD) type and electrostatics with gravitation are obtained. We obtain and compare the Lagrange equalities and their generalizations for different types of the Vlasov and EMHD equations. The conveniences of writing the EMHD equations in twice divergent form are discussed. We analyze exact solutions to the Vlasov–Poisson–Poisson equations with the presence of gravitation where we have different types of nonlinear elliptic equations for trajectories of particles with critical mass m2 = e2/G, which has an obvious physical sense, where G denotes the gravitation constant and e is the electron charge. As a consequence we have different behaviors of particles: divergence or collapse of their trajectories.

The Quantum Mechanics as Also a Case of the Ether Elasticity Theory

The Schrodinger equation ensues from the following axiom: in Cartesian coordinates and in absence of gravitation, to the component , (), of the momentum tensor is associated the operator . We show here this equation is a particular case of the equation that governs, even in presence of gravitation, the oscillatory displacements of the points of the ether shown to be a specific elastic medium. That is to say that the Schrodinger equation of which the solutions are the scalar state functions is a particular case of the equation of the vectorial waves propagated in the ether. As shown in previous publications, a mobile particle is a superposition of these waves that form a globule moving like this particle; here we show, in particular that, in a bound state, it is the interferences of these waves that creates the so called “quantum states”. The ether elasticity theory therefore do not only generalizes the quantum mechanics, but also gives the physical signification of the quantum phenomena.

On the Meaning of the Principle of General Covariance

We present a definite formulation of the Principle of General Covariance (GCP) as a Principle of General Relativity with physical content and thus susceptible of verification or contradiction. To that end it is useful to introduce a kind of coordinates, that we call quasi-Minkowskian coordinates (QMC), as an empirical extension of the Minkowskian coordinates employed by the inertial observers in flat space-time to general observers in the curved situations in presence of gravitation. The QMC are operationally defined by some of the operational protocols through which the inertial observers determine their Minkowskian coordinates and may be mathematically characterized in a neighbourhood of the world-line of the corresponding observer. It is taken care of the fact that the set of all the operational protocols which are equivalent to measure a quantity in flat space-time split into inequivalent subsets of operational prescriptions under the presence of a gravitational field or when the observer is not inertial. We deal with the Hole Argument by resorting to the tool of the QMC and show how it is the metric field that supplies the physical meaning of coordinates and individuates point-events in regions of space-time where no other fields exist. Because of that the GCP has also value as a guiding principle supporting Einstein’s appreciation of its heuristic worth in his reply to Kretschmann in 1918.

Plane thermal transpiration of a rarefied gas in the presence of gravitation

Plane thermal transpiration of a rarefied gas that flows horizontally in the presence of gravitation is studied based on the Boltzmann equation. Assuming that the temperature gradient along the walls is small, the asymptotic analysis for a slow variation in the flow direction is conducted. The semi-analytical solution that is valid for arbitrary values of the mean free path and the gravitational strength is derived, and the problem is reduced to solving the spatially one-dimensional Boltzmann equation. This reduced problem is solved numerically for a hard-sphere molecular gas for small values of gravitational strength, and the behavior of the flow is studied based on the numerical solution. The effect of weak gravitation is no longer negligible when the gas is so rarefied that the mean free path is comparable to the maximum range that the molecules travel along the parabolic path within the channel. This phenomenon has been observed in the plane Poiseuille flow of a highly rarefied gas, and a similar phenomenon also occurs in the plane thermal transpiration considered in the present paper.

Density gradient effects on the magnetorotational instability

The effects of the equilibrium density gradient on non-axisymmetric magnetorotational instability are investigated in a pure axial magnetic field for ideal incompressible plasmas. A second-order ordinary differential equation is employed to determine the magnetic field perturbation and the full dispersion relationship regarding the non-axisymmetric magnetohydrodynamic instability in the presence of gravitation and density gradient effects. By means of local linear analysis, the reduced dispersion relationship is derived with a small azimuthal wavenumber. Spatial variations in the radial field perturbation magnitude cannot be neglected in the calculation since this term has the same order of magnitude as LD, which is the scale length of radial density gradient. The analytical expression of the instability growth rate is presented. Our analysis shows that the instability criterion is modified by the density gradient which has a stabilizing effect when increasing outwards and conversely a destabilizing effect when decreasing outwards. The growth rate increases with LD when LD is small. For a sufficiently large LD, the growth rate decreases with increasing LD. The magnetic field exerts a similar effect on the growth rate and can totally quench the instability. The non-axisymmetric effect introduces a frequency shift and increases the growth rate but does not affect the instability criterion.

Optical anisotropy of schwarzschild metric within equivalent medium framework

It is has been long known that the curved space in the presence of gravitation can be described as a non-homogeneous anisotropic medium in flat geometry with different constitutive equations. In this article, we show that the eigenpolarizations of such medium can be exactly solved, leading to a pseudo-isotropic description of curved vacuum with two refractive index eigenvalues having opposite signs, which correspond to forward and backward travel in time. We conclude that for a rotating universe, time-reversal symmetry is broken. We also demonstrate the applicability of this method to Schwarzschild metric and derive exact forms of refractive index. We derive the subtle optical anisotropy of space around a spherically symmetric, non-rotating and uncharged blackhole in the form of an elegant closed-form expression, and show that the refractive index in such a pseudo-isotropic system would be a function of coordinates as well as the direction of propagation. Corrections arising from such anisotropy in the bending of light are shown and a simplified system of equations for ray-tracing in the equivalent medium of Schwarzschild metric is found.

Role of gravitation in solving a haptic comparison problem

The effect of haptic perception-reproduction task performed by means of a force feedback handle was studied under ground-based conditions and on board an orbital station. In contrast to visual perception, which exhibits a pronounced domination of vertically and horizontally oriented stimuli in such experiments, haptic perception did not display a dependence of responses on the tilt of the reference stimulus in the presence or absence of gravity. Thus, when solving a purely haptic problem, the CNS uses only proprioception, even in the presence of gravitation.

Nonlinear transport in a binary mixture in the presence of gravitation

The effect of gravity on the tracer particles immersed in a dilute gas of mechanically different particles and subjected to the steady planar Couette flow is analyzed. The results are obtained from the Gross–Krook (GK) kinetic model of a binary mixture and the description applies for arbitrary values of both velocity and temperature gradients. The GK equation is solved by means of a perturbation method in powers of the field around a nonequilibrium state which retains all the hydrodynamic orders in the shear rate a and the thermal gradient ε. To first order in the gravity field, we explicitly determine the hydrodynamic profiles and the partial contributions to the momentum and heat fluxes associated with the tracer species. All these quantities are given in terms of a, ε, and the mass and size ratios. The shear-rate dependence of some of these quantities is illustrated for several values of the mass ratio showing that in general, the effect of gravity is more significant when the particles of the gas are lighter than the tracer particles.

Dyon field equations in the presence of gravitation

Maxwell’s-Dirac field equations of dyons are formulated in the presence of gravitation and the corresponding Lorentz force equation of motion, energy-momentum tensor and Einstein’s field equations are derived consistently from an invariant action principle.

Covariance in General Relativity and Scale-Covariance in Scale-Relativity Theory, Quadratic Invariants and Leibniz Rule

We recall the principle of general covariance which allows us, in general relativity, to deduce laws of physics which hold in the presence of gravitation from laws which hold without gravitation, and which is implemented by the minimal prescription ( η μν ,∂ α )→ ( g μν ,∇ α ). Then, we examine the formal prescription of scale-relativity theory from which we should be able to deduce laws which hold at quantum scales from laws which hold at classical scales. This prescription requires us to replace, in classical equations, the total time derivatives d/d t by a scale-covariant derivative d/d t. We show that such a prescription has actually to be extended. Indeed, it does not allow us to obtain a whole set of complex scale-covariant equations, which yield, in all cases, the right corresponding quantum equations. We exhibit many basic cases for which the substitution ( η μν , ∂ α )→ ( g μν ,∇ α ) is efficient in general relativity, while the prescription d/d t→d/d t does not lead to the right equations in scale-relativity. These cases concern the Hamilton–Jacobi equation, the form of energy — more generally the quadratic invariants — and the electromagnetic case. Indeed, we find that the usual quadratic form of nonrelativistic and relativistic invariants does not hold in this framework and that a divergence term appears in addition to the quadratic term. Moreover, we find that a current term is present with the Lorentz force in the equations of motion with an electromagnetic field. Finally, we point out that the operator d/d t does not fulfil the Leibniz rule. We show that this fact may be related to the canonical commutation relations in quantum mechanics. Moreover, we show how it would be possible to connect, in a systematic way, the use of this operator with many relations of quantum mechanics, in particular, those where differential relations appear to be given by the correspondence principle. Finally, we show that we can recover the usual form of many equations — especially the fundamental Leibniz rule — by extending the above-mentioned prescription by introducing a symmetric product .

Nonlinear heat transport in a dilute gas in the presence of gravitation

In this paper we evaluate corrections to the Navier-Stokes constitutive equations induced by the action of a gravitational field $\mathbf{g}=\ensuremath{-}g\mathbf{z}\^{}$ in a gas subjected to a thermal gradient parallel to a field with no convection. The analysis is performed from an exact perturbation solution of the Boltzmann equation for Maxwell molecules through second order in the field. The reference state (zeroth-order approximation) corresponds to the exact solution of the Boltzmann equation in the pure planar Fourier flow, which holds for arbitrary values of the thermal gradient. The results show that the pressure tensor becomes anisotropic, so that the momentum flux along the field direction is enhanced: ${(P}_{z}z\ensuremath{-}p)/p\ensuremath{\approx}{14.4(p}^{\ensuremath{-}2}{\ensuremath{\eta}}^{2}g\ensuremath{\partial}\mathrm{ln}T/\ensuremath{\partial}{z)}^{2}$. In addition, the heat flux increases (decreases) with respect to its Navier-Stokes value when the gas is heated from above (below): ${q}_{z}{/q}_{z}^{\mathrm{NS}}\ensuremath{-}1\ensuremath{\approx}{20.7(p}^{\ensuremath{-}2}{\ensuremath{\eta}}^{2}g\ensuremath{\partial}\mathrm{ln}T/\ensuremath{\partial}z)$.

Geometro-stochastically quantized fields with internal spin variables

The use of internal variables for the description of relativistic particles with arbitrary mass and spin in terms of scalar functions is reviewed and applied to the stochastic phase space formulation of quantum mechanics. Following Bacry and Kihlberg a four-dimensional internal spin space S̄ is chosen possessing an invariant measure and being able to represent integer as well as half integer spins. S̄ is a homogeneous space of the group SL(2,C) parametrized in terms of spinors α∈C2 and their complex conjugates ᾱ. The generalized scalar quantum mechanical wave functions may be reduced to yield irreducible components of definite physical mass and spin [m,s], with m⩾0 and s=0,12,1,32,… , with spin described in terms of the usual (2s+1)-component fields. Viewed from the internal space description of spin this reduction amounts to a restriction of the variable α to a compact subspace of S̄, i.e., a “spin shell” Sr=2s2 of radius r=2s in C2. This formulation of single particles or single antiparticles of type [m,s] is then used to study the geometro-stochastic (i.e., quantum) propagation of amplitudes for arbitrary spin on a curved background space–time possessing a metric and axial vector torsion treated as external fields. A Poincaré gauge covariant path integral-like representation for the probability amplitude (generalized wave function) of a particle with arbitrary spin is derived satisfying a second order wave equation on the Hilbert bundle constructed over curved space–time. The implications for the stochastic nature of polarization effects in the presence of gravitation are pointed out and the extension to Fock bundles of bosonic and fermionic type is briefly mentioned.

Hamiltonian Poincaré gauge theory of gravitation

We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of gravitation, and to gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincaré group, taken as the local spacetime group of the gravitational gauge theory, with SO(3) as the classification subgroup. The Wigner-like rotation induced by the nonlinear approach singles out the role of time and allows us to deal with ordinary SO(3) vectors. We apply the general result to the Einstein - Cartan action, study the constraints, and obtain Einstein's classical equations in the extremely simple form of time evolution equations of the coframe. As a consequence of our approach, we identify the gauge-theoretical origin of the Ashtekar variables.

Bifurcation of the equivariant minimal interfaces in a hydromechanics problem

In this work we study a deformation of the minimal interface of two fluids in a vertical tube under the presence of gravitation. We show that a symmetry of the base of tube let us to apply a method developed earlier by the first author and based on the Crandall‐Rabinowitz bifurcation theorem. Using the natural symmetry of the corresponding variational problem defined by a symmetry of region and restricting the functional to spaces of invariant functions we show the existence of bifurcation, and describe its local picture, for interfaces parametrized by the square and disc.

Shock wave propagation in non-ideal fluids

Expressions for the variation of shock strength and its propagation in non-ideal fluids are presented by using the method developed by Whitham. The effects of the presence of rotation, rotation and magnetic field on the strength and propagation velocity of shock waves have been discussed separately. Finally, the effects of the presence of gravitation on the shock strength and on propagation velocity have been studied.

Quantized fiber dynamics for extended elementary objects involving gravitation

The geometro-stochastic quantization of a gauge theory for extended objects based on the (4, 1)-de Sitter group is used for the description of quantized matter in interaction with gravitation. In this context a Hilbert bundle ℋ over curved space-time B is introduced, possessing the standard fiber ℋ\(_{\bar \eta }^{(\rho )} \), being a resolution kernel Hilbert space (with resolution generator\(\tilde \eta \)and generalized coherent state basis) carrying a spin-zero phase space representation of G=SO(4, 1) belonging to the principal series of unitary irreducible representations determined by the parameter ρ. The bundle ℋ, associated to the de Sitter frame bundle P(B, G), provides a geometric arena with built-in fundamental length parameter R (taken to be of the order of 10−13 cm characterizing hadron physics) yielding, in the presence of gravitation, a quantum kinematical framework for the geometro-stochastic description of spinless matter described in terms of generalized quantum mechanical wave functions, Ψxρ(ξ, ζ), defined on #x210B;. By going over to a nonlinear realization of the de Sitter group with the help of a section ξ(x) on the soldered bundle E, associated to P, with homogeneous fiber V′4⋍G/H, one is able to recover gravitation in a de Sitter gauge invariant manner as a gauge theory related to the Lorentz subgroup H of G. ξ(x) plays the dual role of a symmetry-reducing and an extension field. After introducing covariant bilinear source currents in the fields Ψxρ(ξ, ζ) and their adjoints determined by G-invariant integration over the local fibers in ℋ, a quantum fiber dynamical (QFD) framework is set up for the dynamics at small distances in B determining the geometric quantities beyond the classical metric of Einstein's theory through a set of current-curvature field equations representing the source equations for axial vector torsion and the de Sitter boost contributions to the bundle connection (the latter defining the soldering forms of the Cartan connection in P(B, G) in the nonlinear gauge). The presented bundle framework yields a theory for quantized material objects in interaction with gravitation, the long-range metrical part of which remains classical.

Diamagnetic Abundance Differentiation in the Solar System

Chemical abundances in the solar corona or solar wind compared to those in the photosphere differentiate according to first ionization potential (FIP). We suggest that the effect is the result of diamagnetic diffusion pumps operating in the presence of gravitation and diverging magnetic structures. We then comment briefly on implications concerning abundances in the solar system and chemically peculiar stars.