General Gravitational Field Research Articles

Mathematical Modeling of Refraction Characteristics of Electromagnetic Radiation at Stochastic Gravitational Field

Numerical-analytical modeling is used for estimation of gravitational noise influence on propagation of electromagnetic radiation at gravitational field of a group of astrophysical objects. The method bases on numerical integrate of system of light differential equations in the Euler’s form, added differential equations for calculation of statistic moments of side fluctuations of light at a picture plane of observer. The influence of gravitation was taken into account by introducing of the effective refraction index of vacuum, expressed through a gravitational potential. Visions about spatial correlation function of inhomogeneities of effective refraction index of vacuum are used as model. Calculating of gravitation effects of group astrophysical objects are performed under assumption additive contribution of field of every objects in general gravitational field. Modeling of the refraction characteristics of electromagnetic radiation is performed for a various configurations of gravitation field. Results of calculating are shown at a picture plane of observer. The blurring effects of gravitational lensing are investigated at dependence from position of localized area of gravitational noise and astrophysical objects. It’s showed that for case of single-component gravitational field full coverage of object by area of gravitational noise match maximum blurring of lensing effect. The features of gravitational focusing are determined at dependence from position of area noise for asymmetrical twocomponent gravitational field, where one of objects coverage by area of gravitational noise. Offered tool of modeling can be used for both investigation of gravitational lensing of multi-component gravitational field in presence variety of limited area of gravitational noise and under conditions uniform spatial distribution of stochastic gravitational inhomogeneities. Also it can use for recovering of gravitational potentials of non-radiating (hidden) objects by characteristics of received electromagnetic radiation of remote space sources.

Newtonian gravitational waves from a continuum

Gravitational waves are being shown to derive directly from Newtonian dynamics for a continuous mass distribution, e.g. compressible fluids or equivalent. It is shown that the equations governing a continuous mass distribution, i.e. the inviscid Navier–Stokes equations for a general variable gravitational field g ( t , x ) , are equivalent to a form identical to the Maxwell equations from electromagnetism, subject to a specified condition. The consequence of this equivalence is the creation of gravity waves that propagate at a finite speed. The latter implies that Newtonian gravitation as presented in this paper is not ‘spooky action at a distance’ but rather is similar to electromagnetic waves propagating at finite speed, despite the apparent form appearing in the integrated field formula. In addition, this proves that, in analogy to the Maxwell equations, the Newtonian gravitation equations are Lorentz invariant for waves propagating at the speed of light. Since gravitational waves were so far derived only from Einstein’s general relativity theory, it becomes appealing to check if there is a connection between the Newtonian waves presented in this paper and the general relativity type of waves at least in a certain limit of overlapping validity, i.e. as a flat-space approximation. The latter is left for follow-up research.

Macroscopic Effect of Quantum Gravity in General Static Isotropic Gravitational Field

In this paper we calculated the self-interaction of the gravitational field, and analyzed the effect of the self-interactions in a general staticisotropic gravitational field using a semi classical approach. We found that the effects of the self-interaction on the gravitational field can be used to explain dark matter.

Quantum scattering of fermion by gravitational field with Kerr metric

Neutrinoless double beta decay has not been observed so far, and its existence cannot be disproved. Therefore the question whether neutrinos are Majorana particles is still inconclusive. In this paper, we hope to investigate the possibility of distinguishing neutrino fermion types by gravitational fields from the perspective of gravitational scattering of fermions. The Levi-Civita connection is decomposed according to the parity transformation. Under the perturbation therory of gravitational field to fermion quantum scattering and weak gravitational approximation, it is found that the difference between Dirac and Majorana fermion quantum scattering matrix elements of general metric gravitational field comes from similar vector parts under parity transformation; the scattering of the gravitational field on the Kerr metric confirms that the difference in scattering among different types of fermions is related to the angular momentum of the Kerr gravitational source, whose scattering matrix elements are proportional to the square of the product of the mass of the gravitational source and the angular momentum. The above results provide another possible way to distinguish fermion types by gravitational fields.

Post-Newtonian corrections to Schrödinger equations in gravitational fields

In this paper we extend the WKB-like ‘non-relativistic’ expansion of the minimally coupled Klein–Gordon equation after (Kiefer and Singh 1991 Phys. Rev. D 44 1067–76; Lämmerzahl 1995 Phys. Lett. A 203 12–7; Giulini and Großardt 2012 Class. Quantum Grav. 29 215010) to arbitrary order in c−1, leading to Schrödinger equations describing a quantum particle in a general gravitational field, and compare the results with canonical quantisation of a free particle in curved spacetime, following (Wajima et al 1997 Phys. Rev. D 55 1964–70). Furthermore, using a more operator-algebraic approach, the Klein–Gordon equation and the canonical quantisation method are shown to lead to the same results for some special terms in the Hamiltonian describing a single particle in a general stationary spacetime, without any ‘non-relativistic’ expansion.

Robin Boundary Condition for Casimir Plates in a General Weak Gravitational Field

AbstractThe energy of the massless scalar field inside parallel Casimir plates in a general weak gravitational field under the influence of Robin boundary conditions is calculated. The mode frequencies are found in asymptotic limits and consistency of results with the literature is shown. Experimental evidence for detection of corrections is explored.

Electromagnetic thermal corrections to Casimir energy

In [B. Nazari, Mod. Phys. Lett. A 31, 1650007 (2016)], we calculated finite temperature corrections to the energy of the Casimir effect of two conducting parallel plates in a general weak gravitational field. The calculations was done for the case a scalar field was present between the plates. Here we find the same results in the presence of an electromagnetic field.

Thermal corrections to the Casimir energy in a general weak gravitational field

We calculate finite temperature corrections to the energy of the Casimir effect of a two conducting parallel plates in a general weak gravitational field. After solving the Klein–Gordon equation inside the apparatus, mode frequencies inside the apparatus are obtained in terms of the parameters of the weak background. Using Matsubara’s approach to quantum statistical mechanics gravity-induced thermal corrections of the energy density are obtained. Well-known weak static and stationary gravitational fields are analyzed and it is found that in the low temperature limit the energy of the system increases compared to that in the zero temperature case.

Casimir effect of two conducting parallel plates in a general weak gravitational field

We calculate the finite vacuum energy density of the scalar and electromagnetic fields inside a Casimir apparatus made up of two conducting parallel plates in a general weak gravitational field. The metric of the weak gravitational field has a small deviation from flat spacetime inside the apparatus and we find it by expanding the metric in terms of small parameters of the weak background. We show that the found metric can be transformed via a gauge transformation to the Fermi metric. We solve the Klein-Gordon equation exactly and find mode frequencies in Fermi spacetime. Using the fact that the electromagnetic field can be represented by two scalar fields in the Fermi spacetime, we find general formulas for the energy density and mode frequencies of the electromagnetic field. Some well-known weak backgrounds are examined and consistency of the results with the literature is shown.

Dirac particle spin in strong gravitational fields

Dynamics of the Dirac particle spin in general strong gravitational fields is discussed. The Hermitian Dirac Hamiltonian is derived and transformed to the Foldy-Wouthuysen (FW) representation for an arbitrary metric. The quantum mechanical equations of spin motion are found. These equations agree with corresponding classical ones. The new restriction on the anomalous gravitomagnetic moment (AGM) by the reinterpretation of Lorentz invariance tests is obtained.

Scalar particle in general inertial and gravitational fields and conformal invariance revisited

The new manifestation of conformal invariance for a massless scalar particle in a Riemannian spacetime of general relativity is found. Conformal transformations conserve the Hamiltonian and wave function in the Foldy-Wouthuysen representation. Similarity of manifestations of conformal invariance for massless scalar and Dirac particles is proved. New exact Foldy-Wouthuysen Hamiltonians are derived for both massive and massless scalar particles in a general static spacetime and in a frame rotating in the Kerr field approximated by a spatially isotropic metric. The latter case covers an observer on the ground of the Earth or on a satellite and takes into account the Lense-Thirring effect. High-precision formulas are obtained for an arbitrary spacetime metric. General quantum-mechanical equations of motion are derived. Their classical limit coincides with corresponding classical equations.

Energy-momentum pseudotensor of relic gravitational waves in an expanding universe

We study the energy-momentum pseudotensor of gravitational waves, and examine the one introduced by Landau-Lifshitz for a general gravitational field and the effective one recently used in literature. In the short-wavelength limit after the Brill-Hartle average, both lead to the same gauge-invariant stress tensor of gravitational waves. For relic gravitational waves in the expanding universe, we examine two forms of pressure, ${p}_{\mathrm{gw}}$ and ${\mathcal{P}}_{\mathrm{gw}}$, and trace the origin of their difference to a coupling between gravitational waves and the background matter. The difference is shown to be negligibly small for most cosmic expansion stages starting from inflation. We demonstrate that the wave equation is equivalent to the energy-conservation equation using the pressure ${\mathcal{P}}_{\mathrm{gw}}$ that includes the mentioned coupling.

Dirac fermions in strong gravitational fields

We discuss the dynamics of the Dirac fermions in the general strong gravitational and electromagnetic fields. We derive the general Hermitian Dirac Hamiltonian and transform it to the Foldy-Wouthuysen representation for the spatially isotropic metric. The quantum operator equations of motion are obtained and the semiclassical limit is analyzed. The comparison of the quantum mechanical and classical equations shows their complete agreement. The helicity dynamics in strong fields is discussed. Squaring the covariant Dirac equation explicitly shows a similarity of the interactions of electromagnetic and gravitational fields with a charged and spinning particle.

Analogue Gravity.

Analogue gravity is a research programme which investigates analogues of general relativistic gravitational fields within other physical systems, typically but not exclusively condensed matter systems, with the aim of gaining new insights into their corresponding problems. Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity).

THE HIERARCHY PROBLEM, RADION MASS, LOCALIZATION OF GRAVITY AND 4D EFFECTIVE NEWTONIAN POTENTIAL IN STRING THEORY ON S1/Z2

In this paper, we present a systematical study of braneworlds of string theory on S1/Z2. In particular, starting with the toroidal compactification of the Neveu–Schwarz/Neveu–Schwarz sector in D + d dimensions, we first obtain an effective D-dimensional action, and then compactify one of the D - 1 spatial dimensions by introducing two orbifold branes as its boundaries. We divide the whole set of the gravitational and matter field equations into two groups, one holds outside the two branes, and the other holds on them. By combining the Gauss–Codacci and Lanczos equations, we write down explicitly the general gravitational field equations on each of the two branes, while using distribution theory we express the matter field equations on the branes in terms of the discontinuities of the first derivatives of the matter fields. Afterwards, we address three important issues: (i) the hierarchy problem; (ii) the radion mass; and (iii) the localization of gravity, the four-dimensional Newtonian effective potential and the Yukawa corrections due to the gravitational high-order Kaluza–Klein (KK) modes. The mechanism of solving the hierarchy problem is essentially the combination of the large extra dimension and warped factor mechanisms together with the tension coupling scenario. With very conservative arguments, we find that the radion mass is of the order of 10-2 GeV. The gravity is localized on the visible brane, and the spectrum of the gravitational KK modes is discrete and can be of the order of TeV. The corrections to the four-dimensional Newtonian potential from the higher order of gravitational KK modes are exponentially suppressed and can be safely neglected in current experiments. In an appendix, we also present a systematical and pedagogical study of the Gauss–Codacci equations and Israel's junction conditions across a (D - 1)-dimensional hypersurface, which can be either spacelike or timelike.

Numerical aspects of low Mach number flows in astrophysics: preconditioning techniques

Internal flows inside gravitationally stable astrophysical objects, such as the Sun, normal and compact stars, are rotating, highly compressed and extremely subsonic. Such low Mach number flows are usually encountered when studying, for example, the dynamo action in stars and planets or the nuclear burst on neutron stars and white dwarfs. Handling of such flows numerically on time-scales longer than the dynamical one is complicated and challenging. The aim of this paper is to address the numerical problems associated with the modelling of internal quasi-stationary, rotating low Mach number flows in stars and to discuss possible solution scenarios. It is shown that the quasi-symmetric approximate factorization method (AFM) as a pre-conditioner within a non-linear Newton-type defect-correction solution procedure is best suited for modelling quasi-stationary weakly compressible flows with moderate low Mach numbers. This method is robust as it can be applied to model time-dependent compressible flows without further modifications. The AFM-pre-conditioning techniques are shown to be extendable into three dimensions with an arbitrary equation of state. Classical dimensional splitting techniques, however, such as the alternating direction implicit or line-Gauss–Seidel methods are not suited for modelling compressible low Mach number flows. It is also argued that hot and low Mach number astrophysical flows cannot be considered as an asymptotic limit of incompressible flows, but rather as highly compressed flows with extremely stiff pressure terms. We show that, unlike the pseudo-pressure in incompressible fluids, a Poisson-like treatment for the pressure would smooth unnecessarily physically induced acoustic perturbations, thereby violating the conservation of the total energy. Results of several hydrodynamical calculations are presented, which demonstrate the capability of the solver to search for solutions, that correspond to stationary, viscous and rotating flows with a Mach number as small as as well as to fluid flows that are subject to ultra-strong Newtonian and general relativistic gravitational fields.

Semiclassical bosonic D-brane boundary states in curved spacetime

Abstract In this paper we discuss the existence of quantum D-brane states in the strong gravitational field and in the presence of a constant Kalb-Ramond field. A semiclassical string quantization method in which the spacetime metric g AB and the constant antisymmetric Kalb-Ramond field b AB are treated exactly is employed. In this framework, the semiclassical D-branes are defined at the first order perturbation around the trajectory of the center-of-mass of a string. The set of equations the semiclassical D-branes must satisfy in a general strong gravitational field are given. These equations are solved in the AdS background where it is shown that a D-brane coherent state exists if the operators that project the string fields onto the corresponding Neumann and Dirichlet directions satisfy a set of algebraic constraints. A second set of equations that should be satisfied by the projectors in order that the semiclassical state be compatible with the global structure of the D-brane are derived in the particle limit of a string in the torsionless AdS background.

Role of the form of an angular velocity inflection in the stability of the gas-dust component of plane galaxies

The stability of a rotating gas-dust gravitating disk in the zone of a possible inflection in the angular velocity is examined theoretically. The stability limits are found for a rather wide range of curves in a special model of a dusty, pressure-free medium with the general gravitational field of the galaxy taken into account. Applications to real galaxies are discussed.

Deformed surfaces in holographic interferometry. Similar aspects in general gravitational fields

In the first part some principles of the large deformation analysis in holographic Interferometry are briefly outlined. This may also give a link to the second part here. Modifications of the set-up at the reconstruction should recover the previously invisible fringes. The spacing and the contrast of them are characterized by the fringe and visibility vectors. The relevant derivative of the path difference involves the polar decomposition of the deformation gradient into strain and rotation and the image aberration implies further changes of geodesic curvature and of surface curvatures. In the second part these considerations lead then to similar aspects for hypersurfaces, before all to an interpretation by two virtual deformations for the Schwarzschild-solution of the gravitation. That is further usefull for non-spherical gravitational fields, for the invariants there and for the TOV-relation between pressure and density. The null-geodesics or light rays can also be interpreted by these virtual deformations. An approach towards the Kerr-solution for rotating stars is added. As for the linearisation a connection is outlined which confirms the non-existence of gravitational waves.

Asymptotic structure of radiation in higher dimensions

We characterize a general gravitational field near conformal infinity (null, spacelike or timelike) in spacetimes of any dimension. This is based on an explicit evaluation of the dependence of the radiative component of the Weyl tensor on the null direction from which infinity is approached. Behaviour similar to a peeling property is recovered, and it is shown that the directional structure of radiation has a universal character that is determined by the algebraic type of the spacetime. This is a natural generalization of analogous results obtained previously in the four-dimensional case.