M. E. Kahil
Recently, path equations have been obtained for charged, spinning objects in brane world models, using a modified Bazanski Lagrangian. In this study, path deviation equations of extended objects are derived. The significance of moving extended objects in brane world models is examined. Motion in non- symmetric brane world models is also considered.
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Paths of test particles, rotating and charged objects in brane-worlds using a modified Bazanski Lagrangian are derived. We also discuss the transition to their corresponding equations in four dimensions. We then make a comparison between the given equations in brane-worlds (BW) and their analog in space-time-matter (STM) theory.
Path and path deviation equations for neutral, charged, spinning and spinning charged test particles, using a modified Bazanski Lagrangian, are derived. We extend this approach to strings and branes. We show how the Bazanski Lagrangian for charged point particles and charged branes arises `a la Kaluza-Klein from the Bazanski Lagrangian in 5-dimensions.
A covariant simultaneous action for branes in an arbitrary curved background spacetime is considered. The action depends on a pair of independent field variables, the brane embedding functions, through the canonical momentum of a reparametrization invariant geometric model for the brane, and an auxiliary vector field. The form of the action is analogous to a symplectic potential. Extremization of the simultaneous action produces at once the equations of motion and the Jacobi equations for the brane geometric model, and it also provides a convenient shortcut towards its second variation. In thi…
The problem of motion for different test particles, charged and spinning objects of constant spinning tensor in different versions of bimetric theory of gravity is obtained by deriving their corresponding path and path deviation equations, using a modified Bazanski in presence of Riemannian geometry. This method enables us to find path and path deviation equations of different objects orbiting very strong gravitational fields.
Path and path deviation equations for charged, spinning and spinning charged objects in different versions of Kaluza-Klein (KK) theory using a modified Bazanski Lagrangian have been derived. The significance of motion in five dimensions, especially for a charged spinning object, has been examined. We have also extended the modified Bazanski approach to derive the path and path deviation equations of a test particle in a version of non-symmetric KK theory.
Motion of Spinning and Spinning Deviation Density Tensors in Riemannian Geometry
本文基于Bazanski拉格朗日量推导了扩展客体自旋密度及偏差张量的运动方程，并探讨了变质量运动与自旋流体特例，将其与广义相对论规范理论相联系。
Fractal Clifford Spaces (FCS) may be considered as a challenging approach to the unification of micro-physics and macro-physics. Trajectories of these manifolds are described by different poly-vectors describing paths and their deviation equations for not only to test particles but also for charged, rotating and rotating charged objects. Due to relaxing the condition of differentiability for all extended objects in the manifold. In this approach, a specialized Bazanski Lagrangian will be discussed to describe the fractal version of extended objects in a fractal space-time.
Dilaton gravity with general brane localized interactions is investigated. Models with corrections up to arbitrary order in field derivatives are considered. Effective gravitational equations of motion at the brane are derived in the covariant approach. Dependence of such brane equations on the bulk quantities is discussed. It is shown that the number of the bulk independent brane equations of motion depends strongly on the symmetries assumed for the model and for the background. Examples with two and four derivatives of the fields are presented in more detail.
Analytic solutions for the motion of spinning particles near brane-world black hole
本研究得到膜世界时空中旋转测试粒子运动方程的解析解与轨道频率偏移，发现潮汐电荷减小会增大节点及近星点进动（近星点进动效应随自旋增强），为该时空下带自旋极端质量比旋进引力波形研究提供基础。
We investigate the motion of a test particle in higher dimensions due to the presence of extended sources like D$p$-branes by studying the motion in the transverse space of the brane. This is contrasted with the motion of a point particle in the Schwarzschild background in higher dimensions. Since D$p$-branes are specific to 10-dimensional space time and exact solutions of geodesic equations for this particular space time has not been possible so far for the Schwarzschild background, we focus here to find the leading order solution of the geodesic equation (for motion of light rays). This enab…
Equations of non-geodesic and non-geodesic deviations for different particles are obtained, using a specific type of classes of the Bazanski Lagrangian. Such type of paths has been found to describe the problem of variable mass in the presence of Riemannian geometry. This may give rise to detect the effect of dark matter which reveals the mystery of motion of celestial objects that are not responding neither to Newtonian nor Einsteinian gravity. An important link between non-geodesic equations and the dipolar particle or fluids has been introduced to apply the concept of geometization of physi…
The idea that the quantum space-time of microphysics may be fractal everywhere was intensively investigated recently, and several authors have presented the geodesic equations of different fractal space - times. In the present work we obtain the geodesic and the geodesic deviation equations in fractal space-times by using the Bazanski method. We also extend this approach to obtain the equations of motion for spinning and spinning charged particles in the above-mentioned spaces, in a similar way to their counterparts in Riemannian geometry.
In this note, we consider the equations of motion for charged branes in AdS space and show that they can be cast into one-dimensional coupled Toda type. Then we solve the equations of motion to construct static charged AdS brane solutions which are invariant under translation along $p$ directions and have toroidal symmetry. The solutions are described by mass, charges and a dilaton coupling constant.
We consider intersecting black branes with strong gravitational waves propagating along their worldvolume in the context of supergravity theories. Both near-horizon and space-filling gravitational wave modes are included in our ansatz. The equations of motion (originally, partial differential equations) are shown to reduce to ordinary differential equations, which include a Toda-like system. For special arrangements of intersecting black branes, the Toda-like system becomes integrable, permitting a more thorough analysis of the gravitational equations of motion.
We consider branes as "points" in an infinite dimensional brane space ${\cal M}$ with a prescribed metric. Branes move along the geodesics of ${\cal M}$. For a particular choice of metric the equations of motion are equivalent to the well known equations of the Dirac-Nambu-Goto branes (including strings). Such theory describes "free fall" in ${\cal M}$-space. In the next step the metric of ${\cal M}$-space is given the dynamical role and a corresponding kinetic term is added to the action. So we obtain a background independent brane theory: a space in which branes live is ${\cal M}$-space and …
We obtain the most general static intersecting brane solutions by directly solving the relevant equations of motion analytically and in complete generality. These solutions reduce to the known ones in special cases, and contain further a class of new static solutions which are horizonless. We describe their properties and discuss their physical relevance. Along the way, we also describe the features of the brane energy momentum tensors, the equations of motion, and their solutions which arise as consequences of the intersection rules and the U duality symmetries of M theory.
We give the equations of motion for a self-gravitating Dirac p-brane embedded in an even co-dimension spacetime. The dynamics of the bulk are dictated by Lovelock gravity and permit matching conditions, even when the codimension is strictly greater than 2. We show that the equations of motion involve both induced Lovelock densities on the brane and regular extrinsic curvature terms. The brane dynamics can be derived from an exact (p+1)-dimensional induced action. The Dirac charge is carried by an overall (solid) angle defect which sets the Planck scale on the brane. In particular, if the codim…
By carefully analyzing the geodesic motion of a test particle in the bulk of brane worlds, we identify an extra force which is recognized in spacetime of one lower dimensions as a non-gravitational force acting on the particle. Such extra force acts on the particle in such a way that the conventional particle mechanics in one lower dimensions is violated, thereby hinting at the higher-dimensional origin of embedded spacetime in the brane world scenario. We obtain the explicit equations describing the motion of the bulk test particle as observed in one lower dimensions for general gravitating c…
Brane motion in a compact space: adiabatic perturbations of brane-bulk coupled fluids
本文研究膜在紧致空间中运动时，与体流体耦合的膜流体绝热扰动的传播，发现非耗散情形下的有效声速可能超光速，对膜世界宇宙学有重要影响。
End of the World Branes from Dimensional Reduction
本文研究对黑洞 Wick 转动得到的雪茄几何做维度约化后涌现的世界尽头膜，通过体与边界运动方程推导其张力，并在 M 理论特定背景中发现张力呈 exp(-3Phi) 行为，从而揭示 0A 型弦理论强耦合区域存在此类膜。
The topology of extra dimensions can break global Lorentz invariance,singling out a globally preferred frame even in flat spacetime. Through experiments that probe global topology, an observer can determine her state of motion with respect to the preferred frame. This scenario is realized if we live on a brane universe moving through a flat space with compact extra dimensions. We identify three experimental effects due to the motion of our universe that one could potentially detect using gravitational probes. One of these relates to the peculiar properties of the twin paradox in multiply-conne…
The vacuum solutions in brane gravity differ from those in 4D by a number of additional terms and reduce to the familiar Schwarzschild metric at small distances. We study the possible roles that such terms may play in the precession of planetary orbits, bending of light, radar retardation and the anomaly in mean motion of test bodies. Using the available data from Solar System experiments, we determine the range of the free parameters associated with the linear term in the metric. The best results come from the anomalies in the mean motion of planets. Such studies should shed some light on the…
In this paper we have considered the structure of the non-projectable Horava-Melby-Thompson (HMT) gravity to find braneworld scenarios. A relativistic scalar field is considered in the matter sector and we have shown how to reduce the equations of motion to first-order differential equations. In particular, we have studied thick brane solutions of both the dilatonic and Randall-Sundrum types.
We propose a mechanism of reheating after inflation in multi-throat scenarios of warped extra dimensions. Validity of an effective field theory on the standard model (SM) brane requires that the position of the SM brane during inflation be different from the position after inflation. The latter is supposed to be near the tip of the SM throat but the former is not. After inflation, when the Hubble expansion rate becomes sufficiently low, the SM brane starts moving towards the tip and eventually oscillates. The SM fields are excited by the brane motion and the universe is reheated. Since interac…
We study inflation arising from the motion of a BPS D3-brane in the background of a stack of k parallel D5-branes. There are two scalar fields in this set up-- (i) the radion field R, a real scalar field, and (ii) a complex tachyonic scalar field chi living on the world volume of the open string stretched between the D3 and D5 branes. We find that inflation is realized by the potential of the radion field, which satisfies observational constraints coming from the Cosmic Microwave Background. After the radion becomes of order the string length scale l_s, the dynamics is governed by the potentia…
In this note we study the possibility of obtaining dark energy solution in a D-brane scenario in a warped background that includes brane-position dependent corrections for the non-perturbative superpotential. The volume modulus is stabilized at instantaneous minima of the potential. Though the model can account for the existence of dark energy within present observational bound - fine-tuning of the model parameters becomes unavoidable. Moreover, the model does not posses a tracker solution.
We consider the motion of test particles in a thick brane version of Randall-Sundrum type II model. It is known that gravity alone cannot explain the confinement of test particles in this kind of brane. In this paper we show that a stable confinement in a domain wall is possible by admitting a direct interaction between test particles and a scalar field. This interaction is implemented by a modification of the Lagrangian of the particle which is inspired by a Yukawa-type interaction between fermions and scalar fields.
We study braneworlds in a five dimensional bulk, where cosmological expansion is mimicked by motion through AdS$_5$. We show that the five dimensional graviton reduces to the four dimensional one in the late time approximation of such braneworlds. Inserting a fixed regulator brane far from the physical brane, we investigate quantum graviton production due to the motion of the brane. We show that the massive Kaluza-Klein modes decouple completely from the massless mode and they are not generated at all in the limit where the regulator brane position goes to infinity. In the low energy limit, th…
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this generalized dynamics to the motion of test particles in a static, spherically symmetric metric. A significant consequence of the new framework is to generate an effective negative pressure on a cosmological surface whose expansion is manifest by the particle trajectory via embedding geometry \cite{bwg,embed2,embed,pal}. This formalism thus may give rise to a s…
I point out a symmetry, between equations of state for polytropic fluids, in the equation of motion of a spherically symmetric singular shell embedded in 4-d and 5-d vacuum spacetimes. In particular the equation of motion of a shell consisting of radiation has the same form as for a vacuum shell or domain wall.
In the present work, it is shown that, the application of the Bazanski approach to Lagrangians, written in AP-geometry and including the basic vector of the space, gives rise to a new class of path equations. The general equation representing this class contains four extra terms, whose vanishing reduces this equation to the geodesic one. If the basic vector of the AP-geometry is considered as playing the role of the electromagnetic potential, as done in a previous work, then the second term (of the extra terms) will represent Lorentz force while the fourth term gives a direct effect of the ele…
Intrinsic quantum dynamics of particles in brane gravity
本文研究膜引力中粒子的牛顿动力学，发现粒子沿额外维度的振荡与动能成正比，其经典稳定性导出玻尔-索末菲量子化条件，且该运动等同于不含时薛定谔方程，为束缚态产生量子化能谱。
Brane model of universe is considered for a particle. Conservation laws inside the brane are obtained. Equation of motion is derived for a particle using variation principle from these conservation laws. This equation includes terms accounting the variation of brane topology. Its solution is obtained at some approximations and dispersion relation for a particle is derived.
Analytical solutions of Maxwell equations in background spacetime of black hole in braneworld immersed in external uniform magnetic field have been found. Influence of both magnetic and brane parameters on effective potential of the radial motion of charged test particle around slowly rotating black hole in braneworld immersed in uniform magnetic field has been investigated by using Hamilton-Jacobi method. Exact analytical solution for dependence of the radius of the innermost stable circular orbits (ISCO) $r_{\rm ISCO}$ from brane parameter for motion of test particle around nonrotating isola…
We study the properties of the covariant supersymmetric and kappa-symmetric action for a system of N nearly coincident M0-branes (mM0 system) in flat eleven dimensional (11D) superspace and obtain supersymmetric equations for this dynamical system. Although a single M0-brane is the massless 11D superparticle, center of energy motion of the mM0 system is characterized by a nonnegative constant mass M constructed from the matrix fields describing the relative motion of mM0 constituents. We show that a bosonic solution of the mM0 equations can be supersymmetric iff this effective mass vanishes, M…
Classical tests of General Relativity in braneworld scenarios have been investigated recently with the purpose of posing observational constraints on parameters of some models of infinitely thin brane. Here we consider the motion of test particles in a thick brane scenario that corresponds to a regularized version of the Garriga-Tanaka solution, which describes a black hole solution in RSII model, in the weak field regime. By adapting a mechanism previously formulated in order to describe the confinement of massive tests particles in a domain wall (that simulates classically the trapping of th…
We elaborate the superembedding description of 'simple' D = 10, N = 1 five-brane and discuss the possible application of the superembedding approach in search for the equations of motion of the mysterious SO(32) heterotic five brane on this basis.
Properties of multiple D0-brane system: 11D origin, equations of motion and their solutions
本研究探究10维多D0-膜系统的性质，推导其11维起源、含任意正定函数的运动方程组及解，建立其相对运动方程与最大超对称SU(N) Yang-Mills理论方程的解对应关系，明确二者非规范等价但超对称解一致。
In the braneworld scenario ordinary standard model matter and on-gravitational fields are confined by some trapping mechanism to the 4-dimensional universe constituting the D3-branes which are embedded in a (4 + n)-dimensional manifold referred to as the bulk (n being the number of extra dimensions). The notion of particle confinement is necessary for theories with non-compact extra dimensions, otherwise, the particles would escape from our 4-dimensional world along unseen directions. In this paper, we have considered a five-dimensional warped product space-time having an exponential warping f…
We consider gravitationally induced perturbations of relativistic Dirac--Goto--Nambu membranes and strings (or {\it p}-branes). The dynamics are described by the first and second fundamental tensors, and related curvature tensors in an {\it n}-dimensional spacetime. We show how equations of motion can be derived for the perturbations within a general gauge and then discuss how various simple gauge choices can be used to simplify the equations of motion for specific applications. We also show how the same equations of motion can be derived from an effective action by a variational principle. Fi…
Using the thin-shell formalism we discuss the motion of domain walls in de Sitter and anti-de Sitter (AdS) time-dependent bulks. This motion results in a dynamics for the brane scale factor. We show that in the case of a clean brane the scale factor describes both singular and non-singular universes, with phases of contraction and expansion. These phases can be understood as quotients of AdS spacetime by a discrete symmetry group. We discuss this effect in some detail, and suggest how the AdS/CFT correspondence could be applied to obtain a non perturbative description of brane-world string cos…
Homogeneous cosmology in the braneworld can be studied without solving bulk equations of motion explicitly. The reason is simply because the symmetry of the spacetime restricts possible corrections in the 4-dimensional effective equations of motion. It would be great if we could analyze cosmological perturbations without solving the bulk. For this purpose, we combine the geometrical approach and the low energy gradient expansion method to derive the 4-dimensional effective action. Given our effective action, the standard procedure to obtain the cosmological perturbation theory can be utilized …
Several physical natures of charged brane-world black holes have been investigated. At first, time-like and null geodesics of the charged brane-world black holes are presented. We also analyze all the possible motions by plotting the effective potentials for various parameters for circular and radial geodesics. Secondly, we investigate the motion of test particles in the gravitational field of charged brane-world black holes using Hamilton-Jacobi (H-J) formalism. We have considered charged and uncharged test particles and examine its behavior both in static and non-static cases. Thirdly, therm…
Brane model of universe is considered for free particle. Conservation laws on the brane are obtained using the symmetry properties of the brane. Equation of motion is derived for a particle using variation principle from these conservation laws. This equation includes terms accounting the variation of brane radius. Its solution is obtained at some approximations and dispersion relation for a particle is derived.
We derive the gauge invariant perturbation equations for a 5-dimensional bulk spacetime in the presence of a brane. The equations are derived in full generality, without specifying a particular energy content of the bulk or the brane. We do not assume Z_2 symmetry, and show that the degree of freedom associated with brane motion plays a crucial role. Our formalism may also be used in the Z_2 symmetric case where it simplifies considerably.
The motion of a dynamical system on an $n$-dimensional configuration space may be regarded as the lightlike shadow of null geodsics moving in an $(n+2)$ dimensional spacetime known as its Einsenhart-Duval lift. In this paper it is shown that if the configuration space is $n$-dimensional Euclidean space, and in the absence of magnetic type forces, the Eisenhart-Duval lift may be regarded as an $(n+1)$-brane moving in a flat $(n+4)$ -dimensional space with two times. If the Eisenhart-Duval lift is Ricci flat, then the $(n+1)$-brane moves in such a way as to extremise its spacetime volume. A stri…
We argue that in fat brane-world scenarios the light propagating in vacuum will, because of massive ``Kaluza-Klein'' (KK) excitations, experience a refraction. The motion of a photon inside a fat brane can be decomposed in the longitudinal and transverse directions with respect to the surface of the brane. Since the light observable propagation is related only with the longitudinal motion, the observed speed of light depends on the value of the momentum transverse fraction contributing as the massive KK excitations. This is directly connected with the energy of the particles emitting the light…
We investigate the question of how an observer in 4D perceives the five-dimensional geodesic motion. We consider the interpretation of null and non-null bulk geodesics in the context of brane theory, space-time-matter theory (STM) and other non-compact approaches. We develop a "frame-invariant" formalism that allows the computation of the rest mass and its variation as observed in 4D. We find the appropriate expression for the four-acceleration and thus obtain the extra force observed in 4D. Our formulae extend and generalize all previous results in the literature. An important result here is …
By considering the p-brane motion in G/K symmetric space bulk we identify the G-invariant bulk metric in the solvable lie algebra gauge of the brane action. After calculating the Levi-Civita connection of this bulk metric we use it in the Gauss equation to compute the braneworld curvature in terms of the bulk coordinates. Finally, by making use of the Gauss equation in the braneworld Einstein equation we present a geometrical method of implementing the first fundamental form in the gravitating brane dynamics for the specially chosen symmetric space bulk case leading to an Einstein equation sol…
Recently it has been suggested to use the perigee of the proposed LARES/WEBER-SAT satellite in order to measure the secular precession which would be induced on such Keplerian orbital element by a weak-field modification of gravity occurring in some Brane-World scenarios put forth by Dvali, Gabadadze and Porrati. This precession, derived for the first time by Lue and Starkman, amounts to 4\times 10-3 milliarcseconds per year for an Earth orbiting satellite. In this paper we show that, according to the recently released EIGEN-CG01C Earth gravity model the quite larger systematic errors due to t…
We consider a 5-dimensional model with geometry ${\cal M} = {\cal M}_4 \times {\cal S}_1$, with compactification radius $R$. The Standard Model particles are localized onto a brane located at y=0, with identical branes localized at different points in the extra dimension. Objects located on our brane can orbit around objects located on a brane at a distance $d=y/R$, with an orbit and a period significantly different from the standard Newtonian ones. We study the kinematical properties of the orbits, finding that it is possible to distinguish one motion from the other in a large region of the i…
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