A Spherical Symmetrical Spacetime Solution in Finsler Gravity

Several physical principles of Finsler gravity are proposed in this paper, and I apply the principles to construct a Finsler gravity action, which satisfy the condition that the action can be reduced to the General Relativity action once the metric is independent from the tangent vector. I also get a spacetime solution in Finsler spacetime with the tangent vector y _φ , moreover the solution indicates that the metric relies on the property of test particle in Finsler spacetime.     

Finsler-spacetime tangent bundle

The Levi-Civita connection coefficients of the spacetime tangent bundle, for the case of a Finsler spacetime, are reduced to the form given by Yano and Davies for a generic tangent bundle of a Finsler manifold. A useful expression is also obtained for the Riemann curvature scalar of a Finsler-spacetime tangent bundle.     

Weak gravitational field in Finsler–Randers space and Raychaudhuri equation

The linearized form of the metric of a Finsler–Randers space is studied in relation to the equations of motion, the deviation of geodesics and the generalized Raychaudhuri equation are given for a weak gravitational field. This equation is also derived in the framework of a tangent bundle. By using Cartan or Berwald-like connections we get some types “gravito-electromagnetic” curvature. In addition we investigate the conditions under which a definite Lagrangian in a Randers space leads to Einstein field equations under the presence of electromagnetic field. Finally, some applications of the weak field in a generalized Finsler spacetime for gravitational waves are given.     

Kähler spacetime tangent bundle

Requirements are delineated for the spacetime tangent bundle to be Kählerian. In particlar, an almost complex structure is constructed in the case of a Finsler spacetime, and its covariant derivative in terms of the bundle connection is shown to be vanishing, provided the gauge curvature field is vanishing. The Levi-Civita connection coefficients and the Riemann curvature scalar are also specified for the Kähler spacetime tangent bundle.     

Differential geometry of spacetime tangent bundle

Conditions are investigated under which the Levi-Civita connection of the spacetime tangent bundle corresponds to that of a generic tangent bundle of a Finsler manifold. Also, requirements are specified for the spacetime tangent bundle to be almost complex or Kählerian.This paper is an expanded version of an invited paper presented at the Second International Wigner Symposium, Goslar, Germany, July 1991.     

Complex spacetime tangent bundle

It is demonstrated that the spacetime tangent bundle, in the case of a Finsler spacetime, is complex, provided that the gauge curvature field vanishes. This is accomplished by determining the conditions for the vanishing of the Nijenhuis tensor in the anholonomic frame adapted to the spacetime connection.     

Generalized relativistic dynamics in a non-inertial reference frame

Generalized relativistic field equations have been derived for dynamics in a non-inertial reference frame interpreted as a Finsler space where events are specified by both spacetime coordinates and corresponding velocities (tangent vectors). The field equations follow in two alternative forms from exact general conservation laws derived through application of Cartan covariant differentiation within the framework of Finsler geometry. Velocity-dependent (curvature) terms in the field equations can account for the anisotropy of the gravitational field, together with the associated acceleration and expansion of the universe.     

Super-Luminal Effects for Finsler Branes as a Way to Preserve the Paradigm of Relativity Theories

Using Finsler brane solutions [see details and methods in: S. Vacaru, Class. Quant. Grav. 28:215001, 2011], we show that neutrinos may surpass the speed of light in vacuum which can be explained by trapping effects from gravity theories on eight dimensional (co) tangent bundles on Lorentzian manifolds to spacetimes in general and special relativity. In nonholonomic variables, the bulk gravity is described by Finsler modifications depending on velocity/momentum coordinates. Possible super-luminal phenomena are determined by the width of locally anisotropic brane (spacetime) and induced by generating functions and integration functions and constants in coefficients of metrics and nonlinear connections. We conclude that Finsler brane gravity trapping mechanism may explain neutrino super-luminal effects and almost preserve the paradigm of Einstein relativity as the standard one for particle physics and gravity.     

Finsler Geometry and Relativistic Field Theory

Finsler geometry on the tangent bundle appears to be applicable to relativistic field theory, particularly, unified field theories. The physical motivation for Finsler structure is conveniently developed by the use of gauge transformations on the tangent space. In this context a remarkable correspondence of metrics, connections, and curvatures to, respectively, gauge potentials, fields, and energy-momentum emerges. Specific relativistic electromagnetic metrics such as Randers, Beil, and Weyl can be compared.     

Modified dispersion relations in Hořava–Lifshitz gravity and Finsler brane models

We study possible links between quantum gravity phenomenology encoding Lorentz violations as nonlinear dispersions, the Einstein–Finsler gravity models, EFG, and nonholonomic (non-integrable) deformations to Hořava–Lifshitz, HL, and/or Einstein’s general relativity, GR, theories. EFG and its scaling anisotropic versions formulated as Hořava–Finsler models, HF, are constructed as covariant metric compatible theories on (co) tangent bundle to Lorentz manifolds and respective anisotropic deformations. Such theories are integrable in general form and can be quantized following standard methods of deformation quantization, A-brane formalism and/or (perturbatively) as a nonholonomic gauge like model with bi-connection structure. There are natural warping/trapping mechanisms, defined by the maximal velocity of light and locally anisotropic gravitational interactions in a (pseudo) Finsler bulk spacetime, to four dimensional (pseudo) Riemannian spacetimes. In this approach, the HL theory and scenarios of recovering GR at large distances are generated by imposing nonholonomic constraints on the dynamics of HF, or EFG, fields.     

Fermion Tunnelling of a New Form Finslerian Black Hole

We improve the fermion tunnelling theory proposed by Kerner and Mann, and research into the fermion tunnelling radiation from a Finslerian black hole. The Finsler black hole put forward by Rutz is a solution of Einstein＇s vacuum field equations in Finsler theory. We study the radiation from the black hole with a semi-classical method, and the result proves that the tunnelling rate depends on the tangent vector.     

Gravitational Deflection of Light in Rindler-Type Potential as a Possible Resolution to the Observations of Bullet Cluster 1E0657-558

The surface density Σ-map and the convergence κ-map of Bullet Cluster 1E0657-558 show that the center of baryonic matters separates from the center of gravitational force,and the distribution of gravitational force do not possess spherical symmetry.This hints that a modified gravity with difference to Newtonian inverse-square law at large scale,and less symmetry is worth investigating.In this paper,we study the dynamics in Randers-Finsler spacetime.The Newtonian limit and gravitational deflection of light in a Rindler-type potential is focused in particular.It is shown that the convergence in Finsler spacetime could account for the observations of Bullet Cluster.     

Fine structure constant variation or spacetime anisotropy?

Recent observations on the quasar absorption spectra supply evidence for the variation of the fine structure constant α. In this paper, we propose another interpretation of the observational data on the quasar absorption spectra: a scenario with spacetime inhomogeneity and anisotropy. Maybe the spacetime is characterized by the Finsler geometry instead of the Riemann one. The Finsler geometry admits fewer symmetries than the Riemann geometry does. We investigate the Finslerian geodesic equations in the Randers spacetime (a special Finsler spacetime). It is found that the cosmological redshift in this spacetime deviates from the one in general relativity. The modification term to the redshift could be generally revealed as a monopole plus dipole function of spacetime locations and directions. We suggest that this modification corresponds to the spatial monopole and dipole of α variation in the quasar absorption spectra.     

Connections and geodesics in the spacetime tangent bundle

Recent interest in maximal proper acceleration as a possible principle generalizing the theory of relativity can draw on the differential geometry of tangent bundles, pioneered by K. Yano, E. T. Davies, and S. Ishihara. The differential equations of geodesics of the spacetime tangent bundle are reduced and investigated in the special case of a Riemannian spacetime base manifold. Simple relations are described between the natural lift of ordinary spacetime geodesics and geodesics in the spacetime tangent bundle.     

On the extension of geometric optics from Riemannian to Riemann-Cartan spacetime

In the extension to Riemann-Cartan spacetime, the optical properties of electromagnetic waves are found to depend strongly on the nature of the Lorentz gauge condition. If the Lorentz gauge condition is treated similar to the non-minimal extension of the electromagnetic field to Riemann-Cartan spacetime, then the optical properties of waves are identical to those in riemannian spacetime. If the gauge is treated as an intrinsically Riemann-Cartan condition, then, to the same order of approximation, the optical properties of waves remain the same, except that the polarization vector is no longer parallel propagated along the wave vector.     

An Analytic Approximation for Researching Tunneling Rate from Black Hole in Proca Field

The analytic solution of a static spherical symmetrical Proca black hole is discussed in this paper. As in the massive vector field, Proca black hole can be considered as the analogy of RN background plus a perturbation with the same order as μ ² due to the mass of vector particle μ satisfying μ ² ? 1. Through the action of Proca field, we find the analytic form with the first and arbitrary order approximation. Furthermore, we divide the results into 3 groups according to the real zero solutions of the background (i.e., spacetime in massless vector field). Finally we analyze the Hawking radiation of such black hole, which is significant for constructing black hole thermodynamic.     

Some rigidity theorems for locally symmetrical Finsler manifolds

In this paper we study some rigidity properties for locally symmetrical Finsler manifolds and obtain some results. We obtain the local equivalent characterization for a Finsler manifold to be locally symmetrical and prove that any locally symmetrical Finsler manifold with nonzero flag curvature must be Riemannian. We also generalize a rigidity result due to Akbar-Zadeh.     

Beyond the speed of light on Finsler spacetimes

As a prototypical massive field theory we study the scalar field on the recently introduced Finsler spacetimes. We show that particle excitations exist that propagate faster than the speed of light recognized as the boundary velocity of observers. This effect appears already in Finsler spacetime geometries with very small departures from Lorentzian metric geometry. It switches on for a sufficiently large ratio of the particle four-momentum and mass, and is the consequence of a modified version of the Coleman–Glashow velocity dispersion relation. The momentum dispersion relation on Finsler spacetimes is shown to be the same as on metric spacetimes, which differs from many quantum gravity models. If similar relations resulted for fermions on Finsler spacetimes, these generalized geometries could explain the potential observation of superluminal neutrinos claimed by the Opera Collaboration.     

Fermat principle in Finsler spacetimes

It is shown that, on a manifold with a Finsler metric of Lorentzian signature, the lightlike geodesics satisfy the following variational principle. Among all lightlike curves from a point q (emission event) to a timelike curve γ (worldline of receiver), the lightlike geodesics make the arrival time stationary. Here “arrival time” refers to a parametrization of the timelike curve γ. This variational principle can be applied (i) to the vacuum light rays in an alternative spacetime theory, based on Finsler geometry, and (ii) to light rays in an anisotropic non-dispersive medium with a general-relativistic spacetime as background.     

基于递归T矩阵的离散随机散射体散射特性研究

本文根据电磁场矢量球波函数多极点展开原理及矢量叠加定理提出了递归T矩阵算法的矢量形式,并且基于矢量递归T矩阵算法建立了多散射球模拟离散随机散射体散射的三维电磁散射模型.通过计算不同尺寸、随机分布散射球的散射以及分析散射球间的高阶散射效应,结果表明:矢量递归T矩阵算法具有很高的计算精度,算法中包含多散射体间的高阶散射效应,因此能够精确计算多散射体总的散射效应.本文所建模型可应用于土壤湿度探测工程中评估地表下掩埋离散随机散射体散射对雷达回波信号产生的影响.