Representation of Physical Fields as Einstein Manifold

In this work we investigate the possibility to represent physical fields as Einstein manifold. Based on the Einstein field equations in general relativity, we establish a general formulation for determining the metric tensor of the Einstein manifold that represents a physical field in terms of the energy-momentum tensor that characterises the physical field. As illustrations, we first apply the general formulation to represent the perfect fluid as Einstein manifold. However, from the established relation between the metric tensor and the energy-momentum tensor, we show that if the trace of the energy-momentum tensor associated with a physical field is equal to zero then the corresponding physical field cannot be represented as an Einstein manifold. This situation applies to the electromagnetic field since the trace of the energy-momentum of the electromagnetic field vanishes. Nevertheless, we show that a system that consists of the electromagnetic field and non-interacting charged particles can be represented as an Einstein manifold since the trace of the corresponding energy-momentum of the system no longer vanishes. As a further investigation, we show that it is also possible to represent physical fields as maximally symmetric spaces of constant scalar curvature.

Gravitational Space-Time Curve Generation via Accelerated Charged Particles

A force with an acceleration that is equal to multiples greater than the speed of light per unit time is exerted on a cloud of charged particles. The particles are resultantly accelerated to within an infinitesimal fraction of the speed of light. As the force or acceleration increases, the particles’ velocity asymptotically approaches but never achieves the speed of light obeying relativity. The asymptotic increase in the particles’ velocity toward the speed of light as acceleration increasingly surpasses the speed of light per unit time does not compensate for the momentum value produced on the particles at sub-light velocities. Hence, the particles’ inertial mass value must increase as acceleration increases. This increase in the particles’ inertial mass as the particles are accelerated produce a gravitational field which is believed to occur in the oscillation of quarks achieving velocities close to the speed of light. The increased inertial mass of the density of accelerated charged particles becomes the source mass (or Big “M”) in Newton’s equation for gravitational force. This implies that a space-time curve is generated by the accelerated particles. Thus, it is shown that the acceleration number (or multiple of the speed of light greater than 1 per unit of time) and the number of charged particles in the cloud density are surjectively mapped to points on a differential manifold or space-time curved surface. Two aspects of Einstein’s field equations are used to describe the correspondence between the gravitational field produced by the accelerated particles and the resultant space-time curve. The two aspects are the Schwarzchild metric and the stress energy tensor. Lastly, the possibility of producing a sufficient acceleration or electromagnetic force on the charged particles to produce a gravitational field is shown through the Lorentz force equation. Moreover, it is shown that a sufficient voltage can be generated to produce an acceleration/force on the particles that is multiples greater than the speed of light per unit time thereby generating gravity.

黎曼流形中的非零截面曲率子流形

对非零截面曲率子流形何时是Ｅｉｎｓｔｅｉｎ流形的问题进行讨论，获得了一些结果．

点云场景认知模式——泛化点云

随着传感器技术和观测平台的迅速发展,点云大数据作为新型遥感的主要数据形式,已经逐渐成为场景感知的重要信息载体,并在地质灾害态势感知、自然资源定量调查和道路交通安全服务等国家重大战略需求中发挥了越来越显著的作用。与此同时,点云观测装备和国家重大战略需求的双重驱动促使空间场景从感知迈向了认知,也对认知处理的算法和算力提出了新的要求。为此,本文以点云场景认知的基本框架为线索,分析了多源点云耦合观测的研究现状,总结了点云场景认知处理的关键进展及其在国家重大战略需求中的典型应用,并凝练了点云场景认知当前面临的主要问题。在此基础上,本文聚焦点云场景认知的前沿挑战,避开传统欧氏空间而转到高维张量流形空间进行点云数据处理,提出了“泛化点云”的科学概念和技术框架,为突破点云场景认知处理的算法和算力提供研究思路。