在不对称的界面上,符合方法和分析在广义相对论中的分析
G Taujanskas1, J A Valiente Kroon2
1Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, CB3 0WB, UK.
概括
这篇评论涵盖了60年的数学广义相对论,重点是罗斯.
科学领域:
- 数学物理学的数学物理.
- 一般相对论一般相对论.
- 非对称分析的分析.
背景情况:
- 介绍了2023年5月皇家学会胡克讨论会的会议记录.
- 突出了过去60年来数学广义相对论中关键概念的历史发展.
研究的目的:
- 为了提供一个历史概述的罗斯的合规紧化.
- 讨论零无限的概念和相关的基本发展.
- 为了将这些话题置于数学广义相对论的更广泛领域的背景下.
主要方法:
- 历史审查和基础概念的综合.
- 对数学广义相对论发展的分析.
- 专注于合规方法和非对称分析.
主要成果:
- 追踪了符合性紧缩和零无限的演变.
- 在60年间,确定了数学广义相对论的基本进步.
- 将非对称方法与相对论中的分析技术联系起来.
结论:
- 这篇文章作为介绍一个特殊的问题,关于对比论的界面,合规方法,和分析在广义相对论.
- 强调罗斯的工作和相关概念在该领域的持久意义.
相关概念视频
Space-Time Curvature and the General Theory of Relativity
2.7K
In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of...
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of...
2.7K
Divergence and Stokes' Theorems
1.6K
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
1.6K
Perpendicular-Axis Theorem
2.8K
The perpendicular-axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two mutually perpendicular concurrent axes lying in the plane of the body.
Consider a circular disc of mass M and radius R lying along an x-y plane. The origin lies at the center of the disc, and the z-axis is perpendicular to the disc's plane. All three axes coincide at the disc's center. The moment of inertia of this...
Consider a circular disc of mass M and radius R lying along an x-y plane. The origin lies at the center of the disc, and the z-axis is perpendicular to the disc's plane. All three axes coincide at the disc's center. The moment of inertia of this...
2.8K
Dimensional Analysis
15.1K
The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
15.1K
Spherical Coordinates
10.2K
Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
10.2K
Differential Form of Maxwell's Equations
471
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
471


