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所在平台: Udemy |
课程主页: https://www.udemy.com/course/mathematical-predictions-of-general-relativity/
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**课程名称：广义相对论的数学预测** **课程概述：** 本課程是“狭义与广义相对论的数学直觉”的续篇，要求具备张量知识。课程将回顾黎曼张量、度规张量、克里斯托费尔符号和爱因斯坦场方程等概念，并运用这些概念，对爱因斯坦及20世纪物理学家们提出的、为广义相对论提供观测证据的数学预测进行推导。 课程将重点探讨两个由爱因斯坦于1915年提出的重要检验： 1. **水星近日点的反常进动：** 在牛顿物理学框架下，行星围绕恒星的轨道应为椭圆，且近日点固定。然而，水星的近日点却存在一个牛顿理论无法解释的进动。爱因斯坦的广义相对论精确地预测了这一进动值，有力地支持了该理论。 2. **光线在引力场中的弯曲：** 爱因斯坦预测，光线在经过大质量物体附近时会发生弯曲。他计算出光线经过太阳边缘时弯曲1.75角秒。1919年，爱丁顿及其团队在日全食观测中证实了这一预测，使爱因斯坦和广义相对论名声大噪。 此外，课程还将推导真空中的引力波，这与2016年以来LIGO等探测器直接探测到的双黑洞合并事件的引力波现象相呼应。 本课程的灵感来源于朗道和栗弗席兹的《场论》。
This course is a sequel to: "Mathematical Intuition behind Special and General Relativity". The knowledge of tensors is a mathematical prerequisite. The following concepts are recalled at the beginning of the course: the Ricci tensor, metric tensor, Christoffel symbols, Einstein's field equations. All these concepts will then be used to make the same mathematical predictions that were made by Einstein and other physicists in the 20th century. These predictions served to establish observational evidence for the theory of general relativity. Two of these tests were proposed by Einstein in 1915, and concerned the unexplained precession of the perihelion of Mercury, as well as the bending of light in gravitational fields. Under Newtonian physics, a two-body system consisting of an object (e.g. planet) orbiting a spherical mass (e.g. the sun) would trace out an ellipse with the system's center of mass located at one of the two foci. The point of closest approach, called the perihelion, is fixed, but Mercury deviates from these predictions by showing a precession which is not predicted by a Newtonian system, not even taking into account the presence of other planets. This anomalous advance of the perihelion of Mercury's orbit was first recognized in the 19th century as a problem in celestial mechanics. Analysis of available observations showed that the actual rate of the precession disagreed from that predicted from Newton's theory. Einstein showed that general relativity agrees closely with the observed amount of perihelion shift. This powerful factor motivated the adoption of general relativity.Also, Einstein predicted that starlight would bend around a massive object; in particular, he calculated the correct value for light bending: 1.75 arcseconds for light that skirts the edge of the sun. The observations were performed by Arthur Eddington and his collaborators during a total solar eclipse in 1919. The result was considered spectacular and made the front page of most major newspapers. It made Einstein and his theory of general relativity world-famous.In the course, we will also derive gravitational waves from Einstein field equations in vacuum. In February 2016, the Advanced LIGO team announced that they had directly detected gravitational waves from a stellar binary black hole merger, with additional detections announced in June 2016, June 2017, and August 2017.This course was inspired by Landau and Lifschitz's volume two: The Classical Theory of Fields.
