# Physics 622

Spring 2022 Instructor: Paul Aspinwall Credits: 1.0, Hours: 3.0 Time: TuTh 10:15AM - 11:30AM Location: Physics 235 Description Introduction to the basic concepts and techniques of General Relativity. The course will cover the fundamentals of tensor calculus, Riemannian geometry, and Einstein's equations, as well as applications to cosmology and black holes. This is a core course for students who want to work in general relativity, cosmology, gravitational lensing, theoretical astrophysics, string theory, or related subjects. Homework will be given weekly. Prerequisites A sound knowledge of multivariable calculus (at least Math 212) and linear algebra (at least Math 218). A basic knowledge of classical mechanics and electromagnetism is desirable but the course will endevour to be self-contained. Exams There might be a mid-term exam. A take-home final will be given due back at the official time of the exam. Synopsis A rough outline is as follows. 0. Special Relativity Minkowski Space Lorentz Transformations I. Manifolds and Tensors Tangent vectors and differentiable maps Curves, vector fields, and one-forms Tensor fields and the abstract index notation II. Riemannian Geometry Covariant derivatives and parallel transport Curvature and geodesics Computing curvature III. The Einstein Field Equations General and special covariance Einstein's equation The weak-field limit IV. Applications Cosmology Robertson-Walker universes The cosmological constant (“dark energy”) The Schwarzschild solution Gravitational red shift Black holes Perihelion precession and bending of light The Kruskal extension Gravitational Waves Emission Binary pulsar decay LIGO results Further Analysis of Black Holes The Reissner-Nordström Solution The Kerr Solution The Ergosphere Black Hole Thermodynamics Textbooks The course will be based on the text: Robert M. Wald, General Relativity, University of Chicago Press, Chicago, 1984. See also Sean M. Carroll, Spacetime and Geometry, An Introduction to General Relativity, Addison Wesley 2004. (See also gr-qc/9712019 for what might be considered to be an earlier form of this book online.)
2022 年春季

0. 狭义相对论

LIGO 结果

Reissner-Nordström 解决方案

Ergosphere

Robert M. Wald，广义相对论，芝加哥大学出版社，芝加哥，1984 年。

Sean M. Carroll，时空与几何，广义相对论导论，Addison Wesley，2004 年。（另请参阅 gr-qc/9712019，了解这本书的早期在线形式。）