### C7.5 General Relativity I (2023-24)

General Prerequisites:
ASO: Special Relativity, B7.1 Classical Mechanics, and B7.2 Electromagnetism.
Course Term: Michaelmas
Course Lecture Information: 16 lectures
Course Weight: 1
Course Level: M
Assessment Type: Written Examination
Course Overview:
The course is intended as an introduction to general relativity, covering both its observational implications and the new insights that it provides into the nature of spacetime and the structure of the universe. Familiarity with special relativity and electromagnetism as covered in the Part A and Part B courses will be assumed. The lectures will review Newtonian gravity, special relativity (from a geometric point of view), and then move on to cover physics in curved space time and the Einstein equations. These will then be used to give an account of planetary motion, the bending of light, the existence and properties of black holes and elementary cosmology.
Learning Outcomes:
By the end of the course, students will understand the tension between special relativity and gravitation, and appreciate the physical considerations (such as the equivalence principle) which motivate the Einstein equations. They will understand tensors and tensor calculus, including notions of covariance and curvature, leading to an understanding of the Einstein equations. They will be able to derive simple physical consequences of the Einstein equations, such as the bending of light and the varying speeds of clocks in gravitational fields. They will be able to interpret the Schwarzschild solution, either as describing the exterior of a spherical body, or as a black hole, and they will understand some simple cosmological solutions and their properties, including the big bang.
Course Synopsis:
Introduction to the idea of “spacetime”. Review of Newtonian gravity. Review of Special Relativity, emphasising a geometric perspective. Difficulties in reconciling Special relativity with gravity, and the equivalence principle. Curved space time: elements of Lorentzian geometry, including vectors, convectors, tensors and their transformations; connections, curvature and geodesic deviation. The Einstein equations, and other physical laws in curved spacetime. Planetary motion and the bending of light. Introduction to black holes; the Schwarzschild solution. Introduction to cosmology: homogeneity and isotropy, and the Friedman-Robertson-Walker solutions.