Gravitation: from Newton to Einstein
arXiv:1902.07287 · doi:10.1007/978-3-030-32001-0
Abstract
This document gathers the notes of a 30-hour review course on gravitation, which I delivered in January 2018 and January 2019 at the African Institute for Mathematical Sciences of Cameroon (AIMS-Cameroon). Its main goal is to propose a big picture of gravitation, where Einstein's relativity arises as a natural increment to Newton's theory. It is designed for bachelor/master students who do not necessarily have prior knowledge about relativity. The students are nevertheless expected to be familiar with the fundamentals of Newton's mechanics and gravitation, for the first chapter to be a mere reformulation of known concepts. The second chapter then introduces special and general relativity at the same time, while the third chapter explores concrete manifestations of relativistic gravitation, notably gravitational waves and black holes. Each section corresponds, on average, to slightly more than a 2-hour black-board lecture. The numerous exercises must be considered part of the course itself; they are intended to stimulate active reading.
107 pages, 23 figures, 77 exercises. Lectures given at the African Institute for Mathematical Sciences of Cameroon (AIMS-Cameroon) in January 2018 and January 2019. V2: Added an introduction and a conclusion, corrected a few typos. V3: sign issue corrected in eq. (II.135)
References in corpus (10)
- Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
- Observation of Gravitational Waves from a Binary Black Hole Merger
- GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
- First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
- The Confrontation between General Relativity and Experiment
- Thermodynamics of Spacetime: The Einstein Equation of State
- An Ordinary Short Gamma-Ray Burst with Extraordinary Implications: Fermi-GBM Detection of GRB 170817A
- Detection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole
- On the gravitational field of a mass point according to Einstein's theory
- Challenges to Self-Acceleration in Modified Gravity from Gravitational Waves and Large-Scale Structure