General Relativity

Uitgebreide vaknaam	General Relativity
Leerdoelen	By the end of the course the students should be able to: 1. Perform basic operations in differential geometry: transform tensors under change of coordinates, compute Christoffel symbols and curvature tensors from metric, explain notions of manifolds, geodesics, parallel transport etc. 2. Compute motion of particles and light in curved spacetime, derive the non-relativistic limit of General Relativity. 3. Be familiar with the Einstein equations and able to apply them and verify that specific metrics obey the equations. Be able to derive gravitational wave solutions from Einstein equations. 4. Describe the physics of local observers and compute the motion of particles in the vicinity of black holes. 5. Derive the basic cosmological models from the Einstein equations and describe their physical properties.
Omschrijving	These lectures will study Einstein's theory of gravity. The module starts with an introduction to the geometry that is required tounderstand the relationship between gravity and the geometrical properties of space and time. In the remaining part of the module we will study three classes of solutions to Einstein's theory: (1) black hole solutions such as the Schwarzschild black hole. We will use these solutions to calculate the perihelion shift of Mercury, one of the predictions of general relativity (2) gravitational wave solutions. We will discuss the detection of gravitational waves (3) cosmological solutions such as the Friedman-Lemaitre-Robertson-Walker cosmology. We will discuss the Big Bang with which the universe started. At the end of the course we will introduce the precise mathematical form of the Einstein equations describing the gravitational interactions.
Uren per week
Onderwijsvorm	Hoorcollege (LC), Opdracht (ASM), Werkcollege (T) (24 LC, 12 T, 38 ASM, 66 self-study)
Toetsvorm	Opdracht (AST), Schriftelijk tentamen (WE)
Vaksoort	master
Coördinator	prof. dr. E.A. Bergshoeff
Docent(en)	prof. dr. E.A. Bergshoeff
Verplichte literatuur	Titel Auteur ISBN Prijs Gravity: an introduction to Einstein's general relativity James B. Hartle Pearson Education, publishing as Addison Wesley 0-8053-8662-9
Entreevoorwaarden	The students should have sufficient knowledge of the Bachelor courses Special Relativity; Classic Mechanics and Electromagnetism.
Opmerkingen	WE 80 % =The written exam consists of a number of exercises, 20% AST Some selected assigned (sub-)exercise will be graded. the final grade should be higher than 5.5 This course was registered last year with course code NAGR-08
Opgenomen in	Opleiding Jaar Periode Type MSc Astronomy: Quantum Universe 1 semester I a verplicht MSc Courses for Exchange Students: Astronomy - Physics - Energy & Environment - semester I a MSc Mathematics and Physics (double degree)  ( Quantum Universe (40 ects)) - semester I a verplicht MSc Physics: Quantum Universe  ( Compulsory courses) - semester I a verplicht MSc Physics: Science, Business and Policy  (Keuzevakken in Quantum Universe) 1 semester I a keuze: QU