## General Relativity

 Faculteit Science and Engineering Jaar 2019/20 Vakcode NAGR-08 Vaknaam General Relativity Niveau(s) master Voertaal Engels Periode semester I a ECTS 5 Rooster rooster.rug.nl

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 to understand the relationship between gravity and the geometrical properties of space/time. Next, the Einstein equations describing the gravitational interactions will be introduced. In the remaining part of the module we will take the Einstein equations as a starting point and study three classes of solutions to these equations: (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 and the cosmic microwave background.
Uren per week
Onderwijsvorm Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)
(LV 24, T12, ASM 38, self study 66)
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
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