General Relativity I (PW-GR1)10 ECTS
(englische Bezeichnung: General Relativity I)
(Prüfungsordnungsmodul: General Relativity I)

Lehrveranstaltungen:

• • General Relativity I
    (Hauptseminar, 4 SWS, Thomas Thiemann, Di, 14:00 - 16:00, HD; Mi, 18:00 - 20:00, HD; course runs in online mode until further notice)
  • Tutorium General Relativity I
    (Vorlesung, 3 SWS, Thomas Thiemann et al., Do, 16:00 - 19:00, HD, HE; course runs in online mode until further notice)

Inhalt:

Contents

1. Mathematical Preliminaries: Differential and Riemannian Geometry
1i. Topological Spaces, differential manifolds
1ii. Tensor field (densities) on differential manifolds
1iii. Tensor algebra and calculus: Lie and exterior derivatives, Killing fields, Stokes’ theorem
1iv. Riemannian manifolds, Riemann, Ricci, torsion tensor; Levi-Civita connection
1v. Geodesics, Geodesic deviation equation, exponential map and Riemann normal coordinates
2. Einstein’s Field Equations
2i. Diffeomorphism invariance, Einstein-Hilbert action, Cosmological constant, Euler-Lagrange equations
2ii. Conserved Energy-momentum tensor, Bianchi identities
2iii. Energy Conditions and their physical significance
2iv Killing’s equation, symmetric space-times, exact solutions
2v. Methods for solving Einstein’s equations: N-bein formalism
3. Spherically symmetric space-times
3i. Stationary and static space times, spherically symmetric space times, Birkhoff’s theorem
3ii. Schwarzschild and Reissner-Nordstrom vacuum solutions and their Kruskal extensions
3iii. Coordinate and curvature singularities, geodesic completeness, black holes, event horizons and Penrose diagrammes
3iv. Tolman-Oppenheimer-Volkoff interior solution and Chandrasekhar limit
3v. Perihelion precession of Mercury, light deflection at the sun, gravitational red shift
4. Spatially homogeneous space times
4i. Definition and Bianchi classification
4ii. Isotropic Friedmann-Robertson-Walker (FRW) space times, (Anti) de Sitter vacuum space times
4iii. Cosmological red shift and Hubble law
4iv. Big bang singularity, horizon problem, inflation
4v. Cosmological standard model (Lambda-CDM)
5. Gravitational waves
5i. Linearised Einstein equations
5ii. Linearised diffeomorphism gauge invariance and de Donder gauge
5iii. Polarisation modes and their detection
5iv. Radiation power of a 2-body systems, quadrupole moment, pulsar rotation frequency decrease
5v. Primordial gravitational waves
6. Applications
6i. Weyl tensor, principal null directions and algebraically special solutions
6ii. Explicit construction of Schwarzschild and Reissner-Nordstrom metric
6iii. Explicit solutions of geodesic motion and wormholes
6iv. Global hyperbolicity, cosmic censorship and causality violation
6v. Explicit construction of FRW metric for general equation of state perfect fluid matter

Lernziele und Kompetenzen:

Learning goals and competences:
Students

• explain the relevant topics of the lecture

• apply the methods to specific examples

Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:

1. Physics (Master of Science)
   (Po-Vers. 2018w | NatFak | Physics (Master of Science) | Gesamtkonto | Physics elective courses | General Relativity I)

Studien-/Prüfungsleistungen:

General Relativity I (Prüfungsnummer: 71491)

Prüfungsleistung, Klausur, Dauer (in Minuten): 120, benotet, 10 ECTS

Anteil an der Berechnung der Modulnote: 100.0 %

Prüfungssprache: Englisch

Erstablegung: WS 2020/2021, 1. Wdh.: WS 2020/2021 (nur für Wiederholer)

1. Prüfer:

Thomas Thiemann

Termin: 16.03.2021, 12:00 Uhr, Ort: HG,HH