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Graduate school "Particles and Interactions"

Topics for bachelor theses at our institute

TU Einführungsvortrag für Erstsemestrige

Black Holes II (136.029)

Lecture notes (v1.0 - please send corrections to grumil@hep.itp.tuwien.ac.at)

LECTURES THROUGH DISTANCE LEARNING (USE TISS)

Exercises week 8 (due on June 9)

Exercises week 7 (due on May 26)

Exercises week 6 (due on May 19)

Exercises week 5 (due on May 12)

Exercises week 4 (due on May 5)

Exercises week 3 (due on April 28)

Exercises week 2 (due on April 21)

Exercises week 1 (due on March 10)

First lecture sheet (horizons and other definitions)

First lecture: Overview and Goal of Lectures

Announcement

Black holes have advanced to the forefront of current research in various disciplines: besides the obvious ones, general relativity, mathematical physics and astrophysics, also string theory, quantum chromodynamics, cosmology, computational physics, quantum gravity and even part of condensed matter physics devote a significant fraction of their resources to the study of black holes. It is thus both a fascinating and timely subject to investigate.

The main purpose of this lecture is a treatment of advanced topics/current research topics in black hole physics.

Topics covered in these lectures:

  • Black hole definition, causal structure and Penrose diagrams
  • Raychaudhuri equation, singularity theorems and area theorem
  • Linearized Einstein equations and gravitational waves
  • Black hole perturbations and quasi-normal modes
  • Black hole thermodynamics
  • Hawking effect
  • Action principle and boundary issues
  • Holographic renormalization and Brown-York stress tensor
  • Asymptotic symmetries and black holes in AdS
  • Gravity aspects of AdS/CFT

Required pre-requisites: the lecture Black Holes I is a necessary pre-requisite (or, equivalently, good knowledge in General Relativity/basics of black hole physics)

Black Holes I (136.028)

LECTURES ARE OVER - BELOW ARE LINKS AND EXERCISES FROM WS 2019/20

Draft of lecture notes (v0.0 - please send corrections to grumil@hep.itp.tuwien.ac.at)

Summary and Outlook

Discovery of gravitational waves (summary for public)

Exercises week 10 (due on January 21)

Addendum to lecture notes: 1-page derivation of Kerr

Exercises week 9 (due on January 14)

Exercises week 8 (due on January 7)

Exercises week 7 (due on December 17)

Exercises week 6 (due on December 10)

Exercises week 5 (due on December 3)

Exercises week 4 (due on Novemver 26)

Exercises week 3 (due on November 12)

Movie of journey into Schwarzschild black hole (by Andrew Hamilton)

Exercises week 2 (due on November 5)

Exercises week 1 (due on October 22)

First lecture: Overview and History

Announcement

Black holes have advanced to the forefront of current research in various disciplines: besides the obvious ones, general relativity, mathematical physics and astrophysics, also string theory, quantum chromodynamics, cosmology, computational physics, quantum gravity and even part of condensed matter physics devote a significant fraction of their resources to the study of black holes. It is thus both a fascinating and timely subject to investigate.

The main purpose of this lecture is a comprehensive introduction to black hole physics.

Topics covered in these lectures:

  • History of black holes
  • Phenomenology of and experiments with black holes
  • Gravitational collapse and Chandrasekhar limit
  • Metric and geodesic equation
  • Geodesics for Schwarzschild black holes
  • Curvature and basics of differential geometry
  • Hilbert action and Einstein equations
  • Spherically symmetric black holes and Birkhoff theorem
  • Rotating black holes: the Kerr solution
  • Geodesics for Kerr black holes
  • Accretion disks and black hole observations
  • Black hole analogs in condensed matter physics

Required pre-requisites: good knowledge of special relativity is required; basic knowledge of general relativity is helpful, but not required; no prior knowledge of astrophysics, particle physics or cosmology is required

Gravity and holography in lower dimensions I (136.073)

Venue: Seminar room FH 3rd floor, yellow tower
Time: 9:00-11:00 (Tuesdays)

First lecture: October 2, 2018

Exercises week 10 (due on January 15)

Exercises week 9 (due on January 8)

Exercises week 8 (due on December 4)

Exercises week 7 (due on November 27)

Exercises week 6 (due on November 13)

Exercises week 5 (due on November 6)

Exercises week 4 (due on October 30)

Exercises week 3 (due on October 23)

Exercises week 2 (due on October 16)

Exercises week 1 (due on October 9)

Seventh lecture sheet (AdS3/CFT2) [draft version; still in preparation]

Sixth lecture sheet (Canonical realization of asymptotic symmetries)

Fifth lecture sheet (Gravity in two dimension)

Fourth lecture sheet (Gravity in three dimension)

Third lecture sheet (Cartan formulation)

Second lecture sheet (Asymptotic Killing vectors)

First lecture sheet (Summary of gravity with boundaries)

Slides of first lecture

Announcement

Topics covered in these lectures:

  • gravity with boundaries
  • asymptotic Killing vectors
  • Cartan formulation
  • gravity in two and three dimensions
  • canonical boundary charges
  • asymptotic symmetry algebras
  • central extensions
  • AdS_3/CFT_2
  • holographic renormalization
  • correlation functions
  • holographic entanglement entropy
  • ... and possibly selected research topics

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