Graduate/Specialist Course FS20:
Theory of Black Holes
Prerequisites, Timetable, Outline, Literature, and more ...
Corona Measures:
Summary and Overview
Much of the current and ongoing work on Quantum Gravity is motivated by
the puzzles raised by the mysterious and suprising thermodynamic properties exhibited
by Black Holes at the semi-classical level. The key observations here,
regarding both classical and semi-classical General Relativity,
go back to the 1970s. It is impossible to appreciate, let alone
understand or judge, current activities and efforts in this field
without a knowledge of these developments and discoveries
from over 40 years ago.
Nevertheless, in spite of the importance of these discoveries, and in
spite of the fact that they have had as much an impact on theoretical
gravitational physics as the more or less simultaneous development of
the Standard Model of Particle Physics has had on theoretical particle
physics, they do not appear to be part of the standard
theoretical physicists' curriculum today.
The primary aim of this course will be to (partially) fill this gap! As a consequence,
the target audience for this course are not just Master or Graduate students, but
basically anybody in theoretical physics who would like to have a better understanding
of these matters.
Starting from and building on the
properties of the Rindler metric (Minkowski space
in accelerated coordinates) and the Schwarzschild Black Hole metric,
which I will review (but will assume some familiarity with), I want to
deal with the following topics (at a necessarily somewhat, and at times
even very, cursory level):
- Classsical Theory of Black Holes
(Penrose Diagrams, uniqueness (no hair) theorems, definitions and properties of
Black Hole Horizons, and the
Laws of Black Hole Mechanics).
The treatment here will necessarily be largely cursory and heuristic,
because most of these results are rigorous mathematical theorems, and
probably most of you will not be interested in the details of these.
However, it is good (and indispensable for the following) to know the facts.
- Semi-Classical Theory of Black Holes
(Unruh Effect,
Hawking Temperature, Black Hole Evaporation, Bekenstein-Hawking Black Hole
Entropy, and the Laws of Black Hole Thermodyamics).
The treatment here will again necessarily be largely cursory and heuristic,
because I do not have the time to develop the techniques of QFT in Curved Spacetime
required to rigorously derive these results.
In this respect, this course
differs crucially from other graduate courses I have given in the past, such as
Introduction to QFT in Curved
Spacetime, where I was able to provide a detailed derivation of
Hawking radiation (and other quantum effects), but never had time to discuss
the far-reaching implications of these calculations.
- Implications and Outlook
(in particular in relation to the extremely subtle (and as a consequence
much abused and misunderstood) so-called
Information Paradox and its consequences).
To a certain extent, the course will therefore (unintentionally) trace some of the
work of Stephen Hawking on these subjects. For a very recent brief and
non-technical biographical account of his work, see
(in the course, we will deal with the subjects mentioned in sections 7, 9, 10 and 14
of this article).
Prerequisites
- Basics of General Relativity (general formalism; Rindler, Schwarzschild,
Kruskal)
- Basic Basics of Quantum Field Theory (canonical quantisation of free scalar fields,
vacuum and creation and annihilation operators) and Statistical Mechanics (better yet,
finite temperature QFT)
Schedule
- Time and Place: Thursday 14.15 -- 17.00 Room B001
- Starting Date: Thursday, February 20th
- Duration: 1st half of FS20 (5-7 weeks, depending on the energy and interest
of lecturer and audience ...)
Tentative Outline / Preliminary List of Topics
- Introduction: Motivation and Overview
- Review of Rindler Space and the Schwarzschild Black Hole
- Carter-Penrose Conformal Diagrams
- Guided Visit to the Zoo of Black Hole Solutions
- Horizons and the Classical Theory of Black Holes
- Unruh Effect, Hawking Temperature and Hawking Radiation
- Aspects of Black Hole Entropy and Black Hole
Thermodynamics
- Outlook/Wild Stuff: Information Paradox / Firewalls etc
Formalities / Information for Theory Master Students
- Please regard this course as an optional additional course.
The main Specialist Course offered by the ITP this semester is
the course
Conformal Field Theory by
Susanne Reffert, which you
are strongly encouraged to attend.
- This course can be validated as a Specialist Course. To that end
you will need to do a homework project / presentation based on the contents of the
course. Details to be discussed at a later stage with whoever is interested in this.
Literature
- State of the Art ((Post-)Modern Black Hole Thermodynamics)
- Classical Theory of Black Holes
- My GR Lecture Notes: Lecture Notes on General Relativity (for some of the more elementary things)
- The Classic: S. Hawking, G. Ellis,
The large scale structure of space-time (for some of the earlier classical results)
- The superb Cambridge (Part III) Lecture Notes on Black Holes (for almost everything we will cover, but done with much more expertise and detail than I will be able
to offer):
- Monographs on QFT in Curved Spacetime
- N. Birrell, P. Davies: Quantum Fields in Curved Space
- V. Mukhanov, S. Winitzki: Quantum Effects in Gravity
- L. Parker, D. Toms: Quantum Field Theory in Curved Spacetime
- R. Wald: Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics
- see also
- chapter 14 of R.M. Wald: General Relativity
- chapter 09 of S. Carroll: Spacetime and Geometry, an Introduction to General Relativity
- Semi-Classical Theory of Black Holes I (Hawking Radiation)
- Semi-Classical Theory of Black Holes II (Black Hole Thermodynamics)
- Black holes and information loss paradox
- Selected Original Articles (internal UniBe access only)
Contact
- Matthias Blau, Office 220a