Physics 776---Advanced Gravitation Theory---Spring 2005

Black Hole Thermodynamics


Notes and papers of TJ

Introductory Lectures on Black Hole Thermodynamics, T. Jacobson (pdf, postscript)

Black holes: inside and out, T. Jacobson (3 pages of notes for a talk to beginning graduate students)

Introduction to Quantum Fields in Curved Spacetime and the Hawking Effect, Ted Jacobson

Horizon Entropy, Ted Jacobson and Renaud Parentani

Thermodynamics of Spacetime: the Einstein Equation of State, T. Jacobson (PRL version, arxiv version)

A Note on Hartle-Hawking Vacua
PRD version, arXiv version

Highly recommended

Black Holes and Time Warps
by Kip Thorne
A book for the general public, but very interesting at all levels. Includes much historical material about the context and the personalities. Most relevant to this course are Chapter 7, The Golden Age, and Chapter 12, Black Holes Evaporate.

Black Holes
P.K. Townsend
Lecture notes for a 'Part III' course 'Black Holes' given in DAMTP, Cambridge. The course covers some of the developments in Black Hole physics of the 1960s and 1970s.

The Thermodynamics of Black Holes, R.M. Wald (Living Reviews version, arxiv version)


Gravity: An Introduction to Einstein's General Relativity
by James B. Hartle

Undergraduate level but I used it for the the graduate intro class. Straightorward with loads of astrophysical examples, avoids fancy math.

Spacetime and Geometry: An Introduction to General Relativity
by Sean Carroll

Readable brief introduction, including most of the mathematical concepts.
The Large Scale Structure of Spacetime
by SW Hawking and GFR Ellis

Hard core mathematical foundations, including many black hole results.

General Relativity
by RM Wald

The current standard for a rigorous and complete treatment. Mathematically abstract.

Specialized books
Black Holes: The Membrane Paradigm
by Kip S. Thorne, Richard H. Price, Douglas A. MacDonald

Black Hole Physics - Basic Concepts and New Developments, by Valeri P. Frolov, Igor D. Novikov

Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (Chicago Lectures in Physics)
<>by Robert M. Wald


The Nature of Space and Time,  S.W. Hawking (especially the second lecture)

Hawking Radiation and Black Hole Thermodynamics

Author: Don N. Page

An inexhaustive review of Hawking radiation and black hole thermodynamics is given, focusing especially upon some of the historical aspects as seen from the biased viewpoint of a minor player in the field on and off for the past thirty years.

Classic Physical Review and Physical Review Letters Papers

Some important classic papers in the development of black hole thermodynamics, published in The Physical Review, available  at The UMD has a subscription so you can access these from a campus computer, or from elsewhere using your library card number, at Click the Research Port.

On Continued Gravitational Contraction
J. R. Oppenheimer and H. Snyder
Phys. Rev. 56 , 455-459 (1939)

Past -Future Asymmetry of the Gravitational Field of a Point Particle
D. Finkelstein
Phys. Rev. 110 , 965-967 (1958)

Gravitational Collapse and Space-Time Singularities
R. Penrose
Phys. Rev. Lett. 14 , 57-59 (1965)
Penrose Black Hole Singularity Paper

Event Horizons in Static Vacuum Space-Times
W. Israel
Phys. Rev. 164 , 1776-1779 (1967)

Gravitational Collapse with Asymmetries
V. de la Cruz, J. E. Chase, and W. Israel
Phys. Rev. Lett. 24 , 423-426 (1970)

Reversible and Irreversible Transformations in Black-Hole Physics
D. Christodoulou
Phys. Rev. Lett. 25 , 1596-1597 (1970)

Gravitational Radiation from Colliding Black Holes
S. W. Hawking
Phys. Rev. Lett. 26 , 1344-1346 (1971)
Hawking Area Theorem Paper

Black Holes and Entropy
J. D. Bekenstein
Phys. Rev. D 7, 2333-2346 (1973)

Generalized second law of thermodynamics in black-hole physics
J. D. Bekenstein
Phys. Rev. D 9, 3292-3300 (1974)

Black holes and thermodynamics
S. W. Hawking
Phys. Rev. D 13 , 191-197 (1976)

Notes on black-hole evaporation
W. G. Unruh
Phys. Rev. D 14 , 870-892 (1976)

Energy-momentum tensor near an evaporating black hole
P. C. W. Davies, S. A. Fulling, and W. G. Unruh
Phys. Rev. D 13 , 2720-2723 (1976)

Origin of the particles in black-hole evaporation
W. G. Unruh
Phys. Rev. D 15 , 365-369 (1977)

Action integrals and partition functions in quantum gravity
G. W. Gibbons and S. W. Hawking
Phys. Rev. D 15 , 2752-2756 (1977)
Cosmological event horizons, thermodynamics, and particle creation
G. W. Gibbons and S. W. Hawking
Phys. Rev. D 15 , 2738-2751 (1977)