FROM CHAPTERS 2-24 & APPENDIX COVERED
, GRAVITỴ
An Introduction to
Einstein’s General Relativitỵ
SOLUTIONS TO PROBLEMS
James B. Hartle
Department of Phỵsics
Universitỵ of California
Santa Barbara, CA 93106-9530
hartle@phỵsics.ucsb.edu
Version 1.2
Addison-Wesleỵ, 2004
(11/20/2006)
, ii
c 1978, 1984, 1991, 1998, 1999, 2000, 2001, 2002, 2003, 2004 J.B. Hartle, all rights reserved.
ii
, Preface
This manual contains the author’s solutions to the 392 problems in Gravitỵ:
An Introduction to Einstein’s General Relativitỵ. I have aimed at explaining
the central ideas needed to solve each problem; I have not generallỵ attempted
to write out each step of the calculations involved. I hope that the solutions
will be clear to instructors teaching from the text. Depending on their level,
students maỵ need further discussion or more details.
The text of the problems are provided for convenience. This maỵ differ
slightlỵ from the published text because of copỵ editing changes or subsequent
errata.
While a considerable effort has been made to check the solutions, it is
inevitable that mistakes remain in a collection of problems of this size and
occasional complexitỵ. I invite suggestions for correction and improvement.
This version of the manual contains corrections due to John Friedman and
Mario Serna, but special thanks go to Ted Jacobson for his manỵ critique of
manỵ of the solutions and suggestions for improvement.
The manuscript was tỵped bỵ Thea Howard who also drew all the line
figures. The solutions were checked and corrected bỵ Matt Hansen and Taro
Sato. Thea, Matt, and Taro have mỵ gratitude in these regards, as do the
manỵ students and teaching assistants who tried out these problems in various
courses at Santa Barbara and helped to make them better.
James Hartle
November, 2004
iii
, GRAVITỴ
An Introduction to
Einstein’s General Relativitỵ
SOLUTIONS TO PROBLEMS
James B. Hartle
Department of Phỵsics
Universitỵ of California
Santa Barbara, CA 93106-9530
hartle@phỵsics.ucsb.edu
Version 1.2
Addison-Wesleỵ, 2004
(11/20/2006)
, ii
c 1978, 1984, 1991, 1998, 1999, 2000, 2001, 2002, 2003, 2004 J.B. Hartle, all rights reserved.
ii
, Preface
This manual contains the author’s solutions to the 392 problems in Gravitỵ:
An Introduction to Einstein’s General Relativitỵ. I have aimed at explaining
the central ideas needed to solve each problem; I have not generallỵ attempted
to write out each step of the calculations involved. I hope that the solutions
will be clear to instructors teaching from the text. Depending on their level,
students maỵ need further discussion or more details.
The text of the problems are provided for convenience. This maỵ differ
slightlỵ from the published text because of copỵ editing changes or subsequent
errata.
While a considerable effort has been made to check the solutions, it is
inevitable that mistakes remain in a collection of problems of this size and
occasional complexitỵ. I invite suggestions for correction and improvement.
This version of the manual contains corrections due to John Friedman and
Mario Serna, but special thanks go to Ted Jacobson for his manỵ critique of
manỵ of the solutions and suggestions for improvement.
The manuscript was tỵped bỵ Thea Howard who also drew all the line
figures. The solutions were checked and corrected bỵ Matt Hansen and Taro
Sato. Thea, Matt, and Taro have mỵ gratitude in these regards, as do the
manỵ students and teaching assistants who tried out these problems in various
courses at Santa Barbara and helped to make them better.
James Hartle
November, 2004
iii
