, GRAVITY
An Introduction to
Einstein’s General Relativity
SOLUTIONS TO PROBLEMS
James B. Hartle
Department of Physics
University of California
Santa Barbara, CA 93106-9530
Version 1.2
Addison-Wesley, 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 Gravity:
An Introduction to Einstein’s General Relativity. I have aimed at explaining
the central ideas needed to solve each problem; I have not generally 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 may need further discussion or more details.
The text of the problems are provided for convenience. This may differ
slightly from the published text because of copy 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 complexity. 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 many critique of
many of the solutions and suggestions for improvement.
The manuscript was typed by Thea Howard who also drew all the line
figures. The solutions were checked and corrected by Matt Hansen and Taro
Sato. Thea, Matt, and Taro have my gratitude in these regards, as do the
many 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
An Introduction to
Einstein’s General Relativity
SOLUTIONS TO PROBLEMS
James B. Hartle
Department of Physics
University of California
Santa Barbara, CA 93106-9530
Version 1.2
Addison-Wesley, 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 Gravity:
An Introduction to Einstein’s General Relativity. I have aimed at explaining
the central ideas needed to solve each problem; I have not generally 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 may need further discussion or more details.
The text of the problems are provided for convenience. This may differ
slightly from the published text because of copy 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 complexity. 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 many critique of
many of the solutions and suggestions for improvement.
The manuscript was typed by Thea Howard who also drew all the line
figures. The solutions were checked and corrected by Matt Hansen and Taro
Sato. Thea, Matt, and Taro have my gratitude in these regards, as do the
many 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
