From: Edwin F. Taylor [eftaylor@MIT.EDU]
Sent: Tuesday, July 10, 2001 4:09 AM
To: ataylor@artsaxis.com
Subject: new errata
ERRATA (version of 7/2001)

Exploring Black Holes
Introduction to General Relativity
Edwin F. Taylor and John Archibald Wheeler
Addison Wesley Longman, 2000
ISBN#: 0-201-38423-X

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The following errata have been progressively corrected in
sequential printings of the book, as described below.

You ask: "WHICH PRINTING do I have?" It is a bit
complicated. Sorry.

Look at the back cover of the book. In the graphic at the
top of the back cover, locate the shaded cloud with the
label "Cosmology." You have the THIRD printing if that cloud
intrudes into and slightly overlaps the central yellow box
labeled "This Book Describes . . .". If this cloud is
separated from the yellow box by some space, you have a
first or second printing.

Next, turn to the copyright page in the front of the book,
the page that has the heading "Acknowledgments." The very
last line on that page is a string of numbers. If the FIRST
number in that string is 1 (one), then you have a first
printing. If the first number in that string is 2, then you
have either a second printing or a third printing. The back
cover graphic, described above, allows you to distinguish
between the second and third printing.

The following list of errata is limited to significant
errors. Sequential printings have many more changes than
listed here, most of these changes correcting minor typos,
altering phrases to improve clarity, and so forth.


ERROR IN ALL THREE PRINTINGS
The following is a publisher's error, not an author's error
and has mysteriously survived through three printings. Last
page of the book, facing the inside back cover, Selected
Formulas: Formula [C] should have a dt(shell) on the left
side (not dr). Some copies of the SECOND printing contain
TWO pages of Selected Formulas inside the back cover. When
there are two pages, the one nearest to the back cover
contains the error in Formula [C]. Formulas on the page next
to it, one page nearer the front of the book, are correct.


ERRATA IN THE FIRST PRINTING (August 2000)
CORRECTED IN THE SECOND PRINTING (October 2000):

In Acknowledgments (just before the preface), under Book
design, add "Saturn image, lower image in the cover: Erich
Karkoschka, University of Arizona, and NASA"

Project A. Global Positioning System, page A-1 (first page).
In spring 2000 the US government eliminated the "jitter" in
the GPS satellite signals that reduced the resulting
position accuracy for non-military users. Without this
jitter, the accuracy in latitude and longitude is
approximately plus or minus 10 meters.

Project A. Global Positioning System, page A-4, last
paragraph, first line. The numerical value should be 50 000
nanoseconds per day (NOT 5000 nanoseconds per day)

Chapter 4 exercises, page 4-28, top of right-hand column.
First numeral on the right side of the equation for T(shell)
should be 4 (NOT 2).

Chapter 5, page 5-4, the single line of text between
equations [5] and [6]: In
the equation in that line of text, the term dr squared
should have a subscript
"shell".

Project D, Einstein Rings, page D-16. In QUERY 21 the TWO
references to page 5-21 should be changed to page 5-20.

Project E. Light Slowed Near Sun, pages E-4 and E-5, QUERY 6
and caption to Figure 3: Figure 3 shows results for Venus
when, as seen from Earth, Venus approached, but did not
reach, the edge of Sun. In QUERY 6 we calculated a time
delay for a ray that skimmed the edge of Sun. Therefore the
time delay is longer for this skimming path than for a ray
that passes farther from Sun, the case shown in Figure 3.


ERRATA IN THE FIRST AND SECOND PRINTINGS, CORRECTED IN THE
THIRD PRINTING (February 2001):

Chapter 1, page 1-19, end of first sentence, add "free-float
(inertial)" so that the sentence ends: ". . . as measured in
a given free-float (inertial) frame."

Chapter 2, page 2-11, first Thinker question, last sentence.
Change to: "Is this discrepancy caused by gravitational
stretching (or compression) of the measuring rod?

In the Bird response to this first question, add
parenthetical phrase to first sentence, which then ends: ".
. . . will be subject to gravitational stretching (or
compression if held by the lower end)."

Chapter 2, page 2-20, Box, Sloppy Use of Differentials in
Relativity, change first sentence so that it starts, "In
equations [8] and [9] we have begun to use differentials . .
. "

Project B, page B-13, first paragraph of Section 5, last
sentence of that paragraph. Replace italicized sentence with
the italicized sentence: "Inside the horizon your radius r
decreases inexorably."

Project B, page B-16, equation [21]. Replace the label on
the right side of this equation, currently [21. light] with
the label [21. headlight flash].
On the next page, page B-17, equation [22], replace the
current right-hand label [22. light] with the label [22.
taillight flash].

Project C, page C-1, sentence on lines 6 and 7 from the
bottom. The numbers in this sentence are incorrect. The
sentence should read: "The long (major) axis of the ellipse
rotates at the tiny rate of 574 Seconds of arc (0.159
degrees) per century."

Project F, page F-25, parenthesis after equation [41].
Misner, Thorne, and Wheeler, page 913 does NOT contain
misprints.


ERRATA IN THE FIRST, SECOND, AND THIRD PRINTINGS, TO BE
CORRECTED IN THE FOURTH PRINTING (not yet scheduled as of
July 2001):

Chapter 3, pages 3-21, paragraph just before equation [30].
Replace first sentence in this paragraph with the sentence:
"The maximum free-float horizon to crunch wristwatch time
occurs for a traveler dropping from rest just outside the
horizon."

Chapter 3, page 3-31, exercise 8, first paragraph. Replace
the parenthetical expression that ends this first paragraph
with the following: "(the maximum possible free-float
horizon-to-crunch time, see equations [30] and [31] on page
3-21)."

Chapter 5, page 5-26, last paragraph, third sentence.
Eliminate the word "radially" so that the sentence reads:
"Inside the horizon, inward motion is inevitable and no
stationary shell exists."

ERROR in Project F, The Spinning Black Hole.
NOTE: REVISION OF THIS PROJECT AS A PDF FILE IS AVAILABLE ON
THIS SAME DOWNLOAD PAGE.
This project says several times, incorrectly, that an
observer at rest outside the static limit of a rotating
black hole must fire rockets tangentially to keep from
revolving in the direction of rotation of the black hole.
(This is in addition to the radially-inward rocket blast
needed to maintain constant radial position.) The TANGENTIAL
rocket blast is NOT needed to maintain a stationary
position.

Wrong statements are found on:
page F-7 near the middle of the first paragraph
page F-13, last sentence in the paragraph before QUERY 15
GLOSSARY under "frame dragging"

The following two sentences imply there is a tangential
force where there is none: The second to last sentence in
the paragraph following equation [27], page F-16. Fourth
line from the bottom of the page in the last paragraph on
page F-16.

Cause of error: A faulty analogy, namely that spacetime is
"swept around a rotating black hole like a tornado." In a
tornado you have to lean against the wind, against the
rotation, in order to stand still. NOT SO for standing still
near a rotating black hole!

What is the truth? The ring rider (Section 9 of Project F)
has zero angular momentum, and this rider, along with his
ring, rotates in the direction of rotation of the spinning
black hole. Therefore someone at rest (not rotating around
the black hole) at the same radius (but outside the static
limit) must have angular momentum. This angular momentum is
negative, since such an observer stays behind the positive
rotation of the zero angular momentum rings.

Now suppose that you descend from a great distance along a
radius fixed with respect to the remote stars. As you move
radially inward, the magnitude of your (negative) angular
momentum must increase. So to stay on the radial path of
your descent, you have to fire a rocket tangentially in the
direction of rotation of the black hole, but ONLY WHILE YOU
ARE DESCENDING.

How much will you have to increase your negative angular
momentum as you descend along a fixed radius? The answer
comes from equation [21] on page F-13 with dphi/dtau = 0.
Use equation [15] on the same page to eliminate dt/dtau from
equation [21]. Notice the result that the value of the
angular momentum approaches minus infinity as you descend to
the static limit at r = 2M.

However, if you stop your radial motion outside of the
static limit, you have already achieved the angular momentum
required to keep you from moving tangentially. Your rocket
needs to point only radially inward as you hover at rest
near the rotating black hole.

Project G. Friedmann Universe, page G-9. Two sentences are
missing at the top of this page. "We use the Greek
lower-case symbol eta to describe the angle of rotation of
the wheel. Introduce the following substitution into
equation [19]:"

Inside back cover, Conversion Factors at the bottom. 1 year
= 3.156 (NOT 3.157) times 10 million seconds.


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If you locate an error in the printed textbook,
please forward details to:
eftaylor@mit.edu