SPECIAL AND GENERAL RELATIVITY RESOURCES

FLAT AND CURVED SPACE-TIMES
by George F. R. Ellis and Ruth M. Williams
Oxford University Press, New York, 1988
QC173.59.S65  530.1'1 - dc 19  87-26340  1988
ISBN 0-19-851164-7
ISBN 0-19-851169-8 (pbk.)

FLAT AND CURVED SPACE-TIMES explains special relativity and the
foundations of general relativity theory from a geometric viewpoint.
Space-time geometry is emphasized throughout, and provides the basis of
understanding of the special relativity effects of time dilation,
length contraction, and the relativity of simultaneity. Bondi's
K-calculus is introduced as a simple means of calculating the
magnitudes of these effects, and leads to a derivation of the Lorentz
transformation as a way of unifying these results.  The invariant
interval of flat space-time is generalized to that of curved
space-times, and leads to an understanding of the basic properties of
simple cosmological models and of the collapse of a star to form a
black hole. Appendices enable the advanced student to master the
application of four-tensors to the relativistic study of energy and
momentum, and of electromagnetism.

The authors make recommendations in their afterword suggesting many
fine texts at different levels for student eager to pursue special and
general relativity of which I quote:

"There are many books that present special relativity from various
viewpoints. For the reader wishing to go into more detail at about the
same level as the present book, we suggest SPECIAL RELATIVITY by A. P.
French (Nelson, 1968), or SPACE-TIME PHYSICS by E.F.Taylor and
J.A.Wheeler (Freeman, 1966); these examine in detail the physical
implications of special relativity (the basics of which have been
presented here, but not discussed at great length). For further reading
on general relativity at about the present level, we suggest
Eddington's classic book SPACE, TIME AND GRAVITATION (Harper
Torchbooks, 1959); this was first published in 1920.

"Mathematical foundations and general relativity...  A more detailed
knowledge of either special or general relativity will need more
mathematics than has been assumed in the text. Detailed work in special
relativity will need as a foundation a good knowledge of basic
calculus, such as presented for example in INTRODUCTION TO CALCULUS AND
ANALYSIS by R.Courant and F.John (Interscience, 1965). The foundation
needed in addition in order to understand the mathematics of general
relativity is an understanding of the calculus of several variables. in
particular the meaning and manipulation of partial derivatives as
covered for example in VECTOR ANALYSIS by M.R.Spiegel (Schaum, 1959).
This material will also be needed for more advanced work in special
relativity.

"Most introductions to general relativity proceed from this foundation,
and introduce the needed further mathematics as they go, in particular,
explaining the concepts of tensors (briefly introduced here in the
Appendices) and of tensor derivatives (not presented here). The overall
branch of mathematics needed for a full study of general relativity is
called either Riemannian geometry of differential geometry. An
excellent discussion of this subject is TENSOR CALCULUS by J.L.Synge
and A.Schild (Dover, 1978). There are many texts on general relativity
itself; they are written in varied styles, and different ones will
appeal to different readers. We suggest as an introduction either A
FIRST COURSE IN GENERAL RELATIVITY by B.F.SCHUTZ (Cambridge University
Press, 1985), ESSENTIAL RELATIVITY by W.RINDLER (Springer, 1977), or
GRAVITATION by C.W.Misner, K.S.Thorne, and J.A.Wheeler (Freeman, 1973);
each presents the prerequisite ideas of differential geometry in detail
before discussing both special and general relativity theory and their
applications. A study of one of these books is recommended as a
foundation before tackling advanced texts such as GAVITATION AND
COSMOLOGY by S.Weinberg (Wiley, 1972) or THE LARGE SCALE STRUCTURE OF
SPACE TIME by S.W.Hawking and G.F.R.Ellis (Cambridge University Press,
1973).

"Applications... In the end, the fascination of these theories is in
their applications to the physical world. Some of these are discussed
in the advanced texts mentioned above, but those require considerable
mathematical preparation before full benefit can be derived from them.
However, there are various books that introduce these applications at
about the same level as the present text. Special relativity (together
with quantum mechanics) has fundamental implications for physics in
general (see e.g. THE FEYNMAN LECTURES ON PHYSICS by R.P.Feynman,
R.B.Leighton, and M.Sands, Addison-Wesley, 1963) and in particular for
elementary particle physics (see e.g.  J.E.Dodd, THE IDEAS OF PARTICLE
PHYSICS, Cambridge University Press, 1984). Both special and general
relativity are of importance in understanding high-energy astrophysics,
and this interaction is well discussed in THE PHYSICS-ASTRONOMY
FRONTIER by F.Hoyle and J.V.Narlikar (Freeman, 1980).

"Ultimately one of the most fascinating applications is to the study of
the universe itself, i.e. cosmology. Excellent introductory books of
quite different styles are THE FIRST THREE MINUTES by S.Weinberg (Basic
Books, 1977) and COSMOLOGY by M.Rowan-Robinson (Oxford University
Press, 1977). A thoughtful and in-depth study at the same level as the
present book is COSMOLOGY by E.R.Harrison (Cambridge University Press,
1981), which also deals with ideas of general relativity and
gravitational collapse. If we had to choose from all the excellent
books available a single one to recommend for reading as a companion to
the present volume, it would be this one."


                                               - S. Wormley