 
Astronomía
Scientific
American Bookmarks 
Summary: As longtime readers of Scientific American
probably know, discoveries made over the past century have
revolutionized the study of the cosmos. Indeed, as our January special
report reveals, the universe seems to get stranger and stranger with
each new finding. But if all this talk about the past, present and
future of our universe has left you out in the cold, you might want to
check out the Cosmology Tutorial created by Edward L. Wright 
Scientific
American  Cosmology 
Introducción a al cosmología  Publicaciones de
scientific Am. sobre el tema. 
Cosmology
Tutorial 
Ned Wright's Cosmology Tutorial UCLA My cosmology
tutorial is an attempt to summarize these discoveries. It will be "under
construction" for the foreseeable future as new discoveries are
made. I will attempt to keep these pages uptodate as a resource for
the cosmology courses I teach at UCLA 
Relativity
tutorial 
Ned Wright's Relativity Tutorial UCLA 
Relativity
on the World Wide Web 
Numerosos vinculos a sitios sobre Relatividad general y
Cosmología  En Ingles 
Original by Chris Hillmam (Last modified by Chris Hillman, 24 Jan 2001)
Relativity on
the World Wide Web
To really appreciate the beauty and subtleties of general relativity,
you must grapple with the mathematics, which lies, unfortunately, just
beyond the undergraduate level. Here are some fine graduate level course
notes, tutorial papers, and review papers on the following topics:
 basic
general relativity,
  white
dwarfs and neutron stars,
  gravitational
collapse,
  classical
black holes,
  gravitational
waves,
  cosmology,
  numerical
relativity,
  tests
of general relativity,
  thermodynamics
of black holes,
  further
special topics in gtr,
  quantum
gravity,
  astrophysical
background,
  mathematical
background,
  miscellania. 
Some of these resources are written at the beginning graduate level; others
are more specialized papers and these tend to be more demanding.
Important Note! I don't have a secretary to
help me maintain these pages, and to keep the work manageable, I have only
attempted to list here some representative review papers, not any
individual research papers, however important these might be. I hope the
resources gathered here will help graduate students in any area of physics
get some idea of the wealth of current research in gtr and closely related
areas, and I'd also like to try do what little I can to ``reward'' those
experts who have taken the trouble to try to write review papers of their
special areas of expertise.
 A
Short Course on GR, by William L. Burke, (Physics, UC Santa
Cruz). Topics covered include weak field theory, gravitational waves,
radiation damping, cosmology, the Friedmann and Lemaitre dusts,
singularities, black holes, the Schwarzschild metric and Kruskal's
extension of it. There is an appendix on mathematical notation. This is a
single postscript document (about 75 pages).
  Lecture
Notes on General Relativity by Matthias
Blau (ICTP, Trieste). A very readable and complete set of course
notes, written for advanced undergraduates but also useful to graduate
students, particularly since they cover some topics which are slighted in
other notes. Topics covered include the equivalence principle,
gravitational redshift, tensor analysis, covariant derivatives, Lie
derivatives, Killing vectors and conservation laws, geodesics and
effective potential analysis, the Riemann, Weyl, Ricci, and Einstein
curvature tensors, intrinsic versus extrinsic geometry, the Bianchi
identities, the Jacobi equation for geodesic deviation, the principle of
minimal coupling, the matter tensor and the Einstein field equation,
variational principles, a thorough study of the Schwarzschild solution,
weak field theory and gravitational waves (including detector theory), and
cosmology (vacuum, radiation, and matter dominated FRW models). The
lecture notes end with a very thorough discussion of the KaluzaKlein
theory and and introduction to the notion of a nonabelian gauge theory.
This is a single postscript document (about 180 pages).
  Lecture
Notes on General Relativity, by Sean
M. Carroll (Physics, University of Chicago). From a course taught at
MIT. Topics covered include str, manifolds, covariant derivatives,
connections, curvature, Lie derivatives, pullbacks, Killing vectors, the
Equivalence Principle, the matter tensor, the field equation of gtr (Einstein's
equation), the initial value and variational principle formulations of the
field equation, weak field theory, gravitational waves, a complete
discussion of the Schwarzschild solution, cosmology and the Friedmann
solutions. Carroll's careful discussion of the geometry of the Kerr
solution is particularly noteworthy. The lectures are available as either
html or postscript documents (about 200 pages total).
  General
Relativity, by Petr Hadrava, (Astronomical Institute, Academy
of Sciences of the Czech Republic). Lecture notes (in English) on str and
gtr. Topics include the Equivalence Principle, the field equations, weakfield
theory, the Schwarzschild exterior (vacuum) and interior (stellar
"fluid") solutions, the Friedmann cosmological solutions. Two
mathematical appendices sketch the mathematics of tensor algebra, exterior
algebra, connection, Lie derivatives, Killing vectors, and variational
principles. This is a single postscript document (50 pages).
  Introduction to General
Relativity, by Gerard 't Hooft (Institute for Theoretical
Physics, Utrecht University). Lecture notes (in English) on gtr. Written
for advanced undergraduates, these notes work through the basics in
careful detail, but they would also be good for graduate students. 't
Hooft won the Nobel prize in physics for his work on quantum field theory,
so it is interesting to see his viewpoint on general relativity. This is a
single postscript document (69 pages). 
 Rotating
Stars in Relativity , by Nikolaos Stergioulas (Physics,
University of WisconsinMilwaukee) offers a very nice introduction to
models of rotating stars in hydrostatic equilibrium, as treated in gtr.
Stergioulas also gives an introduction to the important topic of CFS
instabilities, a phenomenom by which certain types of perturbations
in a rotating relativistic star in which frame dragging is significant (e.g.
a rapidly rotating neutron star) can actually be "pumped up"
rather than "damped" by the emission of gravitational radiation.
("CFS" stands for Chandrasekhar, Friedmann, and Schutz, after
the researchers who first established the existence of this intriguing
phenomenom.) See also the review paper by Kokkotas and Schmidt listed below,
for more information about quasinormal modes in the perturbations of
rotating relativistic stars. This is an invited paper in the Living
Reviews series.
  GravitationalWave
Driven Instability of Rotating Relativistic Stars , by John
L. Friedman (Physics, University of WisconsinMilwaukee) and Keith H.
Lockitch (Physics, Penn. State) offers a brief review to rmode
instabilities, the most frequently studied type of CFS instability.
  The
Properties of Matter in White Dwarfs and Neutron Stars , by
Shmuel Balberg and Stuart L. Shapiro (Physics, University of Illinois at
UrbanaChampaign). This readable survey provides an introduction to what
is currently known about the physical properties of condensed matter at
the extreme densities found in white dwarfs and neutron stars, and
examines how well existing theories agree with observations.
  Recent
Progress in Neutron Star Theory , by H. Heiselberg (NORDITA)
and V. Pandharipande (Physics, University of Illinois at UrbanaChampaign).
This is a more advanced survey of the theory of neutron stars, featuring a
huge bibliography!
  Superfluidity
in Relativistic Neutron Stars , by David Langlois (DARC,
Meudon & IAP, Paris) is concise survey of one of the most mysterious
aspects of neutron star interiors: there must be microscopic tubes of
magnetic flux threading the superfluid interior.
  Accretion
Processes Around Black Holes And Neutron Stars: Advective Disk Paradigm ,
by Sandip K. Chakrabarti (S. N. Bose National Center for Basic
Sciences, Calcutta) offers a brief introduction to the physics of
accretion disks, as treated by the most popular model (advection dominated
flow). 
 Gravitational
Collapse and Cosmic Censorship , by Robert M. Wald (Physics,
University of Chicago) offers a review of the theoretical status of the
weak cosmic censorship hypothesis.
  Gravitational
Collapse , by P. S. Joshi (Tata Insitute of Fundamental
Research, Bombay) offers a gentle introduction to some of the most
commonly studied models of gravitationcal collapse, including
 the OS (OppenheimerSnyder) model of an imploding spherical dust
ball,
  the VP (VaidyaPapapetrou) model of imploding spherical shells
massless radiation,
  the LTB(LemaireTolmanBondi) models of inhomogeneous collapsing
dust balls,
  numerical and theoretical studies of collapsing fluid drops,
  numerical and theoretical studies of collapsing scalar fields. 
Unfortunately, colliding gravitational waves are not considered. See
however the review paper by Bicak listed below
for more information about exact solutions modeling the collision of
gravitational plane waves. Joshi's paper appeared in Singularities,
Black Holes and Cosmic Censorship (On the fortieth anniversary of the
Raychaudhuri Equation), IUCAA publication, Pune, India.
  Critical
Phenomena in Gravitational Collapse, by Patrick R Brady and
Mike J Cai offers a concise and very readable introduction to this
important and very surprising recent discovery.
  Critical
Phenomena in Gravitational Collapse, by C. Gundlach (Enrico
Fermi Institute, University of Chicago), a very clear invited review paper
in the Living
Reviews series. It is more detailed than the preceeding paper. (Note:
see the review paper by Coley listed below
for another way in which modern dynamical systems theory is useful in gtr.) 
 Black
Holes, by Paul Townsend (Applied Mechanics and Theoretical
Physics, Cambridge). A very thorough introduction, studies the
Schwarzschild, ReissnerNordstrom, and Kerr solutions using a variety of
coordinate systems. Additional topics include gravitational collapse,
horizons, singularities, CarterPenrose diagrams (aka conformal
compactification), Hawking radiation and black hole thermodynamics. This
is a 145 page postscript document.
  Scattering
by Black Holes, by N. Andersson and B.P. Jensen (Mathematics,
Univerity of Southampton). This excellent survey is one chapter in the
Encyclopedia on Scattering, which will be published by Academic Press. The
paper surveys wave propagation in blackhole spacetimes, diffraction
effects in wave scattering (including "light bending"),
resonances, and quasinormal modes, among other topics.
  Stringy
Black Holes, by Martijn Derix and Jan Pieter van der Schaar (Institute
for Theoretical Physics, Rijksuniversiteit, Groningen, The Netherlands).
An extensive set of htmlified lecture notes. Includes a review of
Schwarzschild and ReissnerNordstrom holes, elecricmagnetic duality,
dilaton holes, axion holes, and much more. 
 The
Gravitational Wave Symphony of the Universe, by B.S.
Sathyaprakash (Physics and Astronomy, Cardiff) offers a concise overview
of the theory of astrophysical sources of gravitational radiation and the
theory of laser interferometric detectors..
  Gravitational
Radiation, by Bernard F Schutz (Max Planck Institute for
Gravitational Physics, Potsdam), offers a very nice introduction to this
subject. This is an article from the Encycopedia of Astronomy and
Astrophysics.
  Gravitational
Wave Astronomy, by Bernard F Schutz (Max Planck Institute for
Gravitational Physics, Potsdam). An readable and well balanced overview of
the theory of the generation and detection of gravitational waves.
Appeared in Class.Quant.Grav. 16 (1999) A131A156.
  Gravitational
Radiation Sources and Signatures, by Lee Samuel Finn (Center
for Gravitational Physics and Geometry, Penn State). An excellent
introduction to the theory of gravitational wave generation by
astrophysical sources, the theory of interferometer detectors such as
LIGO, and a survey of possible signals.
  Gravitational
Radiation from Relativistic Sources , by Luc Blanchet (CNRS,
France). Another very thorough introduction to the theory of gravitational
wave generation by astrophysical sources, more challenging than the
previous one.
  Gravitational
Radiation Theory and Light Propagation , by Luc Blanchet
(CNRS, France), Sergei Kopeikin (Physics & Astronomy, University of
MissouriColumbia) and Gerhard Shaefer (Theoretical Physics Institute,
FriedrichSchiller University, Jena, Germany) offers an introduction to
the propagation of light rays in gravitational fields, including postNewtonian
effects beyond the quadrupole approximation, such as higher order
multipoles, spinspin interactions, and backreaction. Appeared in the
book Gyros, Clocks, and Interferometers: Testing Relativistic Gravity
in Space, ed. C. Laemmerzahl, C.W.F. Everitt, F.W. Hehl, SpringerVerlag,
2000.
  Probing Black
Holes and Relativistic Stars with Gravitational Waves, by Kip
Thorne (Theoretical Astrophysics, Cal Tech). Focuses on the theory of the
LIGO interferometers and similar detectors, and gives a survey of what
kinds of signals astrophysicists expect to ``hear'' with this instruments.
This paper appeared in the book Black Holes and Relativistic Stars:
Proceedings of a Conference in Memory of S. Chandrasekhar, ed. R. M.
Wald, University of Chicago Press, 1999. See also the same author's earlier
survey.
  Gravitational
Wave Experiments and EarlyUniverse Cosmology, by Michele
Maggiore. This is a review of possible signatures of the so called ``relic
waves'' from the very early universe, and the possibilities for detecting
them using LIGO and other interferometers. Appeared in Phys.Rept.
331 (2000) 283367. 
 Gravitation
and Experiment, by Thibault Damour (IHES, DARC) offers a
concise overview of this gigantic subject. Appeared in Proceedings of
Princeton's 250th Anniversary Conference on Critical Problems in Physics (October
31November 2, 1996), Princeton University Press, 1997. See also this
updated review by the
same author, which appears in the year 2000 edition of the Review
of Particle Physics.
  The
Confrontation between General Relativity and Experiment: A 2001 Update,
by Clifford M. Will (Physics, Washington University, St. Louis)
offers a more extensive survey, including the classical solar system tests
and binary pulsar data, together with the prospects for direct detection
of gravitational waves.
  Binarypulsar
tests of strongfield gravity, by Gilles EspositoFarese (Theoretical
Physics, CNRS) gives more detail concerning the very stringent tests posed
by binarypulsar timing (and passed by gtr!), including the work of Taylor
and Hulse on PSR1913+16.
  Astrophysical
Evidence for the Existence of Black Holes by Annalisa Celotti,
John C. Miller, and Dennis W. Sciama (SISSA, Trieste, Italy), offers a
short history of how the existence of astrophysical black holes came to be
essentially universally accepted by astronomers. The paper focuses on the
rather different types of evidence for the two best known classes of
astrophysical black holes: supermassive black holes and solar mass black
holes. Appeared in the millenium issue of Class.Quant.Grav. 16 No
12A (December 1999), A3.
  Supermassive
Black Holes in Active Galactic Nuclei, by John Kormendy
(Univ. Texas at Austin) and Luis C. Ho (Carnegie Observatories). In the
past few decades it has become universally accepted that supermassive
black holes provide the ``engine'' powering active galatic nuclei (AGN's)
such as quasars and Seyfert galaxies. This review article (to appear in The
Encyclopedia of Astronomy and Astrophysics (Institute of Physics
Publishing), discusses the currently available stellar dynamical evidence
for supermassive black holes living at the core of AGN's. 
I have listed here some expository papers on the laws of black holes
mechanics and their reformulation in terms of classical mechanics, using
Hawking's astonishing discovery that black holes radiate with a black body
spectrum and thus have a well defined temperature like any other black body
(which is of course classical a perfect absorber, just like a black hole).
 The
Thermodynamics of Black Holes, by Robert M. Wald. An uptodate
review by the leading expert in this field.
  Introductory
Lectures on Black Hole Thermodynamics, by Ted Jacobson (Insitute
for Theoretical Physics, University of Utrecht). Another uptodate review
by the phsyicist who has made some progress toward deriving the Einstein
field equation from the laws of black hole thermodynamics, rather than the
other way around.
  An Introduction
to Black Hole Evaporation, by Jennie Traschen (Physics,
University of Massachusetts at Amherst). This very readable paper offers a
tutorial in the actual computation of Unruh, Hawking, Gibbons and other
radiation, and examines the end states of evaporation in de Sitter and AdS
backgrounds, in the case of charged and rotating holes. The paper has
appeared in print in Mathematical Methods of Physics, proceedings
of the 1999 Londrina Winter School, ed. by A. Bytsenko and F. Williams,
World Scientific, 2000. 
 Selected
Solutions of Einstein's Field Equations: Their Role in General Relativity
and Astrophysics, by Jiri Bicak (Institute of Theoretical
Physics, Charles University, Prague). This is a comprehensive introduction
to the most important exact solutions in gtr, including the Minkowksi, de
Sitter, antide Sitter background vacuums, the Schwarzschild solution and
charged and rotating generalizations, the TaubNut solution, plane waves,
colliding plane waves, cylindrical waves, and cosmological models. This is
an invited paper from a new book, Einstein Field Equations and Their
Physical Implications, edited by Berndt Schmidt, Springer, 2000. (126
pages).
  The Cauchy
Problem for the Einstein Equations , by H. Friedrich and A.
D. Rendall (Max Planck Institue for Gravitational Physics, Potsdam). This
is a comprehensive introduction to a fundamental but technically rather
involved topic in general relativity. This is a single postscript document
(98 pages). This paper appeared in print in the book Einstein's Field
Equations and their Physical Interpretation, (ed. B. G. Schmidt,
SpringerVerlag, 2000.
  QuasiNormal
Modes of Stars and Black Holes, by Kostas D. Kokkotas and
Bernd G. Schmidt. In Newtonian models of spherical stars, perturbations (e.g.
due to a small lump) can be decomposed into a sum over normal modes,
rather like a multidimensional Fourier series. In gtr, such vibrations are
slowly damped out (or sometimes pumped up!!) by the emission of
gravitational radiation, so they are called quasinormal modes.
This important topic is the subject of this invited review paper in the Living
Reviews series.
  Reflections
on Gravity, by Norbert Straumann (Institute for Theoretical
Physics, University of Zurich). This brief paper offers a nice sketch of
an approach to deriving the EFE which was advocated by Feynman. The basic
idea is to start with Newtonian gravitostatics, considered to consist of
the Poisson equation on Minkowksi spacetime, and then try to follow the
model of how one passes from electrostatics to Maxwell's theory of
electrodynamics (which is Lorentz covariant) and then to quantum
electrodynamics, fixing up the approach as needed. In particular, it turns
out that one must introduce back reaction of the gravitational field on
matter, which leads a kind of infinite series of approximations, which was
cleverly "summed" by Deser. The end result is the EFE! However,
the original metric of flat spacetime turns out to be unobservable and the
original hypothesis of Lorentz covariance becomes moot! Caution!:
Straumann inexplicably fails to mention the fact that the approach he is
discussing only yields a "local mimic" of gtr; unless one
carries the "geometrization" one step further by interpreting
the quantum fields as existing on one of many coordinate charts, one
excludes all the solutions to the EFE which have nontrivial topology. The
following paper covers the ideas Straumann is discussing from a somewhat
different persepective (among many other topics).
  Actions for
Gravity, with Generalizations: A Review, by Peter Peldan (Institute
of Theoretical Physics, Chalmers Technical Univerisity and Goetteborg
University, Sweden) offers a very concise but comprehensive (as of 1993)
review of Lagrangian and Hamiltonian formulations of general relativity,
including Askhetar's "new variables" Hamiltonian formalism. This
is a 61 page postscript document the diagram relating the various
formalisms is alone worth the price of admission. A word of advice:
prospective readers should first study the formulation of classical
mechanics in terms of Lagrangians and Hamiltonians first, and then study
the appendix in Wald carefully and make sure they understand the
distinction between tensors and tensor densities. Without this background,
the reader will soon get lost. This paper appeared in print in the premier
journal in gravitation physics: Class.Quant.Grav. 11 (1994) 1087.
  Topological
Censorship, by Kristin Schleich and Donald M. Witt (Physics,
University of British Columbia, Vancouver) is an expository paper on an
important theorem, the Topological Censorship Theorem (proven by the
authors and John Friedman) which says in essence that any nontrivial
topology of an isolated system such as an individual black hole (possibly
with exotic fields, aka "hair") cannot be observed by distant
observers. The theorem assumes that the spacetime is globally hyperbolic (see
the preceding paper for the definition!) and that the null energy
condition holds. Note well: the first assumption fails for some
very important exact solutions in gtr, e.g. plane waves, and the second
assumption fails for "traversable wormholes" and for at least
some solutions in many proposed classical field theories involving scalar
fields. Nevertheless, this theorem is an important and fairly general
result. This paper appeared in print in Proceedings of the Lake Louise
Winter Institute, Particle Physics and Cosmology, Feb. 2026, 1994,
(World Scientific, 1994).
  New properties
of Cauchy and event horizons, by Robert Budzynski (Physics,
Univ. of Warsaw), Witold Kondracki and Andrzej Krolak (Institute of
Mathematics, Polish Academy of Sciences) discusses the state of our
knowledge concerning the smoothness properties of Cauchy and event
horizons.
  Some Recent
Progress in Classical General Relativity, by Felix Finster,
Joel Smoller, and ShingTung Yau. This is an introduction to the positive
mass theorem and related results in the global analysis of generic
solutions in gtr. The third author won a Fields Medal (the highest award
in mathematics) in part for his role in proving the Positive Mass Theorem.
This appeared in print: J.Math.Phys. 41 (2000) 39433963.
  BoostRotation
Symmetric Spacetimes  Review, by V. Pravda and A. Pravdova (Mathematical
Institute, Academy of Sciences, Prague) offers a readable introduction to
some of the most interesting exact solutions in gtr, including
accelerating pairs of black holes and many more examples. This paper
appeared in print: Czech.J.Phys. 50 (2000) 333376. 
 Quantum
Gravity at the Turn of the Millennium, by Gary Horowitz (Physics,
UC Santa Barbara), offers a concise and very readable (but of course very
sketchy!) overview of the state of the art in the search for a quantum
theory of gravity.
  Here are three very readable expository papers by Carlo Rovelli
(Physics, University of Pittsburgh), one of the leading researchers on
quantum gravity:
As Rovelli points out in one of these papers, this is a very rapidly
developing and extremely active field of research, and his viewpoint
should not be regarded as being the only one reasonable one, or as the
definitive account of what quantum gravity is or should be and how it may
be in the process of becoming a reality.
  Spacetime and
the Philosophical Challenge of Quantum Gravity, by
J.Butterfield (Oxford) and C.J.Isham (Blackett Laboratory, Imperial
College, London) offers a thoughtful discussion of conceptual problems
which arise various approaches to quantum gravity and how these might be
overcome.
  Are We at the
Dawn of QuantumGravity Phenomenology?, by Giovanni AmelinoCamelia
(CERN) reviews recent progress in quantum gravity and argues that,
contrary to a longheld viewpoint, theories of quantum gravity may be
testable.
  String/Mbranes
for Relativists, by Donald Marolf (Physics, Syracuse
University). This offers a tutorial in string theory and Mbrane theory
for gtr students.
  Large N Field
Theories, String Theory and Gravity, by O. Aharony, S. S.
Gubser, J. Maldacena, H. Ooguri, and Y. Oz. This huge review paper covers
the holographic conjecture, connections with conformal field theories and
the antideSitter vacuum, and discusses some possible implications for
the theory of black holes. (261 page postscript document, with figures).
  Superstring
Cosmology, by James E. Lidsey (Astronomy, Queen Mary &
Westfield, London), David Wands (Computer Science and Mathematics,
Portsmouth), and E. J. Copeland (Center for Theoretical Physics, Suffex).
This review stresses the role of duality symmetries in superstring theory
and their cosmological implications. 
 Advanced
Astrophysics, by Neb Duric (Physics and Astronomy, University
of New Mexico). A full length online set of course notes. Covers the
virial theorem, galactic rotation curves, galactic formation, galactic
clusters and other large scale structures, dark matter, the Hubble
expansion, applications of thermodynamics and statistical mechanics to
astrophysics and cosmology, COBE and the CMBR, astrophysics of planets,
white dwarfs, supernovaes, Xray binaries, neutron stars, and black holes,
accretion, the Eddington limit, Reaction Rates and Equilibria in
Astrophysics Planck, Boltzmann and Saha equations, cosmological
nucleosynthesis, solar neutrion problem, EM radiation, magento,
relativistic and thermal bremmsstrahlung, inverse Compton emisssion, and
more.
  Nucleosynthesis
Basics and Applications to Supernovae, by F.K. Thielemann,
T. Rauscher , C. Freiburghaus (Physik und Astronomie, Universitaet Basel),
K. Nomoto, M. Hashimoto (Institute for Theoretical Physics, UC Santa
Barbara), B. Pfeiffer and K.L. Kratz (Institut fuer Kernchemie,
Universitaet Mainz). This is a 52 page introduction to the basic equations
for thermonuclear reaction rates and nuclear reaction networks, and
applications of this theory to nucleosynthesis of heavy elements in aging
stars.
  Topics in
Neutrino Astrophysics, by W. C. Haxton (Physics, University
of Washington, Seattle), offers a 56 page introduction to solar neutrino
problem and its implications.
  A Dying
Universe: The Long Term Fate and Evolution of Astrophysical Objects by
Fred C. Adams and Gregory Laughlin (Physics, Univ. of Michigan). This is a
57 page postscript document, which appeared in Rev.Mod.Phys. 69
(1997) 337372. 
 Differential
Geometry, by Sergei Yakovenko (Weizmann Institute). A
complete set of lecture notes. Topics include manifolds, diffeomorphisms,
partitions of unity, the Whitney embedding theorem, tangent bundle,
algebra of vector fields, Lie derivatives, commutators, points as maximal
ideals, derivations, local rings, differentiable forms, etc.
  The Theory of
Caustics and Wavefront Singularities with Physical Applications, by
Juergen Ehlers (Max Planck Institute for Gravitation Physics, Potsdam) and
Ezra T. Newman (Physics and Astronomy, Pittsburgh). This is a tutorial
paper on the important work of V. I. Arnold and his collaborators, which
is directly applicable to geometric optics (including the propagation of
gravitational waves) in gtr.
  Noncommutative
Geometry for Pedestrians, by J. Madore (Universite de Paris
Sud and Max Planck Institute). As part of his farreaching programme of
reexpressing most of physics and a huge chunk of modern mathematics in
terms of ``noncommutative geometry'', Alain Connes (a Fields's Medalist)
has recently partially reformulated the EFE in terms of operator theory.
This tutorial paper attempts to explain the background for this work. 
 Riemannian
Geometry and General Relativity, the problem sets (with
solutions) from a course taught by Michael Shubin (Mathematics,
Northeastern).
  Exercises in
General Relativity, from courses taught at the DEA of
Theoretical Physics (Ecole Normale Supérieure de Paris) and at the
University of Geneva (19961999) by JeanPhilippe Uzan (Theoretical
Physics, University of Geneva, Switzerland). 
I hope you'll inspired by the online resources listed on this page to go
offline and do some outside reading! Here is a list of recommended
books at a variety of levels. And be sure to get hold of some symbolic
tensor manipulation software this will make your life a lot easier!


Cosmología
 Cosmology
 Cosmological
models (Cargese lectures 1998), by George F. R. Ellis and Henk
van Elst (Physics, University of Cape Town). A beautiful survey of
mathematical models in cosmology, including anisotropic and inhomogeneous
models, with an emphasis on physical and geometric intuition. In my opinion,
this is a must read for every serious student. Appeared in the book Theoretical
and Observational Cosmology, ed. Marc LachiezeRey, Kluwer, 1999, pp
1116.
  Dynamical Systems in
Cosmology, by A. A. Coley (Mathematics, Dalhousie University)
provides an excellent tutorial on the increasingly important role played by
dynamical systems methods in the analysis of ``minisuperspaces'' in cosmology.
See also the Ph.D. thesis
of Andrew P. Billyard.
  An Exposition on
Inflationary Cosmology, by Scott Watson (Physics, University of
North Carolina at Wilmington). This is an undergraduate level
exposition, including a nice sketch of preinflationary cosmology, and is a
natural choice for a first read in this area.
  Cosmic Inflation ,
by Andreas Albrecht (Physics, UC Davis), offers a timely and well
organized graduate level review of the current status of inflationary models
in cosmology.
  Modern
Observational Cosmology, by Greg Bothun (Physics, University of
Oregon), offers a nice overview of this subject as it existed just prior
to the astounding discovery that the cosmological constant is almost certainly
positive.
  The Cosmological
Constant, by Sean Carroll (Physics, University of Chicago),
offers an uptodate review of this concept, which has recently assumed
renewed importance in cosmology. Carroll also discusses the connection with
the (mysteriously nonzero but low) vacuum energy predicted by some grand
unified theories.
  The Case for a
Positive Cosmological Lambdaterm, by Varun Sahni (InterUniversity
Center for Astronomy and Astrophysics, India) and Alexei Starobinsky (Landau
Institute for Theoretical Physics, Moscow). This is article summarizes the
recent and very compelling evidence for a positive cosmological constant.
Appeared in print: Int.J.Mod.Phys. D9 (2000) 373444.
  The Cosmic
Microwave Background and Particle Physics, by Marc Kamionkowski
and Arthur Kosowsky, offers a 43 p. survey of the implications for particle
physics and cosmology of the next generation of CMBR observations. Topics
discussed include upper bounds derived from the best currently available CMBR
data on the amount of various hypothetical kinds of "dark matter",
including massive neutrinos, WIMPs, axions, and vacuum energy. The effect of
possible exotic topologies for spacelike slices is also discussed. Appeared in
print in Ann.Rev.Nucl.Part.Sci. 49 (1999) 77123.
  Gravitational
Lensing in Astronomy , by Joachim Wambsganss (Astrophysikalisches
Institut, Potsdam) offers a gentle introduction to the theory of gravitational
lensing and its applications in cosmology. This is an invited review article
in the Living Reviews
series.
  Probing the
Universe with Weak Lensing, by Y. Mellier (Institut
d'Astrophysique de Paris and Obs. de Paris DEMIRM), offers a 60 p. review of
the cosmological implications of observations of weak lensing events.
  Weak
Gravitational Lensing , by Matthias Bartelmann and Peter
Schneider (MPA Garching), is a 223 p. review of the theory of weak
gravitational lensing, which is very important in the current search for
"dark matter". 
 Numerical
Relativity in 3+1 Dimensions, by Bernd Bruegemann (Max Planck
Institute for Gravitation Physics, Potsdam) offers a concise overview of the
most important concepts and applications of numerical relativity. This was a
review talk for Journees Relativistes 1999.
  Numerical
Hydrodynamics in General Relativity, by Jose A. Font (MPA,
Garching) offers a comprehensive review (76 pages) of the state of the art of
numerical relativistic hydrodynamics, including conservative and hyperbolic
formulations of the EFE and Euler equations which are suitable for numerical
integration. Applications include numerical simulations of gravitational
collapse, accretion onto black holes, and evolution of neutron stars. This is
an invited review paper in the Living
Reviews series. The online version at the Living Reviews website includes
several animated graphics (fun, fun, fun!). 
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