Exclusive 30% discount on books from Oxford University Press

Key Cosmology and Relativity titles, both new and established are now available with a 30% Discount from Oxford.

To obtain your discount visit http://www.oup.com/uk add the book to your shopping basket and use promo code AAFLY6 at the checkout. Offer Expires 31/08/2014

Introduction to 3+1 Numerical Relativity
Miguel Alcubierre


WAS £69.99 NOW £48.99

A First Course in Loop Quantum Gravity
Rodolfo Gambini and Jorge Pullin


WAS £36.50 NOW £25.55

Gravitational Waves
Volume 1: Theory and Experiments
Michele Maggiore


WAS £57.50 NOW £42.25

Relativistic Hydrodynamics
Luciano Rezzolla and Olindo Zanotti
WAS £55.00 NOW £38.50


Relativity: Special, General, and Cosmological
Second Edition
Wolfgang Rindler
WAS £39.99 NOW £27.99


Steven Weinberg


WAS £52.50 NOW £36.75

Book with A. A. Friedmann’s papers on cosmology

Alexander A. Friedmann, Papers On Curved Spaces and Cosmology (Minkowski Institute Press, Montreal 2014), 74 pages


This book contains three papers by Friedmann – “On the Curvature of Space” (1922), “On the Possibility of a World with a Constant Negative Curvature of Space” (1924), and “On the Geometry of Curved Spaces”. The third paper is a 28-page manuscript (dated 15 April 1922) which has not been published even in Russian.

Unlike the existing two English translations of Friedmann’s 1922 and 1924 papers (done from the German publications), now these papers are translated directly from the original Russian texts.

Vesselin Petkov

New book: “Relativistic Hydrodynamics”, by Luciano Rezzolla and Olindo Zanotti

Relativistic Hydrodynamics
Luciano Rezzolla, Olindo Zanotti
Oxford University Press, 2013
Hard back, 752 pages, 128 colour illustrations, available as ebook
Contents and reviews at http://ukcatalogue.oup.com/product/9780198528906.do

Price: 55 GPB/70 EUR; 20% discount available for hyperspace readers. Enter the code AAFLY4 in the promotional code box when adding to the basket (offer valid till 30.11.13).

Relativistic hydrodynamics is a very successful theoretical framework to describe the dynamics of matter from scales as small as those of colliding elementary particles, up to the largest scales in the universe. This book provides an up-to-date, lively, and approachable introduction to the mathematical formalism, numerical techniques, and applications of relativistic hydrodynamics. The topic is typically covered either by very formal or by very phenomenological books, but is instead presented here in a form that will be appreciated both by students and researchers in the field.

The topics covered in the book are the results of work carried out over the last 40 years, which can be found in rather technical research articles with dissimilar notations and styles. The book is not just a collection of scattered information, but a well-organized description of relativistic hydrodynamics, from the basic principles of statistical kinetic theory, down to the technical aspects of numerical methods devised for the solution of the equations, and over to the applications in modern physics and astrophysics. Numerous figures, diagrams, and a variety of exercises aid the material in the book. The most obvious applications of this work range from astrophysics (black holes, neutron stars, gamma-ray bursts, and active galaxies) to cosmology (early-universe hydrodynamics and phase transitions) and particle physics (heavy-ion collisions).

It is often said that fluids are either seen as solutions of partial differential equations or as “wet”. Fluids in this book are definitely wet, but the mathematical beauty of differential equations is not washed out.

Readership: Graduate and post-graduate students, professors, lecturers, and researchers in astrophysics, particle physics, and applied mathematics.

New book: “Special Relativity in General Frames” by Eric Gourgoulhon

Special Relativity in General Frames: From Particles to Astrophysics
Eric Gourgoulhon
Springer, 2013
784 pages

Special relativity is presented by adopting a four-dimensional point of view from the start. A distinctive feature of the book is that it doesn’t restrict itself to inertial frames and considers accelerated and rotating observers. It is thus possible to treat physical effects such as the Thomas precession or the Sagnac effect in a simple yet precise manner. In the final chapters, more advanced topics like tensorial fields in spacetime, exterior calculus, relativistic hydrodynamics and relativistic gravity are addressed. Illustrated by 178 figures and enriched by many historical notes, this book also presents many applications of special relativity, ranging from particle physics (accelerators, particle collisions, quark-gluon plasma) to astrophysics (relativistic jets, active galactic nuclei), and including practical applications (Sagnac gyrometers, synchrotron radiation, GPS). In addition, the book provides some mathematical developments, such as the detailed analysis of the Lorentz group and its Lie algebra.

1. Minkowski Spacetime
2. Worldlines and Proper Time
3. Observers
4. Kinematics 1: Motion with Respect to an Observer
5. Kinematics 2: Change of Observer
6. Lorentz Group
7. Lorentz Group as a Lie Group
8. Inertial Observers and Poincaré Group
9. Energy and Momentum
10. Angular Momentum
11. Principle of Least Action
12. Accelerated Observers
13. Rotating Observers
14. Tensors and Alternate Forms
15. Fields on Spacetime
16. Integration in Spacetime
17. Electromagnetic Field
18. Maxwell Equations
19. Energy-Momentum Tensor
20. Energy-Momentum of the Electromagnetic Field
21. Relativistic Hydrodynamics
22. What about Relativistic Gravitation?
A. Basic Algebra
B. Web Pages
C. Special Relativity Books

More details on http://relativite.obspm.fr/sperel/

New Book: “General Relativity: 1972 Lecture Notes” by Robert Geroch

Robert Geroch’s lecture notes on general relativity are unique in three main respects. First, the physics of general relativity and the mathematics, which describes it, are masterfully intertwined in such a way that both reinforce each other to facilitate the understanding of the most abstract and subtle issues. Second, the physical phenomena are first properly explained in terms of spacetime and then it is shown how they can be “decomposed” into familiar quantities, expressed in terms of space and time, which are measured by an observer. Third, Geroch’s successful pedagogical approach to teaching theoretical physics through visualization of even the most abstract concepts is fully applied in his lectures on general relativity by the use of around a hundred figures.

Although the book contains lecture notes written in 1972, it is (and will remain) an excellent introduction to general relativity, which covers its physical foundations, its mathematical formalism, the classical tests of its predictions, its application to cosmology, a number of specific and important issues (such as the initial value formulation of general relativity, signal propagation, time orientation, causality violation, singularity theorems, conformal transformations, and asymptotic structure of spacetime), and the early approaches to quantization of the gravitational field.

Robert Geroch, General Relativity: 1972 Lecture Notes (Minkowski Institute Press, Montreal 2013)


New book: “Heart of Darkness-Unraveling the Mysteries of the Invisible Universe” by Jeremiah P. Ostriker and Simon Mitton

Authors: Jeremiah P Ostriker and Simon Mitton
Publisher: Princeton University Press
ISBN: 9780691134307

Heart of Darkness is a popular science book (level of reader = college educated) that describes the incredible saga of humankind’s quest to unravel the deepest secrets of the universe. Over the past thirty years, scientists have learned that two little-understood components–dark matter and dark energy–comprise most of the known cosmos, explain the growth of all cosmic structure, and hold the key to the universe’s fate. The story of how evidence for the so-called “Lambda-Cold Dark Matter” model of cosmology has been gathered by generations of scientists throughout the world is told here by one of the pioneers of the field, Jeremiah Ostriker, and his coauthor Simon Mitton.

New book: “Gauge Theories of Gravitation”, M. Blagojevic and F.W. Hehl (eds.)

M. Blagojevic (Belgrade) and F.W. Hehl (Cologne and Columbia, MO), Editors,


Foreword by T.W.B. Kibble, FRS
Imperial College Press, London, April 2013

Part A The Rise of Gauge Theory of Gravity up to 1961
1. From Special to General Relativity Theory
2. Analyzing General Relativity Theory
3. A Fresh Start by Yang–Mills and Utiyama

Part B Poincar´e Gauge Theory
4. Einstein–Cartan(–Sciama–Kibble) Theory as Viable Gravit. Theory
5. General Structure of Poincare Gauge Theory (Including Quadratic Lagrangians)
6. Translational Gauge Theory
7. Fallacies About Torsion 259

Part C Extending the Gauge Group of Gravity
8. Poincare Group Plus Scale Transformations: Weyl–Cartan Gauge Theory of Gravity
9. From the Poincare to the Affine Group: Metric-Affine Gravity
10. Conformal Gauge Theory of Gravity
11. (Anti-)de Sitter Gauge Theory of Gravity
12. From the Square Root of Translations to the Super Poincare Group

Part D Specific Subjects of Metric-Affine Gravity and Poincare Gauge Theory
13. Hamiltonian Structure
14. Equations of Motion for Matter
15. Cosmological Models
16. Exact Solutions
17. Poincare Gauge Theory in Three Dimensions
18. Dislocations and Torsion
19. The Yang Episode: A Historical Case Study

Experts in gravity who want to purchase a copy of the book, can get presently a 25% discount on it. Please go to the link


and quote WSSPPK25 upon checking out your shopping cart. Then you will enjoy a 25% discount.


New book: "Black Holes in Higher Dimensions", edited by Gary Horowitz

A new book devoted to higher dimensional black holes has recently been published. This edited volume includes contributions from the leading experts in the field.

“Black Holes in Higher Dimensions”
Gary T. Horowitz, editor
422 pages
Cambridge University Press

For more information, see http://www.cambridge.org/knowledge/discountpromotion?code=L2BHHD

Minkowski Institute Press and Minkowski's papers on relativity

Dear Colleagues,

This message is to inform you of the launching of a new academic publisher – the Minkowski Institute Press (MIP):


MIP’s first book is: “Hermann Minkowski, Space and Time: Minkowski’s papers on relativity” (Minkowski Institute Press, Montreal 2012), 123 pages.

Minkowski’s three papers have never been published together either in German or English and Das Relativitätsprinzip has not been translated into English so far. More information about the book is available at: http://minkowskiinstitute.org/mip/books/minkowski.html

Its free version is also available there as well as in Apple’s iBookstore:


MIP will publish textbooks (and lecture notes), monographs, and introductory science and technology books for a wider audience. All books will be ebooks, but print on demand is available; we have received advanced orders for the first book and a week ago the first 110 softcover copies were printed, half of which are now already sold.

Four distinct features of MIP are:

(i) offering books at affordable prices as a means to reach more readers all over the world,
(ii) authors receive 20-25% royalties based on the ebook price (royalties options are given in the publishing agreement the authors sign),
(iii) rapid publication; once a book is accepted (after a reasonable review period) and the submitted manuscript is in LaTeX, MIP will try to publish the ebook within a month.
(iv) most of the profit will be one of the steady sources of funding of a new institute (http://minkowskiinstitute.org/); so publishing with MIP will support the Minkowski Institute.

If you would like to receive the MIP Newsletter (announcing new publications), send a blank email to info[AT]minkowskiinstitute.org.

Best wishes,

Vesselin Petkov


Institute for Foundational Studies “Hermann Minkowski”
Montreal, Quebec, Canada


New book: "Patterns in Physics, Toward a Unifying Theory" by Rejean Plamondon

I am pleased to announce the recent publication of my book:

“Patterns in Physics, Toward a Unifying Theory”, by Rejean Plamondon, 214 pages; 49 figures.
Presses Internationales Polytechnique, June 2012.

The main message conveyed throughout the book is that the four basic interactive forces of physics, which are considered to be empirical facts, can be seen as emergent phenomena described by specific mathematical patterns, when seen through the appropriate representation and interpretation schemes. Similarly, in such a model, once a coherent set of physical units is defined, the values of the fundamental constants can be seen as numerical parametric patterns that can be predicted after taking into account the various projections that are required to perform these measurements as well as the physical environment and the specific context in which these estimates are made.

More specifically, in generalizing a statistical pattern recognition methodology, it is possible to point out some basic patterns that could contribute to bridging the gap between quantum mechanics and general relativity. The whole argument stems from two basic principles: the principle of interdependence and the principle of asymptotic congruence. It starts with an analogy between problem-solving methods in physics and the search for solutions in statistical pattern recognition. Based on this heuristic and analogical approach, a probabilistic version of the Einstein field equations is derived and a solution for the case of a weak-field symmetric massive object is proposed on the grounds of the central limit theorem and the Bayes’ law. The model has only one emergent characteristic feature, a constant parameter which can be associated to the intrinsic proper length or the space-time response of the physical system. The resulting field and potential equations can be seen as generalizations of Newton’s empirical law. Once incorporated in the metric it leads to very chllenging predictions, regarding for example the dark matter and dark energy.

Rejean Plamondon

Ecole Polytechnique de Montreal
Quebec, CANADA

New book: "Relativistic Astrophysics of the Transient Universe" by M.H.P.M. van Putten and A. Levinson

Relativistic Astrophysics of the Transient Universe: Gravitation, Hydrodynamics and Radiation
by Maurice H. P. M. Van Putten and Amir Levinson
Cambridge University Press, 2012

Advance praise:
‘Van Putten and Levinson have made an enjoyable compilation of all those strange things that can happen in our Universe, not only providing detailed physical calculations to understand them, but also including descriptions of all the channels of radiation that we can use to receive as much information about them as we can.’
Gerard ‘t Hooft, Utrecht University, from the Foreword

New Book: "The Geometry of Special Relativity" by Tevian Dray

I am pleased to announce the imminent publication of my book:
“The Geometry of Special Relativity”, by Tevian Dray,
150 pages; 70 figures.
A K Peters/CRC Press, 2012.

Publication details are available at: http://www.crcpress.com/product/isbn/9781466510470

This book emphasizes the use of hyperbolic triangle trigonometry to solve problems in special relativity.

An online version of the book also exists in both wiki and PDF formats: http://www.physics.oregonstate.edu/coursewikis/GSR

Please note that the online version does not contain all of the editorial changes in the print edition.

Companion volumes on differential forms and general relativity are planned; early drafts are available at:



Tevian Dray
Professor of Mathematics
Oregon State University


New book: "The General Theory of Relativity: A Mathematical Exposition" by Anadijiban Das and Andrew DeBenedictis

Anadijiban Das and Andrew DeBenedictis
“The General Theory of Relativity: A Mathematical Exposition”
705 pages, 105 figures.
Springer (2012).

“The General Theory of Relativity: A Mathematical Exposition” will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to:

- tensor analysis,
- the special theory of relativity,
- the general theory of relativity and Einstein’s field equations,
- spherically symmetric solutions and experimental confirmations,
- static and stationary space-time domains,
- black holes,
- cosmological models,
- algebraic classifications and the Newman-Penrose equations,
- the coupled Einstein-Maxwell-Klein-Gordon equations,
- appendices covering mathematical supplements and special topics,

Mathematical rigor, yet very clear presentation of the topics make this book a unique text for both university students and research scholars.

For full publication details please see:




"Quantum Gravity" by C. Kiefer (third edition)

Claus Kiefer: “Quantum Gravity” (Third Edition)
International Series of Monographs on Physics 155, 408 pages
Oxford University Press 2012

Table of Contents:

1: Why quantum gravity?
2: Covariant approaches to quantum gravity
3: Parametrized and relational systems
4: Hamiltonian formulation of general relativity
5: Quantum geometrodynamics
6: Quantum gravity with connections and loops
7: Quantization of black holes
8: Quantum cosmology
9: String theory
10: Phenomenology, decoherence, and the arrow of time

For more information, see: http://ukcatalogue.oup.com/product/9780199585205.do

New Book: "Relativistic Cosmology" by G. Ellis, R. Maartens and M. MacCallum

“Relativistic Cosmology” by George F.R. Ellis, Roy Maartens and Malcolm A.H. MacCallum, was published on 22 March 2012.

Full publication details are available at http://www.cambridge.org/9780521381154 as is a sample consisting of the first 10 pages, the index, and the full table of contents. It’s also listed on Amazon but not (yet) on Abe Books. CUP advise that stocks for the US will arrive in about 6 weeks.

The book has 636 pages and 68 black and white illustrations, many of which are also available in colour on the web page above. Extensive references (40 pages of them) are provided.

From the cover:

Cosmology has been transformed by dramatic progress in high-precision observations and theoretical modelling. This book surveys key developments and open issues for graduate students and researchers. Using a relativistic geometric approach, it focuses on the general concepts and relations that underpin the standard model of the Universe.

Part 1 covers foundations of relativistic cosmology whilst Part 2 develops the dynamical and observational relations for all models of the Universe based on general relativity. Part 3 focuses on the standard model of cosmology, including inflation, dark matter, dark energy, perturbation theory, the cosmic microwave background, structure formation and gravitational lensing. It also examines modified gravity and inhomogeneity as possible alternatives to dark energy. Anisotropic and inhomogeneous models are described in Part 4, and Part 5 reviews deeper issues, such as quantum cosmology, the start of the universe and the multiverse proposal.

From Black Clouds to Black Holes by J V Narlikar (3rd edition)

World Scientific Series in Astronomy and Astrophysics – Vol. 13
From Black Clouds to Black Holes
(Third Edition)
by Jayant V Narlikar (Inter University Centre for Astronomy and Astrophysics, India)

This book presents in a simple style the success story of modern astrophysics — how the application of known physics to models of stars can, together with the observational data, help us understand what stars are made of, how they live and how they die. The account is non-technical but scientifically accurate. It is interspersed with anecdotes and analogies to make the subject matter readable and understandable even to a lay reader with some basic scientific background.

- On Stars and Humans
- Light: The Storehouse of Information
- The Vital Statistics of Stars
- How Far are the Stars?
- A Star is Born
- The Secret of Stellar Energy
- The Origin of Chemical Elements
- When Stars Explode
- Very Dense Stars
- Black Holes
- Binary and Variable Stars
- The Quest Continues

Readership: Any reader interested in astronomy.

To enjoy a 25% discount, please quote NAM2012 as your discount code when you make your purchase. This offer is valid till end of April 2012.

"Vignettes in Gravitation and Cosmology" by Sriramkumar and Seshadri

edited by L Sriramkumar (Harish-Chandra Research Institute, India) and T R Seshadri (University of Delhi, India)
World Scientific

This book comprises expository articles on different aspects of gravitation and cosmology that are aimed at graduate students. The topics discussed are of contemporary interest assuming only an elementary introduction to gravitation and cosmology. The presentations are to a certain extent pedagogical in nature, and the material developed is not usually found in sufficient detail in recent textbooks in these areas.

- Non-Linear Gravitational Clustering in an Expanding Universe
- Dark Ages and Cosmic Reionization
- Probing Fundamental Constant Evolution with Redshifted Spectral Lines
- Averaging the Inhomogeneous Universe
- Probing Cosmic Magnetic Fields with the Cosmic Microwave Background Radiation
- Quantum Corrections to the Bekenstein-Hawking Entropy
- Quantum Measurement and Quantum Gravity: Many Worlds or Collapse of the Wave Function?
- Generation and Evolution of Perturbations During Inflation and Reheating
- Patterns in Neural Processing

Readership: Graduate students and researchers interested in the areas of gravitation and cosmology.

Please quote *NAM2012* as a discount code to enjoy 25% discount from now till April 2012 when you purchase a book from our collection.

New book: "3+1 Formalism in General Relativity" by Eric Gourgoulhon

3+1 Formalism in General Relativity: Bases of Numerical Relativity

Eric Gourgoulhon
Springer, 2012
294 pages

1. Introduction
2. Basic Differential Geometry
3. Geometry of Hypersurfaces
4. Geometry of Foliations
5. 3+1 Decomposition of Einstein Equation
6. 3+1 Equations for Matter and Electromagnetic Field
7. Conformal Decomposition
8. Asymptotic Flatness and Global Quantities
9. The Initial Data Problem
10. Choice of Foliation and Spatial Coordinates
11. Evolution Schemes
A. Conformal Killing Operator and Conformal Vector Laplacian
B. Sage Codes

More details at http://relativite.obspm.fr/3p1

New Book by Anja Skaar Jacobsen: "Leon Rosenfeld"

Physics, Philosophy, and Politics in the Twentieth Century
by Anja Skaar Jacobsen (Niels Bohr Archive, Denmark)

Leon Rosenfeld (1904-1974) was a remarkable, many-sided physicist of exceptional erudition. He was at the centre of modern physics and was well-known as Niels Bohr’s close collaborator and spokesman. He also reflected deeply on the history and philosophy of science and its social role from a leftist perspective. His biography illuminates the development, popularization, and reception of quantum physics and its interpretation in addition to the development of the political Left. The book draws extensively from previously untapped, unpublished sources in more than five languages.

This book is for students and professionals studying the history of science.

360pp (approx.)
Publication date: March 2012
ISBN: 978-981-4307-81-9

New relativity books by M. S. Berman

“General Relativity and the Pioneers Anomaly”

This book is an introduction to the General Relativity Theory (GRT) and to the solution of the Pioneers Anomaly by means of relativistic cosmology, a study that is designed to be understood by undergraduate and graduate students alike in the fields of theoretical physics, applied mathematics and space engineering. In fact, this book is the first elementary account of GRT and cosmology to address the NASA problem, which consists of a specific deceleration suffered by two space-probes launched to outer space more than thirty years ago. The other two NASA anomalies, which are, the spin-down of the Pioneers, when they were not disturbed, and the “fly-by” of spacecraft in gravity assists, around the Earth, are explained by Berman, along with the linear deceleration, by the rotation of the Universe, and General Relativity theory.

Pub. Date: 2011 4th quarter
Author: Marcelo Samuel Berman (Instituto Albert Einstein/Latinamerica, Curitiba, Brazil)
Publisher: Nova Science Publishers, New York
ISBN: 978-1-62100-107-2

“Realization of Einstein’s Machian Program”

This book is a solution of the so-called Einstein’s Machian Program, that left Einstein very angry and frustrated, for he was unable to reconcile Relativity Theories with Ernst Mach ideas, that by looking into the Cosmos as a whole, absolute motion could be found. About one hundred years ago, the discussion led to no conclusions among physicists, so that now Berman found that the existence of a Universal rotation, was compatible with General Relativity, and that this rotation is “absolute”. Berman thus solved the problem.

Author: Marcelo Samuel Berman (Instituto Albert Einstein/Latinamerica, Curitiba, Brazil).
Pub. Date: 2012 1st Quarter
publisher: Nova Science Publishers, New York
ISBN: 978-1-61942-164-6

New book – General Relativity Without Calculus

“General Relativity Without Calculus” offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physics. Targeted at first year undergraduates (and advanced high school students) who wish to learn Einstein’s theory beyond popular science accounts, it covers the basics of special relativity, Minkowski space-time, non-Euclidean geometry, Newtonian gravity, the Schwarzschild solution, black holes and cosmology. The quick-paced style is balanced by over 75 exercises (including full solutions), allowing readers to test and consolidate their understanding.

New book by John D Barrow: "The Book of Universes"

New Book Published 2 Feb 2011
The Book of Universes
John D Barrow
Publ. Bodley Head, Random House, UK
354 Pages, 12 chapters, b/w illustrations and photographs

Description: This book for a general audience tells the story of how Einstein’s equations provided a succession of solutions describing possible universes. It follows the history of the discovery of all the different sorts of possible universes that we know about and introduces the characters involved. It describes the latest ideas about inflationary universes, quantum cosmology and multiverses, as well as the best buy model of the observable universe today.

Numerical Relativity: Solving Einstein's Equations on the Computer (New Book)

Numerical Relativity: Solving Einstein’s Equations on the Computer

T. W. Baumgarte and S. L. Shapiro
Cambridge University Press, 2010

Aimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad survey of its challenges and achievements. Assuming only a basic knowledge of classical general relativity, this textbook develops the mathematical formalism from first principles, then highlights some of the pioneering simulations involving black holes and neutron stars, gravitational collapse and gravitational waves. Applications include calculations of coalescing binary black holes and binary neutron stars, rotating stars, colliding star clusters, gravitational and magnetorotational collapse, critical phenomena, the generation of gravitational waves, and many more.

Features of the book include:

- 300 exercises help readers master new material as it is presented.

- Numerous illustrations, many in color, assist in visualizing new geometric concepts and highlighting the results of computer simulations.

- Summary boxes encapsulate some of the most important results for quick reference.

- Applications cover topics of current physical and astrophysical significance.

For details, see http://www.cambridge.org/us/knowledge/isbn/item2707919/?site_locale=en_US

Structures in the Universe by Exact Methods (book)

Authors: Krzysztof Bolejko, Andrzej Krasiński, Charles Hellaby, Marie-Noëlle Célérier

As the structures in our Universe are mapped out on ever larger scales, and with increasing detail, the use of inhomogeneous models is becoming an essential tool for analyzing and understanding them. This book reviews a number of important developments in the application of inhomogeneous solutions of Einstein’s field equations to cosmology. It shows how inhomogeneous models can be employed to study the evolution of structures such as galaxy clusters and galaxies with central black holes, and to account for cosmological observations like supernovae dimming, the cosmic microwave background, baryon acoustic oscillations or the dependence of the Hubble parameter on redshift within classical general relativity. Whatever `dark matter’ and `dark energy’ turn out to be, inhomogeneities exist on many scales and need to be investigated with all appropriate methods. This book is of great value to all astrophysicists and researchers working in cosmology, from graduate students to academic researchers.

The book presents inhomogeneous cosmological models, allowing readers to familiarise themselves with basic properties of these models. It shows how inhomogeneous models can be used to analyse cosmological observations such as supernovae, cosmic microwave background, and baryon acoustic oscillations. The book reviews important developments in the application of inhomogeneous solutions of Einstein’s field equations to cosmology.

For details, see:


Solitons, Instantons and Twistors, M. Dunajski (book)

Solitons, Instantons and Twistors, M. Dunajski (2009),
Oxford University Press


1: Integrability in classical mechanics
2: Soliton equations and the Inverse Scattering Transform
3: The Hamiltonian formalism and the zero-curvature representation
4: Lie symmetries and reductions
5: The Lagrangian formalism and field theory
6: Gauge field theory
7: Integrability of ASDYM and twistor theory
8: Symmetry reductions and the integrable chiral model
9: Gravitational instantons
10: Anti-self-dual conformal structures
Appendix A: Manifolds and Topology
Appendix B: Complex analysis
Appendix C: Overdetermined PDEs