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Relativistic Hydrodynamics, by Luciano Rezzolla, Olindo Zanotti
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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.
- Sales Rank: #1799453 in eBooks
- Published on: 2013-09-26
- Released on: 2013-09-26
- Format: Kindle eBook
Most helpful customer reviews
4 of 4 people found the following review helpful.
A definitive text
By Revanchist
The fields of relativity and hydrodynamics are vast in their own right, and even their intersection constitutes a broad, multidisciplinary area. As a result, most texts on the subject have often focused primarily on 1-2 aspects, skimming over the other parts. This voluminous tome by Rezzolla & Zanotti provides a comprehensive treatment that is simultaneously classical (in the sense of following older monographs) and contemporary (up-to-date on the latest techniques).
It opens with a brief review of GR, which is somewhat utilitarian, but gets across all the points clearly, and develops the tools necessary in all the subsequent sections. Chapter 2 is one of the (many) gems in the book as it provides a lucid and self-contained description of kinetic theory, which underlies the theory of fluids. Particularly noteworthy is the extended discussion of the importance of the equation of state, and the many variants employed in the literature. Chapter 3 enters the core areas of the book - namely relativistic perfect fluids, and the section on irrotational fluids and the conservation laws is particularly noteworthy. Chapter 4 on waves is most welcome as not many texts treat this topic in detail and the discussion of shocks and the Riemann problem is well done. Chapter 5 on detonations is somewhat brief, and a more detailed (albeit Newtonian) treatment exists in the marvellous book by Zel'dovich and Raizer. Another unorthodox and timely topic presented is Chapter 6 that deals with non-perfect fluids, and the sections on causality and thermodynamics are highly commendable.
Part II of the book is really where the monograph sets itself apart from its predecessors. Chapter 7 opens with a neat account of the Einstein-Euler equations, and the discussion on the ADM formalism is well judged. Chapters 8 and 9 concern themselves with a detailed treatment of the numerical methods employed and distinguish clearly between the finite-difference and HRSC methods. In the latter, the discussion of Riemann solvers deserves a particular mention for its combination of brevity and insight. Chapter 10 moves on to higher-order methods, but the discontinuous Galerkin scheme could have been explained in slightly higher detail.
Part III is likely to be of the greatest interest, and importance, to astrophysicists as the applications of the theoretical and numerical methods are presented here. In Chapter 11, a host of topics ranging from blast waves, accretion (spherical and axisymmetric), tori and jets are compactly presented. The book concludes with Chapter 12, with a fine discussion of self-gravitating fluids - the dynamics of binaries is particularly well done. There are also a host of appendices that provide extra mathematical and numerical background, and Appendix C, with a summary of the commonly used tensors, will prove to be particularly useful.
On the whole, "Relativistic Hydrodynamics" is an excellent book that should satisfy all three groups - the theoreticians, the numerical relativists and the astrophysicists - as it offers a nice blend of the three. Instead of consulting older monographs on the subject, or current (but incomplete) review papers on the subject, this book represents a unified source from which instructors and/or researchers can pick and choose their content. The only critique, and a minor one, that can be offered is that Part III could be slightly expanded, as it contains practical applications, and is therefore of high relevance.
4 of 4 people found the following review helpful.
Fundamental book about Relativistic Hydrodynamics
By Dr. Carlo N. Colacino
This is a fundamental book, the ultimate reference for those who want to learn relativistic hydrodinamics. The books starts with a very thorough review of General Relativity (GR), it is not intended as a textbook for GR, but the review is well done and complete. Afterwards the authors deal with the many physical processes where both GR and hydrodynamics play a role. The theory is complete, very well explained, mathematically rigorous but not heavy nor boring. I myself was probably expecting more pages on computer codes currently used nowadays for numerical simulations of complicated astrophysical processes, but this is the only minor shortcoming of this book. Excellent work, which is about to become the reference book for the next 20 years, a must for all those researchers who work in this area and for everyone interested in learning the subject.
1 of 1 people found the following review helpful.
An indispensable guide to Relativistic Hydrodynamics
By Michael Halls-Moore
My personal background is in numerical high-resolution shock-capturing (HRSC) methods in a Newtonian framework. Hence I was interested in the book as a means to help me extend this work to a relativistic setting. In this goal, the book succeeds perfectly.
At the beginning there is a useful and thorough review of General Relativity (GR) but I would assume that any potential reader would have a theoretical physics undergraduate or early graduate introduction to GR prior to picking up the book.
Chapters 2 and 3 concentrate on the underlying kinetic theory of fluids and then extend this to the relativistic regime. For someone with a primarily Newtonian background these chapters were indispensable on "seeing how the relativity fits in". In particular, there is an extended discussion on the various equations of state employed in relativistic hydrodynamics.
I was mostly interested in the second section, which is concerned with numerical methods for relativistic hydrodynamics. Chapter 7 describes how one carries out a "foliation" or "3+1" decomposition of space-time using the ADM formulation, which allows spatial and temporal discretisation of the equations.
Chapters 8-10 then discuss the various computational approaches employed in numerical relativity. Finite Difference Methods are treated first, including discussions on stability analysis and various schemes (Lax-Friedrichs, Lax-Wendroff).
I was particularly impressed by the section on HRSC methods in Chapter 9. Having studied this area in-depth, I found the treatment approachable and sufficiently detailed for a non-specialist to get up to speed. If one wants to go further then one can always look at Toro[1].
Chapter 10 discusses higher order methods such as ENO/WENO and ADER. I've only briefly considered these methods before so this chapter was particularly useful to get a good handle on the area.
The final section of the book concerns applications. There are a wide variety of physical simulations discussed in this section broadly under the banners of non-selfgravitating and self-gravitating fluids. I found that I wanted slightly more detail on some of the simulations so I went to the original papers in certain cases. However, there is plenty of variety in this section and it highlights just how vast the area of relativistic hydrodynamics is.
The book is applicable to a wide range of individuals with varying backgrounds. It contains sufficient diversity for those interested in the theoretical, numerical or practical applications of the methods. Importantly, there is always enough material in the chapters (each of which covers an extremely broad research area in its own right) for an individual to get up to speed with the current literature, and plenty of references are listed in order to continue further research.
While Appendix E presents some of the key aspects of a HRSC code, it would have been nice to see a fully-functional relativistic listing. I appreciate that there are space constraints in a work such as this (as well as associated installation issues that inevitably sideline the discussion), so it is not a huge problem.
I'm quite certain this will become the key text for new students entering the field at graduate level and will remain that way for some time.
[1] Toro, E. (2009). Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer, Berlin.
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