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T. Padmanabhan. Theoretical Astrophysics: Volume 3, Galaxies and Cosmology (eBook, PDF). Theoretical Astrophysics: Volume 3, Galaxies and Cosmology. Theoretical Astrophysics: Volume 1, Astrophysical. Processes (Theoretical Astrophysics (Paperback)). T. Padmanabhan. Click here if your download doesn" t. Theoretical astrophysics vol astrophysical processes. T. Padmanabhan neusihelcodi.ml ISBN:

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Graduate students and researchers in astrophysics and cosmology need a solid under- Theoretical astrophysics: astrophysical processes / T. Padmanabhan. existing text books including my own Theoretical Astrophysics Vol I-III published by Cambridge I thank Vasanthi Padmanabhan for dedicated support and for taking care of the entire of anisotropies. You can download the program from. Theoretical Astrophysics, Volume II: Stars and Stellar Systems This item: Theoretical Astrophysics v3 by T. Padmanabhan Paperback $ In Stock.

Newtonian approximation with cosmological constant Wave equation for Fmn in curved spacetime Structure of the gravitational action principle Deflection of light in the Newtonian approximation Metric perturbation due to a fast moving particle Metric perturbation due to a non-relativistic source Landau—Lifshitz pseudo-tensor in the Newtonian approximation xv xvi 6. Self-coupled scalar field theory of gravity Is there hope for scalar theories of gravity? The italicized adjectives in the above sentence are the key: most of the existing books on the market are either outdated in emphasis, too mathematical for a physicist, not comprehensive or written at an elementary level. For example, the two unique books — L. Landau and E. Misner, K. Thorne and J. Wheeler MTW , Gravitation — which I consider to be masterpieces in this subject are more than three decades old and are out of date in their emphasis. The current book is expected to fill this niche and I hope it becomes a standard reference in this field. Some of the features of this book, including the summary of chapters, are given below.

Researchers and teachers interested in theoretical physics, general relativity, relativistic astrophysics and cosmology will find it useful for their research and adaptable for their course requirements. The section How to use this book, just after this Preface, gives more details of this aspect.

The discussion is presented in a style suitable for physicists, ensuring that it caters xxi xxii Preface for the current interest in gravity among physicists working in related areas.

The large number more than of reasonably nontrivial Exercises makes it ideal for self-study. Another unique feature of this book is a set of Projects at the end of selected chapters. The Projects are advanced level exercises presented with helpful hints to show the reader a direction of attack. Several of them are based on research literature dealing with key open issues in different areas. These will act as a bridge for students to cross over from textbook material to real life research.

Graduate students and grad school teachers will find the Exercises and Projects extremely useful. Advanced undergraduate students with a flair for theoretical physics will also be able to use parts of this book, especially in combination with more elementary books.

Here is a brief description of the chapters of the book and their inter-relationship. Chapters 1 and 2 of this book are somewhat unique and serve an important purpose, which I would like to explain. A student learning general relativity often finds that she simultaneously has to cope with i conceptual and mathematical issues which arise from the spacetime being curved and ii technical issues and concepts which are essentially special relativistic but were never emphasized adequately in a special relativity course!

For example, manipulation of four-dimensional integrals or the concept and properties of the energy-momentum tensor have nothing to do with general relativity a priori — but are usually not covered in depth in conventional special relativity courses. The first two chapters give the student a rigorous training in four-dimensional techniques in flat spacetime so that she can concentrate on issues which are genuinely general relativistic later on. These chapters can also usefully serve as modular course material for a short course on advanced special relativity or classical field theory.

Chapter 1 introduces special relativity using four-vectors and the action principle right from the outset. Chapter 2 introduces the electromagnetic field through the four-vector formalism. I expect the student to have done a standard course in classical mechanics and electromagnetic theory but I do not assume familiarity with the relativistic four-vector notation.

Several topics that are needed later in general relativity are introduced in these two chapters in order to familiarize the reader early on.

Examples include the use of the relativistic Hamilton—Jacobi equation, precession of Coulomb orbits, dynamics of the electromagnetic field obtained from an action principle, derivation of the field of an arbitrarily moving charged particle, radiation reaction, etc.

Chapter 2 also serves as a launch pad for discussing spin-0 and spin-2 interactions, using electromagnetism as a familiar example.

Chapter 3 attempts to put together special relativity and gravity and explains, in clear and precise terms, why it does not lead to a consistent picture. Most textbooks I know except MTW do not explain the issues involved clearly and with adequate Preface xxiii detail. For example, this chapter contains a detailed discussion of the spin-2 tensor field which is not available in textbooks.

It is important for a student to realize that the description of gravity in terms of curvature of spacetime is inevitable and natural. This chapter will also lay the foundation for the description of the spin2 tensor field hab , which will play an important role in the study of gravitational waves and cosmological perturbation theory later on. Having convinced the reader that gravity is related to spacetime geometry, Chapter 4 begins with the description of general relativity by introducing the metric tensor and extending the ideas of four-vectors, tensors, etc.

There are two points that I would like to highlight about this chapter. First, I have introduced every concept with a physical principle rather than in the abstract language of differential geometry. For example, direct variation of the line interval leads to the geodesic equation through which one can motivate the notion of Christoffel symbols, covariant derivative, etc. During the courses I have taught over years, students have found this approach attractive and simpler to grasp.

Second, I find that students sometimes confuse issues which arise when curvilinear coordinates are used in flat spacetime with those related to genuine curvature. This chapter clarifies such issues. Chapter 5 introduces the concept of the curvature tensor from three different perspectives and describes its properties. It then moves on to provide a complete description of electrodynamics, statistical mechanics, thermodynamics and wave propagation in curved spacetime, including the Raychaudhuri equation and the focusing theorem.

I have provided a careful discussion of the surface term in the Einstein—Hilbert action again not usually found in textbooks in a manner which is quite general and turns out to be useful in the discussion of Lanczos— Lovelock models in Chapter I then proceed to discuss the general structure of the field equations, the energy-momentum pseudo-tensor for gravity and the weak field limit of gravity.

After developing the formalism in the first six chapters, I apply it to discuss four key applications of general relativity — spherically symmetric spacetimes, black hole physics, gravitational waves and cosmology — in the next four chapters.

The only other key topic I have omitted, due to lack of space, is the physics of compact stellar remnants. The chapter also discusses the orbits of particles and photons in these spacetimes and the tests of general relativity. These are used in Chapter 8, which covers several aspects of black hole physics, concentrating mostly on the Schwarzschild and Kerr black holes.

It also introduces xxiv Preface important concepts like the maximal extension of a manifold, Penrose—Carter diagrams and the geometrical description of horizons as null surfaces. A derivation of the zeroth law of black hole mechanics and illustrations of the first and second laws are also provided. The material developed here forms the backdrop for the discussions in Chapters 13, 15 and Chapter 9 takes up one of the key new phenomena that arise in general relativity, viz.

A careful discussion of gauge invariance and coordinate conditions in the description of gravitational waves is provided.

I also make explicit contact with similar phenomena in the case of electromagnetic radiation in order to help the reader to understand the concepts better. A detailed discussion of the binary pulsar is included and a Project at the end of the chapter explores the nuances of the post-Newtonian approximation.

Chapter 10 applies general relativity to study cosmology and the evolution of the universe.

Given the prominence cosmology enjoys in current research and the fact that this interest will persist in future, it is important that all general relativists are acquainted with cosmology at the same level of detail as, for example, with the Schwarzschild metric. This is the motivation for Chapter 10 as well as Chapter 13 which deals with general relativistic perturbation theory.

The emphasis here will be mostly on the geometrical aspects of the universe rather than on physical cosmology, for which several other excellent textbooks e. However, in order to provide a complete picture and to appreciate the interplay between theory and observation, it is necessary to discuss certain aspects of the evolutionary history of the universe — which is done to the extent needed.

The second part of the book Frontiers, Chapters 11—16 discusses six separate topics which are reasonably independent of each other though not completely. While a student or researcher specializing in gravitation should study all of them, others could choose the topics based on their interest after covering the first part of the book. Chapter 11 introduces the language of differential forms and exterior calculus and translates many of the results of the previous chapters into the language of forms.

The approach was wellappreciated and the students found it useful and enlightening. The feedback I got very often was that my course — taught at graduate student level — came a year too late! In the Indian educational system, these are the students who will proceed to Ph. D graduate school in the next year. The lectures were viedographed and made available from my institute website to a wider audience.

This book is an expanded version of the course. Many people have contributed to this venture and I express my gratitude to them. To begin with, I thank the Physics Department of Pune University for giving me the opportunity to teach this course to their students in , and many of these students for their valuable feedback.

I thank Suprit Singh who did an excellent job of videographing the lectures. I thank all of them. Angela Lahee of Springer initiated this project viii PREFACE and helped me through its completion, displaying considerable initiative and accommodating my special formatting requirements involving marginal notes. I thank her for her help. It is a pleasure to acknowledge the library facilities available at IUCAA, which were useful in this task.

Padmanabhan Pune, September After introducing i the path integral amplitude and ii the standard Hamiltonian evolution in the case of a non-relativistic particle, we proceed to evaluate the propagator for a relativistic particle.

In the process, you will also learn a host of useful techniques related to propagators, path integrals, analytic extension to imaginary time, etc. I will also clarify how the approach leads to the notion of the antiparticle, and why causality requires us to deal with the particle and antiparticle together.

Disturbing the Vacuum The purpose of this — relatively short — chapter is to introduce you to the key aspect of QFT, viz.

Using an external, classical scalar source J x , we obtain the propagator for a relativistic particle from general arguments related to the nature of creation and destruction events.

These include path integrals, functional calculus, evaluation of operator determinants, analytic properties of propagators and the use of complex time methods. However, the key points are as follows: A. Color Doppler and pulsed Doppler ultrasound, 3D ultrasound, endosonography.

Obstetrics and gynaecology is the most popular application for ultrasound imaging; it has popularized ultrasound greatly and is one of the reasons people are familiar with the technology. The aim of this book is to inform interested readers about the advantages of colour Doppler and three-dimensional ultrasound in gynaecology, infertility and obstetrics. Doppler of the Umbilical Cord Holly Hollis RT R Abstract The use of spectral and color Doppler, and ultrasound, are extraordinary noninvasive tools to evaluate the well - being of a fetus.

It is a simple yet effective device that can assess foetuses considered to be 'small for gestational published in the American Journal of Obstetrics and Gynaecology.