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Variational Approach to Gravity Field Theories

From Newton to Einstein and Beyond

  • Textbook
  • © 2017

Overview

Authors:
  1. Alberto Vecchiato

    1. Astrophysical Observatory of Torino, INAF - National Institute of Astrophysics, Pino Torinese, Italy

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  • Describes an approach to general relativity particularly relevant for physics students
  • Evidences the continuity, from the point of view of theoretical physics, of all the gravity theories as field theories
  • Presents solved exercises and examples throughout the text
  • Meets the needs of students specializing in theoretical physics and those seeking a better understanding of particular aspects of the subject
  • Includes supplementary material: sn.pub/extras

Part of the book series: Undergraduate Lecture Notes in Physics (ULNP)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction and Classical Physics

    1. Front Matter

      Pages 1-1
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    2. A Short Introduction to Field Theories and Variational Approach

      • Alberto Vecchiato
      Pages 3-22

    3. The Geometrical Character of Physics Theories

      • Alberto Vecchiato
      Pages 23-28

    4. Fundamental Principles of Classical Physics

      • Alberto Vecchiato
      Pages 29-56

    5. Classical Physics, Fundamental Principles, and Lagrangian Approach

      • Alberto Vecchiato
      Pages 57-75

  3. Special Relativity

    1. Front Matter

      Pages 77-77
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    2. Special Relativity Setting Up

      • Alberto Vecchiato
      Pages 79-114

    3. Special Relativity in Minkowskian Spacetime

      • Alberto Vecchiato
      Pages 115-141

    4. Gravity and Special Relativity

      • Alberto Vecchiato
      Pages 143-163

  4. General Relativity and Beyond

    1. Front Matter

      Pages 165-165
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    2. Lagrangian Formulation of General Relativity

      • Alberto Vecchiato
      Pages 167-198

    3. Applications

      • Alberto Vecchiato
      Pages 199-238

    4. Beyond General Relativity

      • Alberto Vecchiato
      Pages 239-271

  5. Back Matter

    Pages 273-361
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Keywords

About this book

This book offers a detailed and stimulating account of the Lagrangian, or variational, approach to general relativity and beyond. The approach more usually adopted when describing general relativity is to introduce the required concepts of differential geometry and derive the field and geodesic equations from purely geometrical properties. Demonstration of the physical meaning then requires the weak field approximation of these equations to recover their Newtonian counterparts. The potential downside of this approach is that it tends to suit the mathematical mind and requires the physicist to study and work in a completely unfamiliar environment. In contrast, the approach to general relativity described in this book will be especially suited to physics students. After an introduction to field theories and the variational approach, individual sections focus on the variational approach in relation to special relativity, general relativity, and alternative theories of gravity. Throughoutthe text, solved exercises and examples are presented. The book will meet the needs of both students specializing in theoretical physics and those seeking a better understanding of particular aspects of the subject.

Reviews

“The first impression is good, also because all the proposed exercises and examples are fully solved. … The author’s approach and writing is clear, straightforward, and with specific attention to the connection with the evolution of the physical principles that lie at the basis of gravitation. The book is appropriate for university students, as well as, for more specialists or practitioners of matter.” (Gabriella Bernardi, Astrocom et al., astrocometal.blogspot.de, July, 2017)

Authors and Affiliations

  • Astrophysical Observatory of Torino, INAF - National Institute of Astrophysics, Pino Torinese, Italy

    Alberto Vecchiato

About the author

Alberto Vecchiato graduated in Physics from the University of Padova, Italy, in 1996 and subsequently gained his PhD from the same university for a thesis on relativistic astrometry. He currently works at the Astrophysical Observatory of Torino, Pino Torinese, Italy. Dr. Vecchiato's scientific interests include general relativistic models of light propagation and astrometric measurements; high-precision tests of general relativity; alternative theories of gravity; and space astrometry. He is author of several research papers and a member of the Italian Society of General Relativity and Gravitational Physics (SIGRAV). Dr. Vecchiato has collaborated in various astronomical and astrophysical projects and proposals, he has been a member of the Gaia mission (ESA) since 2001, and in 2006 he became the coordinator of the verification sphere reconstruction pipeline of its data reduction consortium.

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