© 2017

Variational Approach to Gravity Field Theories

From Newton to Einstein and Beyond


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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Introduction and Classical Physics

  3. Special Relativity

    1. Front Matter
      Pages 77-77
    2. Alberto Vecchiato
      Pages 79-114
    3. Alberto Vecchiato
      Pages 115-141
    4. Alberto Vecchiato
      Pages 143-163
  4. General Relativity and Beyond

    1. Front Matter
      Pages 165-165
    2. Alberto Vecchiato
      Pages 167-198
    3. Alberto Vecchiato
      Pages 199-238
    4. Alberto Vecchiato
      Pages 239-271
  5. Back Matter
    Pages 273-361

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. Throughout the 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.


Alternative Gravity Theories Electomagnetism in Special Relativity Lagrangian Approach Newtonian Gravity Post-Newtonian Limit of GR Textbook Variational Approach in General Relativity Textbook Variational Approach in Special Relativity Undergraduate Textbook Gravity Theories

Authors and affiliations

  1. 1.Astrophysical Observatory of TorinoINAF - National Institute of AstrophysicsPino TorineseItaly

About the authors

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.

Bibliographic information


“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.,, July, 2017)