Variational approach to gravity field theories. From Newton to Einstein and beyond
type: Item
instance of: scholarly article
title: Variational approach to gravity field theories. From Newton to Einstein and beyond
zbMATH Open document ID: 1369.83001
DOI: 10.1007/978-3-319-51211-2
author: Alberto Vecchiato
published in: Undergraduate Lecture Notes in Physics
publication date: 2017-02-15T00:00:00Z
review text: It is really a hard task to teach Einstein's theory of General Relativity to undergraduates. It is still harder to teach them theories beyond Einstein. But just this is the aim of the present book. And, as far as I can see: It has been successfully fulfilled. Example: Section 7.3. discusses the question which kind of tensors could be used to describe the gravitational field in view of the fact, that masses are positive and attract each other. This excludes vector fields (known from electrodynamics), but allows for scalar fields and rank 2-tensors. Newton's theory is a scalar theory, General Relativity is based on a rank 2-tensor, and so it appears natural to ask for scalar-tensor theories for describing the possible deviations from General Relativity. The book is organized as follows: the ten main chapters have the following topics: 1. Field theory and variational approach, 2. Geometry and physics, 3. Principle of covariance and equivalence principle, 4. Lagrangian approach, 5., 6. and 7. Special Relativity, 8. and 9. General Relativity, and 10. Beyond General Relativity. The four appendices cover together almost 80 pages, there topics are: Calculus of variations, tensor algebra, Special Relativity, and differential geometry. Publisher's description: ``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 w…
reviewed by: Hans-Jürgen Schmidt
Mathematics Subject Classification ID: 83-01
Mathematics Subject Classification ID: 83A05
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 00A79
Mathematics Subject Classification ID: 83-03
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 83D05
Mathematics Subject Classification ID: 70H40
Mathematics Subject Classification ID: 53Z05
zbMATH DE Number: 6684810
zbMATH Keywords: Newton's theory
zbMATH Keywords: scalar theory
zbMATH Keywords: General Relativity
zbMATH Keywords: rank 2-tensor
zbMATH Keywords: scalar-tensor theories
zbMATH Keywords: deviations from General Relativity
zbMATH Keywords: field theory
zbMATH Keywords: variational approach
zbMATH Keywords: principle of covariance
zbMATH Keywords: equivalence principle
zbMATH Keywords: Lagrangian approach
zbMATH Keywords: Special Relativity
zbMATH Keywords: calculus of variations
zbMATH Keywords: tensor algebra
zbMATH Keywords: differential geometry
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-51211-2
OpenAlex ID: W4237712581
description: scientific article; zbMATH DE number 6684810