Spacetime, geometry and gravitation
type: Item
instance of: scholarly article
title: Spacetime, geometry and gravitation
zbMATH Open document ID: 1197.83003
DOI: 10.1007/978-3-7643-9971-9
author: Pankaj Sharan
published in: Progress in Mathematical Physics
publication date: 2009-03-20T00:00:00Z
full work available at URL: http://cds.cern.ch/record/1339670
review text: This is an introductory book on the general theory of relativity, partly composed in a quite individual style. It is divided into three parts, where each of them could be taken as an independent text. The first part is a preliminary course on general relativity with minimum preparation, starting from a discussion of some features of Newtonian mechanics and Maxwell's electrodynamics, continuing with a consideration of Gauss' work on the geometry of two-dimensional surfaces to introduce the concept of curvature, and ending with basics of general relativity without already saying what the words ``tensor'', ``connection'' etc. geometrically mean. The second part builds the mathematical background of general relativity. It is an introduction to Riemannian geometry containing more mathematics than strictly required for Part III. The third part is a more extensive representation of topics of general relativity. It includes discourses about the energy-momentum tensor of a fluid and the derivation of Einstein's equations from an action principle, and it discusses topics like static and stationary space-times, Fermi-Walker transport, Penrose diagrams, the Schwarzschild and Kerr metrics, and the weak-field approximation of general relativity (followed by the calculation of gravitomagnetic effects and gravitational waves). The book ends with two brief sections on relativistic standard cosmology and the Gauss-Codazzi and the Raychaudhuri equations. It should be mentioned that there are some small deficiencies of this representation. For instance, the author speaks explicitly of the Newton, but only implicitly of the Einstein principle of equivalence, a fact that weakens his arguments in favor of the need of the transition to a curved Riemannian space-time. Or, in two elucidating sections, he extensively explains the structure of the energy-momentum tensor of a fluid as source term in Einstein's equations. But, two sections later, when he discusses electrodynamics it is not menti…
Mathematics Subject Classification ID: 83-01
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 83C10
Mathematics Subject Classification ID: 83C35
Mathematics Subject Classification ID: 83C57
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 85A40
Mathematics Subject Classification ID: 83F05
Mathematics Subject Classification ID: 83C15
zbMATH DE Number: 5530238
zbMATH Keywords: general relativity
zbMATH Keywords: Riemannian geometry
reviewed by: Horst-Heino von Borzeszkowski
MaRDI profile type: Publication
OpenAlex ID: W1661961098
description: scientific article; zbMATH DE number 5530238