By Marvin Blecher
World Scientific
This book provides a concise treatment of general relativity (GR) ideal for a semester course for undergraduate students or first-year graduate students in physics or engineering. After retiring from a career as an experimentalist in nuclear and particle physics, the author decided to teach an introductory course in GR at Virginia Tech, US. Many books are available on this topic, but they normally go into great detail and include a lot of material that cannot be covered in the short time of a semester. This new text by Blecher aims to cover this gap in the literature and provide just the essential concepts of GR.
The author starts with a review of special relativity and of the basic mathematical instruments, and then moves towards the explanation of the way that gravity affects time. This is discussed first for weak gravity via the conservation of energy using a Newtonian formulation with relativistic mass. Later in the book (chapter 5), it is rigorously treated in a completely GR framework. The Schwarzschild metric is also obtained.
In the following sections, GR is discussed in the context of the solar system (chapter 6) and of black holes (chapter 7). In the latter, an appealing example based on the movie Interstellar (Christopher Nolan) is used to discuss why a large gravitational time dilation is possible near a spinning – but not a static – black hole.
Chapter 8 focuses on gravitational waves. The first direct detection of these waves, produced by two black holes that merged into a single one, was announced in February this year, when the book was already going to print. Nevertheless, the author added a discussion on this discovery to the text. The theory of the binary neutron star-system radiation, referred to the binary pulsar discovered by R Hulse and J H Taylor, is also treated, but in the case of elliptical orbits, instead of circular ones as generally done for simplicity in textbooks.
Finally, a chapter is dedicated to cosmology, in which the results of numerical integrations, using the experimental data available for all the energy densities, are discussed.
