Topics in the foundations of general relativity and Newtonian gravitation theory. (Q2889624)

This is an interesting high-level textbook and reference book. It is a four-chapter, 349-page book written for both relativity audiences and philosophy of science audiences. Although it is not meant as an introductory text, the first two chapters summarize the basics of differential geometry and the foundations of general relativity. Interspersed in both are problems for the interested reader to try; solutions are given in an appendix. The remaining two chapters cover the Gödel universe, the concept of rotation in Einstein gravity, and the geometrized form of Newtonian gravity known as Newton-Cartan theory (both the so-called ``Trautman version'' and the ``Künzle-Ehlers version''). The complete logical framework of general relativity is examined in a thorough and mathematically precise manner. The non-standard applications are an asset of the presentation. Any mathematically sophisticated student or researcher interested in the foundations of gravitational theory and/or any of the specific applications would benefit from reading this book.