Essay Review:Topics in the Foundations of General Relativity and Newtonian Gravitation Theory

Abstract

The first portion of this book amounts to a formal introduction to differential geometry and the general theory of relativity (complete with problem sets and solutions). The second amounts to an investigation of special topics pursued by David Malament over the last 4 decades or so. In what follows, I intend to summarize the material. Along the way, I hope to offer some comments on the significance of the work. Before I begin the survey of chapters, it might be helpful to say something about what the book is not. Although there is quite a bit of overlap between the first portion of the book and a standard graduate-level physics text, the two do not fully intersect (more below). In addition, the book does not consider many common topics in the philosophy of space-time physics. For example, there is no discussion of whether space and time are absolute or relational in character (cf. Sklar 1974; Friedman 1983). Finally, one does not find any precisely formulated conjectures of physical or philosophical interest that gesture toward future work (cf. Wald 1984; Earman 1995). It simply is not a book of that kind. Nonetheless, a number of topics developed by Malament in later chapters have generated a significant number of interesting results. (Indeed, I think the previous sentence is wildly understated.) Because Malament does not always do so, I hope to draw attention to some of these lines of inquiry below (a portion of which is still currently active).