Inertia and Gravitation ― The Fundamental Nature and Structure of Space-time

The phenomena of gravitation and inertia are the central themes of this book, and one objective is to shed some new light on the basic laws and structures of the gravitational interaction. Part I is devoted to an extensive, partly new analysis of the law of inertia of Galilei and Newton. The underlying mathematical structure of the Newtonian spacetime is presented and some historical difficulties and controversies - in particular the concepts of free particles and straight lines - are critically analyzed, and connections to projective geometry are examined. The relativistic extensions of the law of gravitation and its intriguing consequences are studied in Part II. This is achieved, following the works of Weyl, Ehlers, Pirani and Schild, from the point of view of the combined conformal and projective structure of spacetime.

Specifically, Mach’s critique of Newton’s Principia was a decisive motivation for Einstein’s creation of General Relativity, and his equivalence principle provided a new look at Inertia.
By analyzing different types of dragging phenomena Part III reviews how far this principle is realized in General Relativity. This is intimately connected to the ’new force’ gravitomagnetism, theoretically predicted by Einstein and Thirring but experimentally confirmed only recently and thus of current interest.