Differential Forms and the Geometry of General Relativity

Book Preface

Tevian Dray - Differential Forms and the Geometry of General Relativity
  
  Differential Forms and
the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little
more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics
of general relativity.
  
  The book contains two intertwined but distinct halves. Designed for advanced
undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than
familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that
describes some of the surprising implications of relativity without introducing more formalism than necessary. This
nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of "index gymnastics" as
much as possible.
  
  The second half of the book takes a more detailed look at the mathematics of
differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual
understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in
general relativity.