The Geometry of Spacetime: An Introduction to Special and General Relativity (Undergraduate Texts in Mathematics)

In 1905, Albert Einstein offered a revolutionary theory - special relativity - to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborates to gain objective knowledge of the world. He has tried to encompass both the general and special theory by using the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus. In 1905, Albert Einstein offered a revolutionary theory--special relativity--to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Eintein's general relativity as a theory of gravity rooted in the differential geomentry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborate to gain objective knowledge of the world. To encompass both the general and special theory, he uses the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus Front Matter....Pages i-xvi Relativity Before 1905....Pages 1-29 Special Relativity — Kinematics....Pages 31-86 Special Relativity — Kinetics....Pages 87-141 Arbitrary Frames....Pages 143-201 Surfaces and Curvature....Pages 203-256 Intrinsic Geometry....Pages 257-328 General Relativity....Pages 329-384 Consequences....Pages 385-434 Erratum to: Relativity Before 1905....Pages 455-455 Erratum to: Special Relativity — Kinematics....Pages 455-455 Erratum to: Special Relativity — Kinetics....Pages 456-457 Erratum to: Arbitrary Frames....Pages 457-458 Erratum to: Surfaces and Curvature....Pages 458-458 Erratum to: Intrinsic Geometry....Pages 458-459 Erratum to: General Relativity....Pages 459-460 Erratum to: Consequences....Pages 460-461 Erratum....Pages 461-463 Back Matter....Pages 435-454 Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory. Relativity Before 1905 Special Relativity - Kinematics Special Relativity - Kinetics Arbitrary Frames Surfaces and Curvatures Intrinsic Geometry General Relativity Consequences Bibliography Index.