Beyond Einstein Perspectives on Geometry, Gravitation, and Cosmology in the Twentieth Century

Beginning with Einstein’s general theory of relativity (GRT), the twentieth century witnessed a series of dramatic developments in physics that exerted a strong impact on the development of modern differential geometry. In conjunction, geometers introduced numerous innovations adapted to or designed for solving problems that arose from space-time physics. Meanwhile, in close collaboration with mathematicians and physicists, astronomers began to reflect on the consequences of GRT for their discipline as well as for modern cosmology.

Beyond Einstein: Perspectives on Geometry, Gravitation, and Cosmology explores the rich interplay between mathematical and physical ideas by studying the interactions of major actors and the roles of important research communities over the course of the last century.

Contributors: A. Ashtekar, J. Earman, J. Ehlers, J. Eisenstaedt, H.J. Fahr, A. Franklin, J. Frauendiener, H. Goenner, D. Kennefick, S. Klainerman, H. Kragh, D. O’Shea, R. Penrose, J. Ritter, T. Sauer, E. Scholz, C. Smeenk, J. Stachel, N. Straumann, R. Wald, S. Walter, C. Will.

Preface.- Part I Mathematical and Physical Underpinnings of Spacetimes.- Figures of Light in the Early History of Relativity (1905–1914).- The Behaviour of Rods and Clocks in General Relativity and the Meaning of the Metric Field.- Hilbert on General Covariance and Causality.- Part II Testing General Relativity and Rival Theories.- Putting General Relativity to the Test: Twentieth Century Highlights and Twenty-First Century Prospects.- Rotating Hollow and Full Spheres: Einsein, Thirring, Lense, and Beyond.- Relativistic Lighthouses: The Role of the Binary Pulsar in Proving the Existence of Gravitational Waves.- The Rise and Fall of the Fifth Force.- Part III Geometry and Cosmology, Past and Present.- Cyclic Models of the Relativistic Universe: The Early History.- Inflation and the Origins of Structure.- Problems with Modified Theories of Gravity, as Alternatives to Dark Energy.- The Unexpected Resurgence of Weyl Geometry in Late 20th-Century Physics.- Part IV Mathematical Motifs in General Relativity and Beyond.- Matter from Space.- The Surprising Resolution of the Poincarén Conjecture.- Unified Field Theory up to the 1960s: Its Development and Some Interactions Among Research Groups.- Part V Quantum Gravity, Conformal Boundaries, and String Theory.- The Formulation of Quantum Field Theory in Curved Spacetime.- Conformal Infinity – Development and Applications.- String Theory and Spacetime Geometry.- Conference Program.