Einstein Constraints and Ricci Flow: A Geometrical Averaging of Initial Data Sets

This book explores a geometric averaging technique using the Ricci flow, allowing comparison of Einstein initial data sets on closed manifolds. It combines Ricci flow theory and Einstein constraints theory, providing a rigorous approach to initial data set averaging in relativistic cosmology. The book is suitable for advanced students and researchers in mathematical physics.

Format: Hardback
Length: 173 pages
Publication date: 11 January 2023
Publisher: Springer Verlag, Singapore

This book presents a comprehensive and self-contained treatment of a geometric averaging technique, inspired by the Ricci flow, which enables the comparison of two distinct Einstein initial data sets, both supported on a given closed n-dimensional manifold. This is a fascinating case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, intersect in a remarkable way. The interaction holds significant importance for applications in relativistic cosmology, providing a mathematically rigorous approach to the problem of averaging initial data sets, particularly when data sets are provided on a closed space-like hypersurface.

The book does not assume prior knowledge of Ricci flow theory, allowing ample space for introducing the necessary techniques. These introductory sections gradually evolve into a detailed discussion of advanced results, including a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory.

This work is intended for advanced students in mathematical physics and researchers alike.

Weight: 453g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811985393
Edition number: 1st ed. 2023