Einstein Constraints and Ricci Flow

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Beschreibung

This book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold.

This is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface.

The book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning 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.

Über den Autor

Mauro Carfora is Professor of Mathematical Physics at the University of Pavia, Italy. He is co-author with Annalisa Marzuoli of the Springer Lecture Notes in Physics Quantum Triangulations (LNP 845 and LNP 942), and illustrator of the popular relativity book Flat and Curved Spacetimes by George. F. R. Ellis and Ruth Williams.

Annalisa Marzuoli is Associate Professor of Mathematical Physics at the University of Pavia, Italy. She is co-author with Jan Ambjørn and Mauro Carfora of the Springer Lecture Notes in Physics The Geometry of Dynamical Triangulations (Springer LNP m50).

Zusammenfassung

Deals with the application of Ricci flow to the comparison and averaging of Einstein's initial data sets

Introduces Ricci flow conjugation between two distinct Einstein initial data sets, providing analysis of its properties

Proves Fourier modes expansion and heat kernel estimates for Ricci flow of independent interest in Ricci flow theory

Inhaltsverzeichnis

Introduction.- Geometric preliminaries.- Ricci ¿ow background.- Ricci ¿ow conjugation of initial data sets.- Concluding remarks.

Details

Erscheinungsjahr:	2023
Fachbereich:	Theoretische Physik
Genre:	Importe , Physik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xii 173 S. 1 s/w Illustr. 32 farbige Illustr. 173 p. 33 illus. 32 illus. in color.
ISBN-13:	9789811985393
ISBN-10:	9811985391
Sprache:	Englisch
Einband:	Gebunden
Autor:	Marzuoli, Annalisa Carfora, Mauro
Auflage:	1st edition 2023
Hersteller:	Springer Singapore Springer Nature Singapore
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 16 mm
Von/Mit:	Annalisa Marzuoli (u. a.)
Erscheinungsdatum:	11.01.2023
Gewicht:	0,453 kg

Artikel-ID: 125796851