Einstein Equations: Physical and Mathematical Aspects of General Relativity

This book is based on lectures given at the first edition of the Domoschool, the International Alpine School in Mathematics and Physics, held in Domodossola, Italy, in July 2018. It is divided into two parts.  Part I consists of four sets of lecture

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Sergio Cacciatori Batu Güneysu Stefano Pigola Editors

Einstein Equations: Physical and Mathematical Aspects of General Relativity Domoschool 2018

Tutorials, Schools, and Workshops in the Mathematical Sciences

This series will serve as a resource for the publication of results and developments presented at summer or winter schools, workshops, tutorials, and seminars. Written in an informal and accessible style, they present important and emerging topics in scientific research for PhD students and researchers. Filling a gap between traditional lecture notes, proceedings, and standard textbooks, the titles included in TSWMS present material from the forefront of research.

More information about this series at http://www.springer.com/series/15641

Sergio Cacciatori • Batu G¨uneysu • Stefano Pigola Editors

Einstein Equations: Physical and Mathematical Aspects of General Relativity Domoschool 2018

Editors Sergio Cacciatori Department of Science and High Technology University Insubrien Como, Italy

Batu G¨uneysu Mathematisches Institut Humboldt-Universit¨at zu Berlin Berlin, Germany

Stefano Pigola Department of Science and High Technology University Insubrien Como, Italy

ISSN 2522-0969 ISSN 2522-0977 (electronic) Tutorials, Schools, and Workshops in the Mathematical Sciences ISBN 978-3-030-18060-7 ISBN 978-3-030-18061-4 (eBook) https://doi.org/10.1007/978-3-030-18061-4 Mathematics Subject Classification (2010): 83C05, 83C15, 83C20, 83C35, 83C40, 83C47, 83C57 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This book is published under the imprint Birkhäuser, www.birkhauser-science.com, by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

This book presents four lecture courses and, in addition, nine talks given at the first