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Einstein Equations: Local Energy, Self-Force, and Fields in General Relativity

Domoschool 2019

  • Book
  • © 2022

Overview

Editors:
  1. Sergio Luigi Cacciatori

    1. Department of Science and High Technology, University of Insubria, Como, Italy

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    You can also search for this editor in PubMed   Google Scholar

  2. Alexander Kamenshchik

    1. Department of Physics and Astronomy, University of Bologna, Bologna, Italy

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Guides early career researchers through recent breakthroughs in math and physics
  • Features four courses from experts on research topics such as geometry and analysis in blackhole spacetimes
  • Highlights the continued development of general relativity and its connection to areas within math and physics

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Main Lectures

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Introduction to the Wang–Yau Quasi-local Energy

      • Pengzi Miao
      Pages 3-23

    3. Gravitational Self-force in the Schwarzschild Spacetime

      • Donato Bini, Andrea Geralico
      Pages 25-61

    4. Geometry and Analysis in Black Hole Spacetimes

      • Lars Andersson
      Pages 63-112

    5. Study of Fundamental Laws with Antimatter

      • Marco Giammarchi
      Pages 113-120

  3. Proceedings

    1. Front Matter

      Pages 121-121
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    2. Quantum Ergosphere and Brick Wall Entropy

      • Lennart Brocki, Michele Arzano, Jerzy Kowalski-Glikman, Marco Letizia, Josua Unger
      Pages 123-132

    3. Geodesic Structure and Linear Instability of Some Wormholes

      • Francesco Cremona
      Pages 133-153

    4. New Trends in the General Relativistic Poynting–Robertson Effect Modeling

      • Vittorio De Falco
      Pages 155-168

    5. Brief Overview of Numerical Relativity

      • Mario L.  Gutierrez Abed
      Pages 169-189

    6. Length-Contraction in Curved Spacetime

      • Colin MacLaurin
      Pages 191-211

    7. Exact Solutions of Einstein–Maxwell(-Dilaton) Equations with Discrete Translational Symmetry

      • Jiří Ryzner, Martin Ĺ˝ofka
      Pages 213-233

    8. Exact Solutions of the Einstein Equations for an Infinite Slab with Constant Energy Density

      • Tereza Vardanyan, Alexander Yu. Kamenshchik
      Pages 235-250

    9. Emergence of Classicality from an Inhomogeneous Universe

      • Adamantia Zampeli
      Pages 251-258
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Keywords

About this book

This volume guides early-career researchers through recent breakthroughs in mathematics and physics as related to general relativity. Chapters are based on courses and lectures given at the July 2019 Domoschool, International Alpine School in Mathematics and Physics, held in Domodossola, Italy, which was titled “Einstein Equations: Physical and Mathematical Aspects of General Relativity”. Structured in two parts, the first features four courses from prominent experts on topics such as local energy in general relativity, geometry and analysis in black hole spacetimes, and antimatter gravity. The second part features a variety of papers based on talks given at the summer school, including topics like:

  • Quantum ergosphere
  • General relativistic Poynting-Robertson effect modelling
  • Numerical relativity
  • Length-contraction in curved spacetime
  • Classicality from an inhomogeneous universe

Einstein Equations: Local Energy, Self-Force, and Fields in General Relativity will be a valuable resource for students and researchers in mathematics and physicists interested in exploring how their disciplines connect to general relativity.

Editors and Affiliations

  • Department of Science and High Technology, University of Insubria, Como, Italy

    Sergio Luigi Cacciatori

  • Department of Physics and Astronomy, University of Bologna, Bologna, Italy

    Alexander Kamenshchik

About the editors

Sergio Luigi Cacciatori is an Associate Professor at the Department of Science and High Technology at the University of Insubria in Como, Italy. His research interests regard Theoretical and Mathematical Physics with particular interests in General Relativity, Quantum Field Theory, Supergravity and Superstring Theories and Analogue Gravity. He is author of more than 100 publications of scientific articles and founder of the Domoschool, the International Alpine School of Mathematics and Physics in Domodossola, Italy.

Alexander Kamenshchik is a Full Professor at the Department of Physics and Astronomy at the University of Bologna. His research interests regard Theoretical and Mathematical Physics and involve Classical and Quantum Cosmology, unification models for dark matter and dark energy, Tachyonic models, initial conditions in Quantum Cosmology, Mathematical Methods for Perturbative Cosmology. He is author of more than 200 scientific articles. In 2017 he was awarded by the Russian Academy of Sciences with the A.A. Friedmann Prize for the cycle of works “New directions in cosmology of the early and modern Universe”.

Bibliographic Information

  • Book Title: Einstein Equations: Local Energy, Self-Force, and Fields in General Relativity

  • Book Subtitle: Domoschool 2019

  • Editors: Sergio Luigi Cacciatori, Alexander Kamenshchik

  • Series Title: Tutorials, Schools, and Workshops in the Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-3-031-21845-3

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022

  • Hardcover ISBN: 978-3-031-21844-6Published: 16 March 2023

  • Softcover ISBN: 978-3-031-21847-7Published: 16 March 2024

  • eBook ISBN: 978-3-031-21845-3Published: 15 March 2023

  • Series ISSN: 2522-0969

  • Series E-ISSN: 2522-0977

  • Edition Number: 1

  • Number of Pages: X, 258

  • Number of Illustrations: 6 b/w illustrations, 27 illustrations in colour

  • Topics: Differential Geometry, Cosmology

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