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Dynamics of Extremal Black Holes

  • Book
  • © 2018

Overview

Authors:
  1. Stefanos Aretakis

    1. University of Toronto, Toronto, Canada

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  • Presents the main mathematical difficulties concerning the dynamics of extremal black holes
  • Presents the main recent results and techniques in a unified non-technical and illustrative fashion
  • Provides a discussion of the outstanding open problems and offers insights for potential resolutions
  • Provides common ground for communication between different scientific communities including those of pure mathematicians, theoretical physicists and astrophysicists

Part of the book series: SpringerBriefs in Mathematical Physics (BRIEFSMAPHY, volume 33)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Stability and Instability of Extremal Black Holes

    1. Front Matter

      Pages 1-1
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    2. Introduction to General Relativity and Black Hole Dynamics

      • Stefanos Aretakis
      Pages 3-36

    3. Extremal Reissner–Nordström Black Holes

      • Stefanos Aretakis
      Pages 37-70

    4. Extremal Kerr Black Holes

      • Stefanos Aretakis
      Pages 71-81

  3. An Overview of the Proofs

    1. Front Matter

      Pages 83-83
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    2. Asymptotics for Extremal Reissner–Nordström

      • Stefanos Aretakis
      Pages 85-113

    3. Decay Estimates for Extremal Kerr

      • Stefanos Aretakis
      Pages 115-124

    4. A Theory of Conservation Laws on Null Hypersurfaces

      • Stefanos Aretakis
      Pages 125-131
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Keywords

About this book

This Brief presents in a self-contained, non-technical and illustrative fashion the state-of-the-art results and techniques for the dynamics of extremal black holes. Extremal black holes are, roughly speaking, either maximally rotating or maximally charged. Astronomical observations suggest that near-extremal (stellar or supermassive) black holes are ubiquitous in the universe. The book presents various recently discovered characteristic phenomena (such as the horizon instability) that have enhanced our understanding of the dynamics of extremal black holes. The topics should be of interest to pure mathematicians, theoretical physicists and astronomers. This book provides common ground for communication between these scientific communities.

Reviews

“Very attractive feature of the book are the copious figures which greatly aid understanding. … This book will be very useful for beginning graduate students who need to then study the proofs in the primary literature, as well as for researchers who wish to learn about the subject and understand the gist of the proofs without working through all the details.” (Elizabeth Winstanley, zbMath 1419.83002, 2019)

Authors and Affiliations

  • University of Toronto, Toronto, Canada

    Stefanos Aretakis

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