Dynamics of Extremal Black Holes

  • Stefanos Aretakis

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

Table of contents

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

    1. Front Matter
      Pages 1-1
    2. Stefanos Aretakis
      Pages 37-70
    3. Stefanos Aretakis
      Pages 71-81
  3. An Overview of the Proofs

    1. Front Matter
      Pages 83-83
    2. Stefanos Aretakis
      Pages 85-113
    3. Stefanos Aretakis
      Pages 115-124
    4. Stefanos Aretakis
      Pages 125-131

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.


Einstein equations Extremal Reissner-Nordstrom black holes Extremal Kerr black holes Lorentzian geometry Linearized gravity null infinity extremal event horizon Cauchy problem for the Einstein equations sub-extremal black holes trapped surface black holes stability black holes instability Mathematical General Relativity Aretakis instability Black hole dynamics Penrose diagrams Couch-Torrence conformal inversion Murata-Reall-Tanahashi spacetimes Lucietti-Reall gravitational instability Morawetz estimate

Authors and affiliations

  • Stefanos Aretakis
    • 1
  1. 1.University of TorontoTorontoCanada

Bibliographic information