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Dynamics of Extremal Black Holes

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 nea...

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Bibliographic Details
Main Author: Aretakis, Stefanos
Format: eBook
Language:English
Published: Cham Springer International Publishing 2018, 2018
Edition:1st ed. 2018
Series:SpringerBriefs in Mathematical Physics
Subjects:
Gravitation
Mathematical Physics
Classical And Quantum Gravity
Astronomy, Cosmology And Space Sciences
Astronomy
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • Preface
  • Acknowledgements
  • Stability and instability of extremal black holes
  • Introduction to general relativity and black hole dynamics
  • Lorentzian geometry and causality
  • The Einstein field equations
  • Trapped surfaces
  • The Null Infinity
  • Black holes
  • The black hole stability problem
  • The wave equation on black hole exteriors
  • Price's asymptotics for sub-extremal black holes
  • Physical importance of extremal black holes
  • Extremal Reissner-Nordström black holes
  • The geometry of ERN
  • The horizon instability of ERN
  • The precise late-time asymptotics
  • Applications and additional remarks
  • The Murata-Reall-Tanahashi spacetimes
  • The interior of ERN and strong cosmic censorship
  • Extremal Kerr black holes
  • The geometry of EK
  • Stability and instability of EK for scalar perturbations
  • The Lucietti-Reall gravitational instability of EK
  • The Casals-Gralla-Zimmerman work on EK
  • Open problems
  • An overview of the main proofs
  • Asymptotics for ERN
  • Introduction to the vector field method
  • Conservation of the JT –flux
  • The Morawetz estimate
  • The T, P, N hierarchical vector fields
  • The trapping effect on the event horizon
  • Horizon localized and infinity localized hierarchies
  • Energy and pointwise decay
  • Late-time asymptotics
  • Decay estimates for EK
  • Axisymmetry vs Superradiance
  • The Carter separation and frequency localization
  • Physical space{Fourier space correspondence
  • Frequency localized Morawetz estimates
  • Energy and pointwise decay in time
  • A theory of conservation laws on null hypersurfaces
  • The geometry of null foliations
  • Conservation laws for the wave equation
  • The characteristic gluing problem
  • Necessary and sufficient conditions
  • Conservation laws on extremal black holes
  • Bibliography

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