Dynamics of Extremal Black Holes by Stefanos Aretakis
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Dynamics of Extremal Black Holes

Dynamics of Extremal Black Holes


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About the Book

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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Product Details
  • ISBN-13: 9783319951829
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Height: 234 mm
  • No of Pages: 131
  • Series Title: Springerbriefs in Mathematical Physics
  • Weight: 267 gr
  • ISBN-10: 3319951823
  • Publisher Date: 13 Nov 2018
  • Binding: Paperback
  • Language: English
  • Returnable: Y
  • Spine Width: 8 mm
  • Width: 156 mm


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