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El. knyga: Dynamics of Extremal Black Holes

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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.

Recenzijos

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)

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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