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In this paper, the authors study the direct and inverse scattering theory at fixed energy for massless charged Dirac fields evolving in the exterior region of a Kerr-Newman-de Sitter black hole. In the first part, they establish the existence and asymptotic completeness of time-dependent wave operators associated to our Dirac fields. This leads to the definition of the time-dependent scattering operator that encodes the far-field behavior (with respect to a stationary observer) in the asymptotic regions of the black hole: the event and cosmological horizons. The authors also use the miraculous property (quoting Chandrasekhar)-that the Dirac equation can be separated into radial and angular ordinary differential equations-to make the link between the time-dependent scattering operator and its stationary counterpart. This leads to a nice expression of the scattering matrix at fixed energy in terms of stationary solutions of the system of separated equations. In a second part, the authors use this expression of the scattering matrix to study the uniqueness property in the associated inverse scattering problem at fixed energy. Using essentially the particular form of the angular equation (that can be solved explicitly by Frobenius method) and the Complex Angular Momentum technique on the radial equation, the authors are finally able to determine uniquely the metric of the black hole from the knowledge of the scattering matrix at a fixed energy.

Kerr black holes. --- Black holes (Astronomy) --- Inverse scattering transform. --- Dirac equation.

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This textbook introduces the current astrophysical observations of black holes, and discusses the leading techniques to study the strong gravity region around these objects with electromagnetic radiation. More importantly, it provides the basic tools for writing an astrophysical code and testing the Kerr paradigm. Astrophysical black holes are an ideal laboratory for testing strong gravity. According to general relativity, the spacetime geometry around these objects should be well described by the Kerr solution. The electromagnetic radiation emitted by the gas in the inner part of the accretion disk can probe the metric of the strong gravity region and test the Kerr black hole hypothesis. With exercises and examples in each chapter, as well as calculations and analytical details in the appendix, the book is especially useful to the beginners or graduate students who are familiar with general relativity while they do not have any background in astronomy or astrophysics.

Physics. --- Gravitation. --- Astrophysics. --- Astrophysics and Astroparticles. --- Classical and Quantum Gravitation, Relativity Theory. --- Black holes (Astronomy) --- Field theory (Physics) --- Matter --- Physics --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Astronomical physics --- Astronomy --- Cosmic physics --- Properties

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Dive into a mind-bending exploration of the physics of black holesBlack holes, predicted by Albert Einstein's general theory of relativity more than a century ago, have long intrigued scientists and the public with their bizarre and fantastical properties. Although Einstein understood that black holes were mathematical solutions to his equations, he never accepted their physical reality-a viewpoint many shared. This all changed in the 1960s and 1970s, when a deeper conceptual understanding of black holes developed just as new observations revealed the existence of quasars and X-ray binary star systems, whose mysterious properties could be explained by the presence of black holes. Black holes have since been the subject of intense research-and the physics governing how they behave and affect their surroundings is stranger and more mind-bending than any fiction.After introducing the basics of the special and general theories of relativity, this book describes black holes both as astrophysical objects and theoretical "laboratories" in which physicists can test their understanding of gravitational, quantum, and thermal physics. From Schwarzschild black holes to rotating and colliding black holes, and from gravitational radiation to Hawking radiation and information loss, Steven Gubser and Frans Pretorius use creative thought experiments and analogies to explain their subject accessibly. They also describe the decades-long quest to observe the universe in gravitational waves, which recently resulted in the LIGO observatories' detection of the distinctive gravitational wave "chirp" of two colliding black holes-the first direct observation of black holes' existence.The Little Book of Black Holes takes readers deep into the mysterious heart of the subject, offering rare clarity of insight into the physics that makes black holes simple yet destructive manifestations of geometric destiny.

Black holes (Astronomy) --- Frozen stars --- Compact objects (Astronomy) --- Gravitational collapse --- Stars --- A-frame. --- Acceleration. --- Accretion disk. --- Alice and Bob. --- Angular momentum. --- Astronomer. --- Atomic nucleus. --- Binary black hole. --- Binary star. --- Black hole information paradox. --- Black hole thermodynamics. --- Black hole. --- Calculation. --- Circular orbit. --- Classical mechanics. --- Closed timelike curve. --- Cosmological constant. --- Curvature. --- Cygnus X-1. --- Degenerate matter. --- Differential equation. --- Differential geometry. --- Doppler effect. --- Earth. --- Einstein field equations. --- Electric charge. --- Electric field. --- Electromagnetism. --- Ergosphere. --- Escape velocity. --- Event horizon. --- Excitation (magnetic). --- Frame-dragging. --- Galactic Center. --- General relativity. --- Gravitational acceleration. --- Gravitational collapse. --- Gravitational constant. --- Gravitational energy. --- Gravitational field. --- Gravitational redshift. --- Gravitational wave. --- Gravitational-wave observatory. --- Gravity. --- Hawking radiation. --- Inner core. --- Kerr metric. --- Kinetic energy. --- LIGO. --- Length contraction. --- Lorentz transformation. --- Magnetic field. --- Mass–energy equivalence. --- Maxwell's equations. --- Metric expansion of space. --- Metric tensor. --- Milky Way. --- Minkowski space. --- Negative energy. --- Neutrino. --- Neutron star. --- Neutron. --- Newton's law of universal gravitation. --- No-hair theorem. --- Nuclear fusion. --- Nuclear reaction. --- Orbit. --- Orbital mechanics. --- Orbital period. --- Penrose process. --- Photon. --- Physicist. --- Primordial black hole. --- Projectile. --- Quantum entanglement. --- Quantum gravity. --- Quantum mechanics. --- Quantum state. --- Quasar. --- Ray (optics). --- Rotational energy. --- Roy Kerr. --- Schwarzschild metric. --- Schwarzschild radius. --- Solar mass. --- Special relativity. --- Star. --- Stellar mass. --- Stephen Hawking. --- Stress–energy tensor. --- String theory. --- Supermassive black hole. --- Temperature. --- Theory of relativity. --- Thought experiment. --- Tidal force. --- Time dilation. --- Wavelength. --- White hole. --- Wormhole.