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The papers in this volume cover a wide range of subjects covering the most recent developments in Celestial Mechanics from the theoretical point of nonlinear dynamical systems to the application to real problems. We emphasize the papers on the formation of planetary systems, their stability and also the problem of habitable zones in extrasolar planetary systems. A special topic is the stability of Trojans in our planetary system, where more and more realistic dynamical models are used to explain their complex motions: besides the important contribution from the theoretical point of view, the results of several numerical experiments unraveled the structure of the stable zone around the librations points. This volume will be of interest to astronomers and mathematicians interested in Hamiltonian mechanics and in the dynamics of planetary systems.

Space research --- Cosmology --- Astrophysics --- Theory of relativity. Unified field theory --- astrofysica --- relativiteitstheorie --- ruimte (astronomie) --- ruimtevaart --- kosmologie

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The theory, observations, and applications of gravitational lensing constitute one of the most rapidly growing branches of astrophysics. The gravitational deflection of light generated by mass concentrations along a light path produces magnification, multiplicity, and distortion of images and delays photon propagation from one line of sight relative to another. The huge amount of scientific work on gravitational lensing produced over the last decade has clearly revealed its already substantial and wide impact and its potential for future astrophysical applications. The up-to-date contributions in this book are based on the lecture notes of the 33rd Saas-Fee Advanced Course of the Swiss Society of Astronomy and Astrophysics, entitled Gravitational Lensing: Strong, Weak, and Micro. The book comprises four complementary parts, written by leading experts in the field, constituting a genuine textbook about gravitational lensing: ¢ Peter Schneider - Part 1: Introduction to Gravitational Lensing and Cosmology ¢ Christopher Kochanek - Part 2: Strong Gravitational Lensing ¢ Peter Schneider - Part 3: Weak Gravitational Lensing ¢ Joachim Wambsganss - Part 4: Gravitational Microlensing Students and researchers alike will benefit from this comprehensive presentation of the astrophysical and astronomical aspects of gravitational lensing.

Space research --- Cosmology --- Astrophysics --- Theory of relativity. Unified field theory --- astrofysica --- relativiteitstheorie --- ruimte (astronomie) --- kosmologie

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  This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics.  It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman's characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac's famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group.  This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt  to the presence of gravitational fields that cannot be considered  negligible. The second is to understand some of the basic features of  a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recent astronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a knowledge of linear algebra in the first three chapters, a bit of real analysis in the fourth and, in two appendices, some elementary point-set topology.   The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title.   Reviews of first edition:     ¦ a valuable contribution to the pedagogical literature which will be enjoyed by all who delight in precise mathematics and physics.  (American Mathematical Society, 1993)    Where many physics texts explain physical phenomena by means of mathematical models, here a rigorous and detailed mathematical development is accompanied by precise physical interpretations.  (CHOICE, 1993)   ¦ his talent in choosing the most significant results and ordering them within the book can't be denied. The reading of the book is, really, a pleasure.  (Dutch Mathematical Society, 1993)    

Differential topology --- Mathematical physics --- Theory of relativity. Unified field theory --- Geophysics --- zwaartekracht --- wiskunde --- relativiteitstheorie --- geofysica --- topologie

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As a result of significant research over the past 20 years, black holes are now linked to some of the most spectacular and exciting phenomena in the Universe, ranging in size from those that have the same mass as stars to the super-massive objects that lie at the heart of most galaxies, including our own Milky Way. This book first introduces the properties of simple isolated holes, then adds in complications like rotation, accretion, radiation, and magnetic fields, finally arriving at a basic understanding of how these immense engines work. Black Hole Astrophysics ¢ reviews our current knowledge of cosmic black holes and how they generate the most powerful observed pheonomena in the Universe; ¢ highlights the latest, most up-to-date theories and discoveries in this very active area of astrophysical research; ¢ demonstrates why we believe that black holes are responsible for important phenomena such as quasars, microquasars and gammaray bursts; ¢ explains to the reader the nature of the violent and spectacular outfl ows (winds and jets) generated by black hole accretion.

Astrophysics --- Theory of relativity. Unified field theory --- Geophysics --- zwaartekracht --- astrofysica --- relativiteitstheorie --- geofysica

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Some major developments of physics in the last three decades are addressed by highly qualified specialists in different specific fields. They include renormalization problems in QFT, vacuum energy fluctuations and the Casimir effect in different configurations, and a wealth of applications. A number of closely related issues are also considered. The cosmological applications of these theories play a crucial role and are at the very heart of the book; in particular, the possibility to explain in a unified way the whole history of the evolution of the Universe: from primordial inflation to the present day accelerated expansion. Further, a description of the mathematical background underlying many of the physical theories considered above is provided. This includes the uses of zeta functions in physics, as in the regularization problems in QFT already mentioned, specifically in curved space-time, and in Casimir problems as.

Cosmology --- Mathematical physics --- Theory of relativity. Unified field theory --- Geophysics --- zwaartekracht --- wiskunde --- relativiteitstheorie --- geofysica