If the talented Russian physicist Alexander Alexandrovich Friedmann had to be introduced with a single sentence, the most appropriate sentence would be the title of his biography translated from the Russian: Alexander A. Friedmann: The Man who Made the Universe Expand. Indeed, he was the first to realize in 1922 that Einstein's equations have solutions which describe not only a stationary Universe as Einstein initially believed, but also a non-stationary world. Friedmann won the debate with Einstein over the admissibility of such solutions, but his life was too short and he could not see the triumph of his views when the experimental evidence fully supported his predictions and demonstrated that the Universe was expanding. This book contains three papers by Friedmann - "On the Curvature of Space", "On the Possibility of a World with a Constant Negative Curvature of Space", and "On the Geometry of Curved Spaces". The third paper is a 28-page manuscript (dated 15 April 1922) which has not been published even in Russian. Unlike the existing two English translations of Friedmann's 1922 and 1924 papers (done from the German publications), now these papers are translated directly from the original Russian texts.

This text explains special relativity and the basics of general relativity from a geometric viewpoint. Space-time geometry is emphasised throughout, and up-to-date information is provided on black holes, gravitational collapse, and cosmology.

The theory of relativity describes the laws of physics in a given space-time. However, a physical theory must provide observational predictions expressed in terms of measurements, which are the outcome of practical experiments and observations. Ideal for readers with a mathematical background and a basic knowledge of relativity, this book will help readers understand the physics behind the mathematical formalism of the theory of relativity. It explores the informative power of the theory of relativity, and highlights its uses in space physics, astrophysics and cosmology. Readers are given the tools to pick out from the mathematical formalism those quantities that have physical meaning and which can therefore be the result of a measurement. The book considers the complications that arise through the interpretation of a measurement, which is dependent on the observer who performs it. Specific examples of this are given to highlight the awkwardness of the problem.

Quantum mechanics and quantum field theory on one hand and Gravity as a theory of curved space-time on the other are the two great conc- tual schemes of modern theoretical physics. For many decades they have lived peacefully together for a simple reason: it was a coexistence wi- out much interaction. There has been the family of relativists and the other family of elementary particle physicists and both sides have been convinced that their problems have not very much to do with the problems of the respective other side. This was a situation which could not last forever, because the two theoretical schemes have a particular structural trait in common: their claim for totality and universality. Namely on one hand all physical theories have to be formulated in a quantum mechanical manner, and on the other hand gravity as curved space-time influences all processes and vice versa. It was therefore only a question of time that physically relevant domains of application would attract a general int- est, which demand a combined application of both theoretical schemes. But it is immediately obvious that such an application of both schemes is - possible if the schemes are taken as they are. Something new is needed which reconciles gravity and quantum mechanics. During the last two de- des we are now doing the first steps towards this more general theory and we are confronted with fundamental difficulties.

This book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Although the treatment is general, special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe. The last decade has witnessed a phenomenal growth in this subject. This is the first attempt to collect and unify the vast literature that has contributed to this development. All the major technical results are presented, and the theory is developed carefully from first principles. Here is everything that students or researchers will need to embark upon calculations involving quantum effects of gravity at the so-called one-loop approximation level.

The main goal and impact of modern string theory is to provide a consistent quantum theory of gravity. This book provides an updated collection of original new developments and fundamental research in string theory in connection with gravity and physics at the Planck energy scale. Topics treated in this volume by pioneering researchers in the field include: classical and quantum string dynamics in strong gravitational fields, space-time singularities, black holes and cosmological backgrounds; particle and string scattering at the Planck energy scale; string cosmology and its observational consequences; the new features of multistrings and of quantum particle transmutation for strings in curved spacetimes. The book deals with (i) the several new methods developed to solve the highly nonlinear string dynamics in curved spactimes: approximative perturbative methods, asymptotic expansions, exact local expansions and exact global (over the whole world sheet) string solitonic solutions, (ii) the string energy momentum tensor and the equation of state for the string matter, the stretching of the string size in spacetimes with event horizons and near spacetime singularities, (iii) the canonical and semiclassical quantization of strings in curved spacetimes and the physical effects found for: the mass spectrum, structure of levels, scattering amplitudes, number operator and particle transmutation. Contents:String Theory in Cosmological Spacetimes (H J de Vega & N Sánchez)Evolution of a String Network in Backgrounds with Rolling Horizons (M Gasperini, M Giovannini, K A Meissner & G Veneziano)Particle Transmutation and Fermion Number Violation from the Scattering of Strings and Superstrings in Curved Spacetimes (H J de Vega, M Ramón Medrano & N Sánchez)Particle and String Scattering at the Planck Scale (C O Lousto & N Sánchez)Strings in Curved Spacetimes: The Null String Approach (H J de Vega & A Nicolaidis)Strings and Multi-Strings in Black Hole and Cosmological Spacetimes (A L Larsen & N Sánchez)Integrable Field Theories (C Destri & H J de Vega)Von Neumann and Shannon-Wehrl Entropy for Squeezed States and Cosmological Particle Production (M Gasperini & M Giovannini)Preheating and Reheating in Inflationary Cosmology: A Pedagogical Review (D Boyanovsky, H J de Vega, R Holman & J F J Salgado)Circular Strings and Multi-Strings in de Sitter and Anti de Sitter Spacetimes (H J de Vega, A L Larsen & N Sánchez)The Two-Dimensional Stringy Black Hole: A New Approach and a New Effect (H J de Vega, J Ramírez Mittelbrun, M Ramón Medrano & N Sánchez)Relic Gravitons from the Pre-Big Bang: What We Know and What We Do Not Know (M Gasperini)Classical Splitting of Fundamental Strings (H J de Vega, J Ramírez Mittelbrun, M Ramón Medrano & N Sánchez)Cosmic Strings and Black Holes (A L Larsen)Strings Next To and Inside Black Holes (H J de Vega & I L Egusquiza)String Dynamics in Cosmological and Black Hole Backgrounds: The Null String Expansion (C O Lousto & N Sánchez)The Black Hole: Scatterer, Absorber and Emitter of Particles (N Sánchez)Une Approche du Temps et des Fréquences. Vers le Mètre et la Seconde (S Débarbat & M Granveaud) Readership: Researchers in string theory, cosmology and particle physics. Keywords:String;Superstring;Inflation;Cosmology;Black Hole