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This book, dedicated to Roger Penrose, is a second, mathematically oriented course in general relativity. It contains extensive references and occasional excursions in the history and philosophy of gravity, including a relatively lengthy historical introduction. The book is intended for all students of general relativity of any age and orientation who have a background including at least first courses in special and general relativity, differential geometry, and topology. The material is developed in such a way that through the last two chapters the reader may acquire a taste of the modern mathematical study of black holes initiated by Penrose, Hawking, and others, as further influenced by the initial-value or PDE approach to general relativity. Successful readers might be able to begin reading research papers on black holes, especially in mathematical physics and in the philosophy of physics. The chapters are: Historical introduction, General differential geometry, Metric differential geometry, Curvature, Geodesics and causal structure, The singularity theorems of Hawking and Penrose, The Einstein equations, The 3+1 split of space-time, Black holes I: Exact solutions, and Black holes II: General theory. These are followed by two appendices containing background on Lie groups, Lie algebras, & constant curvature, and on Formal PDE theory.

General relativity (Physics)

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Cet ouvrage, dans la vision pluridisciplinaire de l'Académie, montre les progrès scientifiques réalisés depuis les premiers travaux d'Albert Einstein et de ses contemporains du début du XXe siècle sur les deux grands piliers de la Physique moderne que sont la Relativité générale et la Mécanique quantique. Il a la prétention de rassembler les résultats et les observations scientifiques les plus significatifs de la fin du XXe siècle et de ce début de troisième millénaire. Malgré les difficultés actuelles des tentatives de leur conciliation en vue de bâtir une théorie unifiée, ces deux théories montrent leur grande pertinence dans leurs domaines respectifs de validité. Elles nous offrent une vision du monde et de l'Univers d'une richesse insoupçonnée. Ce livre comporte quatre parties. 1) Relativité, ondes de l'univers. 2) Dualité ondes/corpuscules de la physique quantique. 3) Ondes, matière et quantification. 4) Une nouvelle révolution scientifique à l'horizon ? La même exigence traverse en filigrane tous les travaux ou réflexions présentés : l'exigence d'accroître et d'affiner constamment les techniques d'observations et d'expérimentations, et de construire parallèlement les outils mathématiques nécessaires à l'analyse de leurs résultats ; l'exigence de tester les implications des théories jusqu'aux dernières limites permises par ces possibilités observationnelles et expérimentales ; pour résumer l'exigence de mettre sans cesse à l'épreuve les théories dans leur conformité aux observations et expériences, et, à travers leur interprétation, dans le rapport que nous leur attribuons à la « réalité » de notre Univers.

SCIENCE / Physics / General. --- General relativity --- quantum physics

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This volume offers a comprehensive overview of our understanding of gravity at both the experimental and the theoretical level. Critical reviews by experts cover topics ranging from astrophysics (anisotropies in the cosmic microwave background, gamma ray bursts, neutron stars and astroparticles), cosmology, the status of gravitational wave sources and detectors, verification of Newton's law at short distances, the equivalence principle, gravito-magnetism, measurement theory, time machines and the foundations of Einstein's theory, to string theory and loop quantum gravity.

General relativity (Physics) --- Particles (Nuclear physics)

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This book investigates Lorentzian structures in the four-dimensional space-time, supplemented either by a covector field of the time-direction or by a scalar field of the global time. Furthermore, it proposes a new metrizable model of gravity. In contrast to the usual General Relativity theory, where all ten components of the symmetric pseudo-metric are independent variables, the gravity model presented here essentially depends only on a single four-covector field, and is restricted to have only three-independent components. However, the author proves that the gravitational field, governed by the proposed model and generated by some massive body, resting and spherically symmetric in some coordinate system, is given by a pseudo-metric that coincides with the well known Schwarzschild metric from General Relativity. The Maxwell equations and electrodynamics are also investigated in the framework of the proposed model. In particular, the covariant formulation of electrodynamics of moving dielectrics and para/diamagnetic media is derived.

Geophysics --- zwaartekracht --- General relativity (Physics) --- Quantum electrodynamics.

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This book brings Einstein's general relativity into action in new ways at scales ranging from the tiny Planck scale to the scale of immense galactic clusters. It presents the case that Einstein's theory of gravity can describe the observed dynamics of galaxies without invoking the unknown "dark matter" required in models based on Newtonian gravity. Drawing on the author's experience as a lecturer and on his own research, the book covers the essentials of Einstein's special and general relativity at a level accessible to undergraduate students. The early chapters provide a compact introduction

General relativity (Physics) --- Gravity. --- Gravitational fields. --- Galaxies.