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On November 25th, 1915, Albert Einstein published his field equations of general relativity and reinvented gravity. Rather than being some mysterious unseen force pulling objects together, gravity, Einstein told the world, is a manifestation of the curvature of space-time caused by the presence of massive objects. But Einstein's theory wasn't born in a vacuum, not even the vacuum of space. Instead, the theory of general relativity relies upon complicated geometry; Einstein worked closely with mathematicians Marcel Grossmann, David Hilbert, Tullio Levi-Civita, and others as he pieced together his theory of gravity. In The Gravity of Math, the writer Steve Nadis and mathematician Shing-Tung Yau tell the story of how our view of the universe has been shaped and informed by mathematics, particularly when it comes to the enigmatic workings of gravity. Mathematicians have played a pivotal role in investigating relativity and gravity, gaining insights on phenomena like black holes, gravitational waves, and the Big Bang - in some cases uncovering key results decades, or even a century, before any experimental or observational data became available. An insightful and comprehensive study, The Gravity of Math explores how our understanding of math has defined our understanding of the universe. Gravity's reach is ostensibly boundless, and so is that of mathematics, which can carry us to the edge of infinity and back.

Gravitation. --- Gravitation. --- Gravitation. --- General relativity (Physics) --- General relativity (Physics) --- Black holes (Astronomy) --- Gravitation. --- Gravitation --- Gravitation --- Relativité générale (physique) --- Relativité générale (physique) --- Trous noirs (astronomie) --- Mathematics --- History --- Mathematics --- History --- Mathematics --- Mathématiques. --- Histoire. --- Mathématiques. --- Histoire. --- Mathématiques.

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This book starts with the mathematical basis of the theory - i.e. provide a brief sketch of the theory of manifolds and frame bundles, tensors and their transformations, relativistic kinematics, and aspects of non-flat space-time geometries. The definition of relevant physical quantities (torsion, curvature, non-metricity, tetrads, connection fields etc.) and important geometry concepts are also included. The main body of the book is devoted to a detailed derivation of the gauge theory of gravitation for scalar, vector (Proca and Maxwell) and Dirac spinor fields. Alternative approaches based on the Noether theorem and on the spinorial representation of the fields are also addressed, as well as important novel features related to the CCGG framework (Birkhoff theorem, field derivative identities etc.). In the last section of the volume the application of the CCGG theory to cosmology will be set out, resulting in a new understanding of dark energy and inflation. .

Elementary particles (Physics). --- Quantum field theory. --- Gravitation. --- Cosmology. --- Elementary Particles, Quantum Field Theory. --- Classical and Quantum Gravity. --- Gauge fields (Physics) --- Gravitation --- Mathematics.

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The book collects a series of articles to review the advances that have been made in the field of gravitational collapse in general relativity and alternative theories of gravity in the past few years. Many approaches to black hole and singularity formation in general relativity and beyond have been proposed over the last few decades. The importance of collapse models is that they provide natural thought experiments where to test the behavior and properties of a variety of approaches to general relativity and its implications for ultra-compact objects in the universe.

General relativity (Physics). --- Gravitation. --- Astrophysics. --- Relativity (Physics). --- General Relativity. --- Gravitational Physics. --- Classical and Quantum Gravity. --- Alternative Relativity.

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Time, space and entanglement are the main characters in this book. Their nature is still a great mystery in physics and we study here the possibility that these three phenomena are closely connected, showing how entanglement can be at the basis of the emergence of time and space within closed quantum systems. We revisit and extend the Page and Wootters theory that was originally introduced in order to describe the emergence of time through entanglement between subsystems in a globally static, quantum Universe. In the book, after providing a complete review of the salient aspects of the theory, we establish a connection with recent research on the foundations of statistical mechanics and we provide a new understanding of the thermalization process. Furthermore, we generalize the framework in order describe the spatial degree of freedom and we provide a model of 3+1 dimensional, quantum spacetime emerging from entanglement among different subsystems in a globally "timeless" and "positionless" Universe. Finally, via the Page and Wootters theory, the evolution of quantum clocks within a gravitational field is treated and a time dilation effect is obtained in agreement with the Schwarzschild solution.

Gravitation. --- Science. --- Quantum physics. --- Mathematical physics. --- Classical and Quantum Gravity. --- Foundations of Physics and Cosmology. --- Quantum Physics. --- Theoretical, Mathematical and Computational Physics.

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This book is a collection of contributions presented at the 16th annual international symposium “Frontiers of Fundamental Physics” (FFP16), supported by Istanbul University. As a document of the latest occurrence of this very important gathering, it presents the most recent advances in fundamental physics and physics teaching. For nearly fifteen years, the FFP has attracted some of the greatest physicists in the world. The broad objective of the entire endeavor has been to enable scholars working in slightly different areas to meet on a single platform. Even with this particular year’s safety restrictions arising from Covid, we feel that the general mission has been carried out as fully as in any year. The book features addresses given by a host of expert contributors, all of which are organized according to seven individual themes. The areas covered include Astronomy and Astrophysics, Particle Physics, Theoretical Physics, Gravitation and Cosmology, Computational Physics, Condensed Matter Physics, Complex Systems and related areas. This book should prove to be a veritable bounty for anyone with an interest in the continued evolution of our understanding of the physical world.

Mathematical physics. --- Astronomy. --- Astrophysics. --- Condensed matter. --- Gravitation. --- Theoretical, Mathematical and Computational Physics. --- Astronomy, Cosmology and Space Sciences. --- Condensed Matter Physics. --- Gravitational Physics.