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This book reviews various modified gravity models, including those with modifications in the pure gravitational sector; those involving extra fields, that is, scalar-tensor and vector-tensor gravity theories; gravity models with Lorentz symmetry breaking; and nonlocal gravity models. The authors discuss both classical and quantum aspects of these theories. The book is unique in bringing together all the current alternatives to Einstein gravity in one source and serves as an excellent starting point for graduate students and other newcomers seeking an overview. This second edition has been expanded with new results from a variety of approaches including f(R,Q,P) gravity, galileon gravity and massive gravity. Extended discussions of Lorentz-breaking terms and of non-local field theory have been added and a completely new chapter is devoted to models based on non-Riemannian geometry.

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

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The main objective of this volume is to discuss the physical properties, observational signals and various probes of compact objects in the Universe. These include black holes, neutron stars, and exotic objects studied in alternative theories of gravity. The text is mainly addressed to postgraduate students and young researchers with the aim of introducing them to these very challenging topics.

Gravitation. --- General relativity (Physics). --- Cosmology. --- Gravitational Physics. --- General Relativity. --- Compact objects (Astronomy)

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This book discusses theoretical predictions and their comparison with experiments of extended and modified classical and quantum theories of gravity. The goal is to provide a readable access and broad overview over different approaches to the topic to graduate and PhD students as well as to young researchers. The book presents both, theoretical and experimental insights and is structured in three parts. The first addresses the theoretical models beyond special and general relativity such as string theory, Poincare gauge theory and teleparallelism as well as Finsler gravity. In turn, the second part is focused on the observational effects that these models generate, accounting for tests and comparisons which can be made on all possible scales: from the universe as a whole via binary systems, stars, black holes, satellite experiments, down to laboratory experiments at micrometer and smaller scales. The last part of this book is dedicated to quantum systems and gravity, showing tests of classical gravity with quantum systems, and coupling of quantum matter and gravity.

Gravitation. --- Relativity (Physics). --- Mathematical physics. --- Cosmology. --- Astrophysics. --- Classical and Quantum Gravity. --- Gravitational Physics. --- Alternative Relativity. --- Theoretical, Mathematical and Computational Physics. --- General relativity (Physics) --- Quantum gravity.

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This book meticulously examines over one hundred documents of research notes by Albert Einstein, many of which were previously unidentified, held in the archives of The Hebrew University of Jerusalem and the Einstein Papers Project at Caltech. Focused on Einstein's quest for a five-dimensional unified field theory of gravitation and electromagnetism, the analysis provides unique insights into his mathematical skills, thinking, and modus operandi. This academic exploration also investigates the role of mathematics in Einstein’s theorizing with a special focus on projective geometry and delta functions.

Physics --- Physics. --- General relativity (Physics). --- Gravitation. --- History of Physics and Astronomy. --- Conceptual Development in Physics. --- General Relativity. --- Gravitational Physics. --- History. --- Unified field theories. --- Einstein, Albert,

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This book provides a mathematical and numerical analysis of many problems which lead to paradoxes in contemporary cosmology, in particular, the existence of dark matter and dark energy. It is shown that these hypothetical quantities arise from excessive extrapolations of simple mathematical models to the whole physical universe. Written in a completely different style to most books on General Relativity and cosmology, the important results take the form of mathematical theorems with precise assumptions and statements. All theorems are followed by a corresponding proof, or an exact reference to the proof. Some nonstandard topics are also covered, including violation of the causality principle in Newtonian mechanics, a critical mathematical and numerical analysis of Mercury's perihelion shift, inapplicability of Einstein's equations to the classical two-body problem due to computational complexity, non-uniqueness of the notion of universe, the topology of the universe, various descriptions of a hypersphere, regular tessellations of hyperbolic spaces, local Hubble expansion of the universe, neglected gravitational redshift in the detection of gravitational waves, and the possible distribution of mass inside a black hole. The book also dispels some myths appearing in the theory of relativity and in contemporary cosmology. For example, although the hidden assumption that Einstein's equations provide a good description of the evolution of the whole universe is considered to be obvious, it is just a null hypothesis which has not been verified by any experiment, and has only been postulated by excessive extrapolations of many orders of magnitude.

Mathematical physics. --- Numerical analysis. --- Astronomy. --- Gravitation. --- Mathematical Physics. --- Numerical Analysis. --- Astronomy, Cosmology and Space Sciences. --- Gravitational Physics. --- Field theory (Physics) --- Matter --- Physics --- Antigravity --- Centrifugal force --- Relativity (Physics) --- Mathematical analysis --- Physical mathematics --- Mathematics --- Properties