Gravitation

Our vast Universe is filled with an enormous amount of matter and energy, which are the source of large gravitational potentials affecting all physical phenomena. Because this fact about the size and contents of the Universe was not known when our fundamental theories of dynamics and relativity were completed by the 1920s, the current theories - based as they are in empty space - fail to incorporate cosmic gravity. Though the current theories are consistent with the majority of empirical facts, there are some crucial discrepancies, which demand a drastic shift to a cosmic gravitational paradigm for the theories of relativity and dynamics. The book is a detailed and widely accessible account of this paradigm, called Cosmic Relativity, supported by ample empirical evidence. It is established that all motional relativistic effects are cosmic gravitational effects. The new theory of Cosmic Relativity solves and answers all outstanding questions and puzzles about dynamics and relativity.

With a rare blend of scientific insight and writing as elegant as the theories it so deftly explains, The Elegant Universe remains unrivaled in its clarity and compulsive readability: "a standard that will be hard to beat" (New York Times Book Review). In this new 25th-anniversary edition, renowned physicist and author Brian Greene, "the single best explainer of abstruse concepts in the world today" (Washington Post), updates this classic work with a new preface and epilogue summarizing impactful theoretical and experimental developments over the past quarter-century. From established science, including relativity and quantum mechanics, to the cutting edge of thinking on black holes, string theory, and quantum gravity, The Elegant Universe makes some of the most sophisticated concepts ever contemplated thoroughly accessible and entertaining, bringing us closer than ever to comprehending how the universe works."Few humans share Greene's mastery of the latest cosmological science and English prose."-Dennis Overbye, New York Times

This book deals with theoretical mechanics. Newton published the "Philosophiæ Naturalis Principia Mathematica" in 1687. In it, he sets out the basic principles of physics that are required to understand the motion of the planets, their moons, and the comets in the solar system. It includes the gravitational (inverse square) law, the inertial principle, and the basic elements of mechanics. Since its publication, a large number of refinements and reformulations have been introduced, thereby adding enormous insight into the structure of mechanics, which is commonly known as ¿classical mechanics¿. All these have in common that by taking a suitable limit, Newton's original principles re-appear. Thus, physicists and mathematicians who work on the subject always have a notion that if their theories do not return to Newton's foundations, then there is something wrong. Newton himself acknowledged that 'if I have seen further (than others), it is by standing on the shoulders of giants'. One of these giants was undoubtedly Galileo who died in the year Newton was born. So, Newton himself adhered to the 'classical limit'.

. The main aim of this book is to shine a spotlight on key experiments and their crucial importance for advancing our understanding of physics. Physics is an empirical science, and experiments have always been a driving force in the development of our understanding of nature. Facts matter. In that sense, the book attempts to be complementary to the many popularizations of theoretical physics, and to counterbalance the frequent emphasis there on more speculative ideas.Experimental physics is also an essential pillar in physics teaching, as well as helping broader audiences to better understand important concepts, particularly in challenging fields such as relativity or quantum physics, where our common sense intuition often fails.Readers are taken on an historical journey, starting with ¿Free Fall¿ and culminating in ¿Spooky Action at a Distance¿. En route they will encounter many important branches of physics, whose main ideas and theoretical description will be given a more empirical meaning. At the end, the reader is invited to reflect on what could be exciting and important directions for fundamental physics. All readers with an undergraduate degree in physical sciences or engineering will enjoy and learn much from this stimulating and original text.

This book treats the subject of gravitational waves (GWs) production in binary stars or black-holes and in the early universe, using tools of quantum field theory which are familiar to graduate students and researchers in particle physics. A special focus is given to the generation of templates of gravitational wave signals from Feynman diagram calculations of transition amplitudes, which interests active researchers in GWs. The book presents field theory concepts, like supersymmetry realized in spinning binaries and soft-graviton theorems, that can have practical applications in novel GW signals, like the memory effect. The book also aims at specialists in both GWs and particle physics addressing cosmological models of phase transition and inflation that can be tested in observations at terrestrial and space based interferometers, pulsar timing arrays, and the cosmic microwave anisotropy observations.

This book provides a concise introduction to the physics of gravitational waves. It is aimed at graduate-level students and PhD scholars. Ever since the discovery of gravitational waves in 2016, gravitational wave astronomy has been adding to our understanding of the universe.Gravitational waves have been detected in the past few years from several transient events such as merging stellar-mass black holes, binary neutron stars, etc. These waves have frequencies in a band ranging from a few hundred hertz to around a kilohertz to which LIGO type instruments are sensitive. LISA will be sensitive to much lower range of frequencies from SMBH mergers. Apart from these cataclysmic burst events, there are innumerable sources of radiation which are continuously emitting gravitational waves of all frequencies. These include a whole mass range of compact binary and isolated compact objects and close planetary stellar entities. This book discusses the gravitational wave background produced in typical frequency ranges from such sources emitting over a Hubble time and the fluctuations in the h values measured in the usual devices. Also discussed are the high-frequency thermal background gravitational radiation from hot stellar interiors and newly formed compact objects. The reader will also learn how gravitational waves provide a testing tool for various theories of gravity, i.e. general relativity and extended theories of gravity, and will be the definitive test for general relativity.

The thesis tackles two distinct problems of great interest in gravitational mechanics ¿ one relativistic and one Newtonian. The relativistic one is concerned with the "first law of binary mechanics", a remarkably simple variational relation that plays a crucial role in the modern understanding of the gravitational two-body problem, thereby contributing to the effort to detect gravitational-wave signals from binary systems of black holes and neutron stars. The work reported in the thesis provides a mathematically elegant extension of previous results to compact objects that carry spin angular momentum and quadrupolar deformations, which more accurately represent astrophysical bodies than mere point particles. The Newtonian problem is concerned with the isochrone problem of celestial mechanics, namely the determination of the set of radial potentials whose bounded orbits have a radial period independent of the angular momentum. The thesis solves this problem completely in a geometrical way and explores its consequence on a variety of levels, in particular with a complete characterisation of isochrone orbits. The thesis is exceptional in the breadth of its scope and achievements. It is clearly and eloquently written, makes excellent use of images, provides careful explanations of the concepts and calculations, and it conveys the author¿s personality in a way that is rare in scientific writing, while never sacrificing academic rigor.

This textbook introduces special relativity with a focus on a profound understanding of the physics behind the theory. The main part of the book is targeted to undergraduates, for physics education, for undergraduate students in natural sciences in general, and even to interested laypersons. To serve these target groups, the book uses only basic mathematics and, in contrast to many other introductions to special relativity, the book is based on a pedagogical approach that relies on geometry and space-time diagrams to make the surprising predictions of the theory particularly clear. Special relativity is a geometric theory, and space-time diagrams are an efficient and easily understandable way to comprehend its implications.The textbook, however, is also suitable for advanced students and enthusiasts that already learned the basics of the special theory of relativity and want to know more. Special digression sections provide plenty of interesting material. Carefully selected problems with solutions and in-depth explanations for all key experiments help deepen the knowledge.

This book presents experimental work conducted on the International Space Station (ISS) in order to characterize metals and alloys in the liquid state. The internationally recognized authors present and discuss experiments performed in microgravity that enabled the study of the relevant volume and surface related properties free of the restrictions of a gravity-based environment. The collection serves also as a handbook of space experiments using electromagnetic levitation techniques. A summary of recent results provides an overview of the wealth of space experiment data, which will ignite further research activities and inspire academics and industrial research departments for their continuous development. 

"This Element critically investigates proposed tabletop experiments controversially claimed to produce and 'witness' the first laboratory quantum gravity phenomena"--

This self-contained monograph provides a mathematically simple and physically meaningful model which unifies gravity, electromagnetism, optics and even some quantum behavior. The simplicity of the model is achieved by working in the frame of an inertial observer and by using a physically meaningful least action principle.The authors introduce an extension of the Principle of Inertia. This gives rise to a simple, physically meaningful action function. Visualizations of the geometryare obtained by plotting the action function. These visualizations may be used to compare the geometries of different types of fields. Moreover, a new understanding of the energy-momentum of a field emerges.The relativistic dynamics derived here properly describes motion of massive and massless objects under the influence of a gravitational and/or an electromagnetic field, and under the influence of isotropic media.The reader will learn how to compute the precession of Mercury, the deflection of light, and the Shapiro time delay. Also covered is the relativistic motion of binary stars, including the generation of gravitational waves, a derivation of Snell's Law and a relativistic description of spin. We derive a complex-valued prepotential of an electromagnetic field. The prepotential is similar to the wave function in quantum mechanics. The mathematics is accessible to students after standard courses in multivariable calculus and linear algebra. For those unfamiliar with tensors and the calculus of variations, these topics are developed rigorously in the opening chapters. The unifying model presented here should prove useful to upper undergraduate and graduate students, as well as to seasoned researchers.

This book consists of contributions from the participants of the Abel Symposium 2019 held in Ålesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity.The chapters are written by leading international researchers, and consist of both survey and research articles. The book gives the reader an insight into the current research in differential geometry and Lie theory, as well as applications of these topics, in particular to general relativity and string theory.

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.

This book, the first in a three-volume set, explains general relativity using the mathematical tool of differential geometry. The book consists of ten chapters, the first five of which introduce differential geometry, which is widely applicable even outside the field of relativity. Chapter 6 analyzes special relativity using geometric language. In turn, the last four chapters introduce readers to the fundamentals of general relativity. Intended for beginners, this volume includes numerous exercises and worked-out example in each chapter to facilitate the learning experience. Chiefly written for graduate-level courses, the book¿s content will also benefit upper-level undergraduate students, and can be used as a reference guide for practicing theoretical physicists.

This book presents a review of various issues related to Lorentz symmetry breaking. Explicitly, we consider (i) motivations for introducing Lorentz symmetry breaking, (ii) classical aspects of Lorentz-breaking field theory models including typical forms of Lorentz-breaking additive terms, wave propagation in Lorentz-breaking theories, and mechanisms for breaking the Lorentz symmetry; (iii) quantum corrections in Lorentz-breaking theories, especially the possibilities for perturbation generating the most interesting Lorentz-breaking terms; (iv) correspondence between non-commutative field theories and Lorentz symmetry breaking; (v) supersymmetric Lorentz-breaking theories; and (vi) Lorentz symmetry breaking in a curved space-time. We close the book with the review of experimental studies of Lorentz symmetry breaking.The importance and relevance of these topics are explained, first, by studies of limits of applicability of the Lorentz symmetry, second, by searches of the possible extensions of the standard model, including the Lorentz-breaking ones, and need to study their properties, third, by the relation between Lorentz symmetry breaking with string theory, fourth, by the problem of formulating a consistent quantum gravity theory, so that various modified gravity models are to be examined.

This book addresses supergravity and supergravity-motivated effective field theories in the context of cosmological model building. Extracting information about quintessence from string theory has attracted much attention in the past few years. The question became more urgent very recently after the possibility of obtaining de Sitter space was called into question. Therefore, there is an interesting debate as to whether de Sitter space or, even, quintessence can be derived from a fundamental theory, string theory or otherwise. This is a very active field of research, and the topics covered in the book render this work very timely.Throughout the book, special care has been taken in demonstrating historical relevance of the field and describing the set of open questions motivating the state-of-the-art research. The first few chapters in each part provide a detailed review of standard perturbative and non-perturbative techniques in supergravity model building, as a way to prepare the reader for the more technical and original subsequent chapters. These early chapters also represent a self-contained review that would be useful for anyone planning to enter this challenging area of study. The subsequent chapters detail research in supergravity-motivated effective field theories, in the first part, and supergravity models, in the second part. One of the important conclusions in this book is that modelling quintessence in perturbative string theory is at least as challenging as modelling de Sitter, placing the wider programme on a collision course with observations.

In A Brief History of Black Holes, award-winning University of Oxford researcher Dr Becky Smethurst charts five hundred years of scientific breakthroughs in astronomy and astrophysics.Right now, you are orbiting a black hole.The Earth orbits the Sun, and the Sun orbits the centre of the Milky Way: a supermassive black hole, the strangest and most misunderstood phenomenon in the galaxy.In this cosmic tale of discovery, Dr Becky Smethurst takes us from the earliest observations of the universe and the collapse of massive stars, to the iconic first photographs of a black hole and her own published findings.A cosmic tale of discovery, Becky explains why black holes aren't really 'black', that you never ever want to be 'spaghettified', how black holes are more like sofa cushions than hoovers and why, beyond the event horizon, the future is a direction in space rather than in time. Told with humour and wisdom, this captivating book describes the secrets behind the most profound questions about our universe, all hidden inside black holes.'A jaunt through space history . . . with charming wit and many pop-culture references' - BBC Sky At Night Magazine

This book addresses the pursuit and further investigation of experimental results by analyzing classic examples from physics. The authors concentrate on the investigation of experimental results by examining case studies from the history of 20th and 21st century physics. Discussions on the discovery of parity nonconservation, the rise and fall of the Fifth Force, the search for neutrinoless double decay, supersymmetry and the expansion of the Standard Model, and measurements of the anomalous magnetic moment of the muons are provided. Experimental results may achieve acceptance to the point that even well known principles, such as conservation of energy and quantization, lose their status as accepted. Such principles and their options are treated on an equal footing as being pursuit worthy even though there is no plausible explanation as to why and how they might have failed.

This textbook gradually introduces the reader to several topics related to black hole physics with a didactic approach. It starts with the most basic black hole solution, the Schwarzschild metric, and discusses the basic classical properties of black hole solutions as seen by different probes. Then it reviews various theorems about black hole properties as solutions to Einstein gravity coupled to matter fields, conserved charges associated with black holes, and laws of black hole thermodynamics. Next, it elucidates semiclassical and quantum aspects of black holes, which are relevant in ongoing and future research. The book is enriched with many exercises and solutions to assist in the learning.The textbook is designed for physics graduate students who want to start their research career in the field of black holes; postdocs who recently changed their research focus towards black holes and want to get up-to-date on recent and current research topics; advanced researchers intending to teach (or learn) basic and advanced aspects of black hole physics and the associated mathematical tools. Besides general relativity, the reader needs to be familiar with standard undergraduate physics, like thermodynamics, quantum mechanics, and statistical mechanics. Moreover, familiarity with basic quantum field theory in Minkowski space is assumed. The book covers the rest of the needed background material in the main text or the appendices.

This book is a small but practical summary of how one can and should learn science. The author argues that science cannot be taught but has to be learnt. Based on historical examples he shows that practicing science means putting one's intellect into the understanding of simple questions like what, why, how and when events around you happen. The reader understands that the search for the cause and effect relationship of so called normal happenings is a very provocative experience and learning science leads one to it. This is underpinned by looking at everyday experiences and how they can help any lay-person learn science.The author also explains the methodology of science and discusses an integrated approach to science communication. Finally he elaborates on the influence and role of science in society. The book addresses interested general readers, teachers and science communicators.

This proceedings volume gathers selected, revised papers presented at the X International Meeting on Lorentzian Geometry (GeLoCor 2021), virtually held at the University of Cordoba, Spain, on February 1-5, 2021. It includes surveys describing the state-of-the-art in specific areas, and a selection of the most relevant results presented at the conference. Taken together, the papers offer an invaluable introduction to key topics discussed at the conference and an overview of the main techniques in use today.This volume also gathers extended revisions of key studies in this field. Bringing new results and examples, these unique contributions offer new perspectives to the original problems and, in most cases, extend and reinforce the robustness of previous findings.Hosted every two years since 2001, the International Meeting on Lorentzian Geometry has become one of the main events bringing together the leading experts on Lorentzian geometry. In this volume, the reader will find studies on spatial and null hypersurfaces, low regularity in general relativity, conformal structures, Lorentz-Finsler spacetimes, and more.Given its scope, the book will be of interest to both young and experienced mathematicians and physicists whose research involves general relativity and semi-Riemannian geometry.