This exploration of the global structure of spacetime within the context of general relativity examines the causal and singular structures of spacetime, revealing some of the curious possibilities that are compatible with the theory, such as 'time travel' and 'holes' of various types. Investigations into the epistemic and modal structures of spacetime highlight the difficulties in ruling out such possibilities, unlikely as they may seem at first. The upshot seems to be that what counts as a 'physically reasonable' spacetime structure in modern physics is far from clear.

The goal of this essay is to discuss the future of discovery in particle physics. Its primary motivation is the 2019 European Strategy update, which aims to determine the future experimental and theoretical priorities for particle physics. A key question is to understand what the standard theory (Standard Model) of particle physics really is, which the author argues has been a foggy notion for several decades which he clarifies. It then is to decide what motivated beyond the Standard Model theories are to be targeted by experiment. This book brightly exposes these theories, and puts current particle physics research into its historical context and points the way toward future work.

This monograph describes the different formulations of Einstein's General Theory of Relativity. Unlike traditional treatments, Cartan's geometry of fibre bundles and differential forms is placed at the forefront, and a detailed review of the relevant differential geometry is presented. Particular emphasis is given to general relativity in 4D space-time, in which the concepts of chirality and self-duality begin to play a key role. Associated chiral formulations are catalogued, and shown to lead to many practical simplifications. The book develops the chiral gravitational perturbation theory, in which the spinor formalism plays a central role. The book also presents in detail the twistor description of gravity, as well as its generalisation based on geometry of 3-forms in seven dimensions. Giving valuable insight into the very nature of gravity, this book joins our highly prestigious Cambridge Monographs in Mathematical Physics series. It will interest graduate students and researchers in the fields of theoretical physics and differential geometry.

As we navigate through life we instinctively model time as having a flowing present that divides a fixed past from open future. This model develops in childhood and is deeply saturated within our language, thought and behavior, affecting our conceptions of the universe, freedom and the self. Yet as central as it is to our lives, physics seems to have no room for this flowing present. What Makes Time Special? demonstrates this claim in detail and then turns to two novel positive tasks. First, by looking at the world "sideways" - in the spatial directions - it shows that physics is not "spatializing time" as is commonly alleged. Even relativity theory makes significant distinctions between the spacelike and timelike directions, often with surprising consequences. Second, if the flowing present is an illusion, it is a deep one worthy of explanation. The author develops a picture whereby the temporal flow arises as an interaction effect between an observer and the physics of the world. Using insights from philosophy, cognitive science, biology, psychology and physics, the theory claims that the flowing present model of time is the natural reaction to the perceptual and evolutionary challenges thrown at us. Modeling time as flowing makes sense even if it misrepresents it.

This book discusses in detail the special theory of relativity without including all the instruments of theoretical physics, enabling readers who are not budding theoretical physicists to develop competence in the field. An arbitrary but fixed inertial system is chosen, where the known velocity of light is measured. With respect to this system a moving clock loses time and a moving length contracts. The book then presents a definition of simultaneity for the other inertial frames without using the velocity of light. To do so it employs the known reciprocity principle, which in this context serves to provide a definition of simultaneity in the other inertial frames. As a consequence, the Lorentz transformation is deduced and the universal constancy of light is established. With the help of a lattice model of the special theory of relativity the book provides a deeper understanding of the relativistic effects. Further, it discusses the key STR experiments and formulates and solves 54 problems in detail.

A Physics Today Best Book of the Year A Forbes "For the Physics and Astronomy Lover in Your Life" Selection "Succinct, accessible, and remarkably timely... This book is a rare find." -Physics Today "Belongs on the shelf of anyone interested in learning the scientific, historical, and personal stories behind some of the most incredible scientific advances of the 21st century." -Forbes The detection of gravitational waves has already been called the scientific breakthrough of the century. Einstein predicted these tiny ripples in the fabric of spacetime over a hundred years ago, but they were only recently perceived directly for the first time. Ripples in Spacetime is an engaging account of the international effort to complete Einstein's project, capture his elusive ripples, and launch an era of gravitational-wave astronomy that promises to explain, more vividly than ever before, our universe's structure and origin. "Schilling's deliciously nerdy grand tour takes us through compelling backstory, current research, and future expectations." -Nature "A lively and readable account... Schilling underlines that this discovery is the opening of a new window on the universe, the beginning of a new branch of science." -Graham Farmelo, The Guardian

Ryan Wasserman explores a range of fascinating questions raised by the possibility of time travel. This volume explores a wide-range of puzzles such as the grandfather paradox, the bootstrapping paradox, and the twin paradox of special relativity. Ryan Wasserman draws out their implications for our understanding of time, tense, freedom, fatalism, causation, counterfactuals, laws of nature, persistence, change, and mereology. Paradoxes of Time Travel is written in an accessible style, and filled with entertaining examples from physics, science fiction, and popular culture.

These three lectures cover a certain aspect of complexity and black holes, namely the relation to the second law of thermodynamics. The first lecture describes the meaning of quantum complexity, the analogy between entropy and complexity, and the second law of complexity. Lecture two reviews the connection between the second law of complexity and the interior of black holes. Prof. L. Susskind discusses how firewalls are related to periods of non-increasing complexity which typically only occur after an exponentially long time. The final lecture is about the thermodynamics of complexity, and "uncomplexity" as a resource for doing computational work. The author explains the remarkable power of "one clean qubit," in both computational terms and in space-time terms. This book is intended for graduate students and researchers who want to take the first steps towards the mysteries of black holes and their complexity.

This fascinating book provides an accessible and up-to-date overview of modern cosmology. In particular, the book discusses the formation of the Cosmic Microwave Background and the evolution of large scale structures in the universe, the distribution of galaxies and clusters of galaxies on very large distance scales. Following a brief introduction, the authors describe the scientific method - how science is done. They then discuss observational cosmology, the instruments and what observations can be done with them, and what is derived from those observations. After discussing the constituents of the universe, including dark matter and dark energy, the authors provide an outline of the forces that shape the universe, with particular emphasis on gravitation. Following this, the reader is taken on a journey in time from the present day back to the very beginning of the universe, a period called inflation, which sets the initial conditions for the subsequent evolution of the universe. The book ends with a brief chapter on what lies beyond. Written by two experts, the book is aimed at the interested lay-person with little or no physics background, but an interest in modern cosmology.

This primer proposes a journey from Newton's dynamics to Einstein's relativity. It constitutes a pedagogical, rigorous, and self-contained introduction to the concepts and mathematical formulation of gravitational physics.In particular, much attention is devoted to exploring and applying the basic tools of differential geometry, that is the language of general relativity. Real-world manifestations of relativity, such as time dilation, gravitational waves, and black holes, are also discussed in detail. This book is designed for third-year bachelor or first-year master students in theoretical physics, who are already familiar with Newton's physics, possibly had an introductory course on special relativity, and who are seeking to learn general relativity on a firm basis.

This undergraduate textbook provides a simple, concise introduction to tensor algebra and analysis, as well as special and general relativity. With a plethora of examples, explanations, and exercises, it forms a well-rounded didactic text that will be useful for any related course. The book is divided into three main parts, all based on lecture notes that have been refined for classroom teaching over the past two decades. Part I provides students with a comprehensive overview of tensors. Part II links the very introductory first part and the relatively advanced third part, demonstrating the important intermediate-level applications of tensor analysis. Part III contains an extended discussion of general relativity, and includes material useful for students interested primarily in quantum field theory and quantum gravity. Tailored to the undergraduate, this textbook offers explanations of technical material not easily found or detailed elsewhere, including an understandable description of Riemann normal coordinates and conformal transformations. Future theoretical and experimental physicists, as well as mathematicians, will thus find it a wonderful first read on the subject.

At its most basic, philosophy is about learning how to think about the world around us. It should come as no surprise, then, that children make excellent philosophers! Naturally inquisitive, pint-size scholars need little prompting before being willing to consider life's "big questions," however strange or impractical. Plato & Co. introduces children and curious grown-ups to the lives and work of famous philosophers, from Socrates to Descartes, Einstein, Marx, and Wittgenstein. Each book in the series features an engaging and often funny story that presents basic tenets of philosophical thought alongside vibrant color illustrations. In Albert Einstein's Flashes of Inspiration, the young Albert Einstein has a very important job: he must deliver electricity to the big Oktoberfest celebration in Munich. As he hurries from one merry-go-round to another, nothing seems to be going as planned. With his sister, Maja, Heinrich the dog, and Niels Bohr, a qualified dwarf-thrower, can he win a battle against the laws of the universe? The key just may lie in the question of whether a dumpling can fly faster than light?

This book provides an introduction to the mathematics and physics of general relativity, its basic physical concepts, its observational implications, and the new insights obtained into the nature of space-time and the structure of the universe. It introduces some of the most striking aspects of Einstein's theory of gravitation: black holes, gravitational waves, stellar models, and cosmology. It contains a self-contained introduction to tensor calculus and Riemannian geometry, using in parallel the language of modern differential geometry and the coordinate notation, more familiar to physicists. The author has strived to achieve mathematical rigour, with all notions given careful mathematical meaning, while trying to maintain the formalism to the minimum fit-for-purpose. Familiarity with special relativity is assumed. The overall aim is to convey some of the main physical and geometrical properties of Einstein's theory of gravitation, providing a solid entry point to further studies of the mathematics and physics of Einstein equations.

This book explains and develops the Dirac equation in the context of general relativistic quantum mechanics in a range of spacetime dimensions. It clarifies the subject by carefully pointing out the various conventions used and explaining how they are related to each other. The prerequisites are familiarity with general relativity and an exposure to the Dirac equation at the level of special relativistic quantum mechanics, but a review of this latter topic is given in the first chapter as a reference and framework for the physical interpretations that follow. Worked examples and exercises with solutions are provided. Appendices include reviews of topics used in the body of the text. This book should benefit researchers and graduate students in general relativity and in condensed matter.

This book serves two main purposes: firstly, it shows, in a simple way, how the possible existence of an extra-spatial dimension would affect the predictions of four-dimensional General Relativity, a model known as the Brane world; secondly, it explains, step-by-step, a new technique called Minimal Geometric Deformation, which was introduced for the purpose of solving the correspondingly modified Einstein field equations. This method gave rise to the Gravitational Decoupling in General Relativity, which is widely used to solve the Einstein field equations in various contexts.

This primer is a collection of notes based on lectures that were originally given at IIT Madras (India) and at IFT Madrid (Spain). It is a concise and pragmatic course on applied holography focusing on the basic analytic and numerical techniques involved. The presented lectures are not intended to provide all the fundamental theoretical background, which can be found in the available literature, but they concentrate on concrete applications of AdS/CFT to hydrodynamics, quantum chromodynamics and condensed matter. The idea is to accompany the reader step by step through the various benchmark examples with a classmate attitude, providing details for the computations and open-source numerical codes in Mathematica, and sharing simple tricks and warnings collected during the author's research experience. At the end of this path, the reader will be in possess of all the fundamental skills and tools to learn by him/herself more advanced techniques and to produce independent and novel research in the field.

This book derives and analyzes all solutions to the Kepler problem with dark energy (DE), presenting significant results such as: (a) all radial infinite motions obey Hubble's law at large times; (b) all orbital infinite motions are asymptotically radial and obey Hubble's law; (c) infinite orbital motions strongly dominate the finite ones. This clearly shows the effect of repulsive DE: In the classical Kepler problem, all orbital motions are finite for negative energies and infinite in the opposite case. Another DE effect is spatial localization of bounded orbits: mostly, they are within the equilibrium sphere, where the attractive Newtonian force outbalances the repulsive force of DE. This problem is of particular current interest due to recent studies of the local flows of galaxies showing domination of DE in their dynamics; the book discusses this observation in detail.

A student-friendly style, over 100 illustrations, and numerous exercises are brought together in this textbook for advanced undergraduate and beginning graduate students in physics and mathematics. Lewis Ryder develops the theory of general relativity in detail. Covering the core topics of black holes, gravitational radiation, and cosmology, he provides an overview of general relativity and its modern ramifications. The book contains chapters on gravitational radiation, cosmology, and connections between general relativity and the fundamental physics of the microworld. It explains the geometry of curved spaces and contains key solutions of Einstein's equations - the Schwarzschild and Kerr solutions. Mathematical calculations are worked out in detail, so students can develop an intuitive understanding of the subject, as well as learn how to perform calculations. The book also includes topics concerned with the relation between general relativity and other areas of fundamental physics. Selected solutions for instructors are available under Resources.

This book presents lecture materials from the Third LOFAR Data School, transformed into a coherent and complete reference book describing the LOFAR design, along with descriptions of primary science cases, data processing techniques, and recipes for data handling. Together with hands-on exercises the chapters, based on the lecture notes, teach fundamentals and practical knowledge. LOFAR is a new and innovative radio telescope operating at low radio frequencies (10-250 MHz) and is the first of a new generation of radio interferometers that are leading the way to the ambitious Square Kilometre Array (SKA) to be built in the next decade. This unique reference guide serves as a primary information source for research groups around the world that seek to make the most of LOFAR data, as well as those who will push these topics forward to the next level with the design, construction, and realization of the SKA. This book will also be useful as supplementary reading material for any astrophysics overview or astrophysical techniques course, particularly those geared towards radio astronomy (and radio astronomy techniques).

Lectures on Astrophysics provides an account of classic and contemporary aspects of astrophysics, with an emphasis on analytic calculations and physical understanding. It introduces fundamental topics in astrophysics, including the properties of single and binary stars, the phenomena associated with interstellar matter, and the structure of galaxies. Nobel Laureate Steven Weinberg combines exceptional physical insight with his gift for clear exposition to cover exciting recent developments and new results. Emphasizing theoretical results, and explaining their derivation and application, this book provides an invaluable resource for physics and astronomy students and researchers.

Based on the author's own work and results obtained by renowned cosmologists, this short book provides a concise introduction to the relatively new research field of cosmological thermodynamics. Starting with a brief overview of basic cosmology and thermodynamics, the text gives an interesting account of the application of horizon thermodynamics to the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) model, the inhomogeneous (Lemaitre-Tolman-Bondi) LTB model, and the gravitationally induced adiabatic particle creation scenario which is considered to be a viable alternative to the concordance Lambda-CDM model of the Universe. Both seasoned and new researchers in this field will appreciate the lucid presentation and the rich bibliography.

This book is the first to provide a comprehensive, readily understandable report on the European Space Agency's Gaia mission that will meet the needs of a general audience. It takes the reader on an exciting journey of discovery, explaining how such a scientific satellite is made, presenting the scientific results available from Gaia to date, and examining how the collected data will be used and their likely scientific consequences. The Gaia mission will provide a complete and high-precision map of the positions, distances, and motions of the stars in our galaxy. It will revolutionize our knowledge on the origin and evolution of the Milky Way, on the effects of mysterious dark matter, and on the birth and evolution of stars and extrasolar planets. The Gaia satellite was launched in December 2013 and has a foreseen operational lifetime of five to six years, culminating in a final stellar catalogue in the early 2020s. This book will appeal to all who have an interest in the mission and the profound impact that it will have on astronomy.

Eleven most important original papers on special and general theories. Seven by Einstein, two by Lorentz, one each by Minkowski and Weyl.

These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The four topics covered are: Surface charges as conserved quantities in theories of gravity; Classical and holographic features of three-dimensional Einstein gravity; Asymptotically flat spacetimes in four dimensions: BMS group and memory effects; The Kerr black hole: properties at extremality and quasi-normal mode ringing. Each topic starts with historical foundations and points to a few modern research directions.

Based on Prof. Lust's Masters course at the University of Munich, this book begins with a short introduction to general relativity. It then presents black hole solutions, and discusses Penrose diagrams, black hole thermodynamics and entropy, the Unruh effect, Hawking radiation, the black hole information problem, black holes in supergravity and string theory, the black hole microstate counting in string theory, asymptotic symmetries in general relativity, and a particular quantum model for black holes. The book offers an up-to-date summary of all the pertinent questions in this highly active field of physics, and is ideal reading for graduate students and young researchers.