After an extensive introduction to the asymptotic safety approach to quantum gravity, this thesis explains recent key advances reported in four influential papers. Firstly, two exact solutions to the reconstruction problem (how to recover a bare action from the effective average action) are provided. Secondly, the fundamental requirement of background independence in quantum gravity is successfully implemented. Working within the derivative expansion of conformally reduced gravity, the notion of compatibility is developed, uncovering the underlying reasons for background dependence generically forbidding fixed points in such models. Thirdly, in order to understand the true nature of fixed-point solutions, one needs to study their asymptotic behaviour. The author carefully explains how to find the asymptotic form of fixed point solutions within the f(R) approximation. Finally, the key findings are summarised and useful extensions of the work are identified. The thesis finishes by considering the need to incorporate matter into the formalism in a compatible way and touches upon potential opportunities to test asymptotic safety in the future.

Tau functions are a central tool in the modern theory of integrable systems. This volume provides a thorough introduction, starting from the basics and extending to recent research results. It covers a wide range of applications, including generating functions for solutions of integrable hierarchies, correlation functions in the spectral theory of random matrices and combinatorial generating functions for enumerative geometrical and topological invariants. A self-contained summary of more advanced topics needed to understand the material is provided, as are solutions and hints for the various exercises and problems that are included throughout the text to enrich the subject matter and engage the reader. Building on knowledge of standard topics in undergraduate mathematics and basic concepts and methods of classical and quantum mechanics, this monograph is ideal for graduate students and researchers who wish to become acquainted with the full range of applications of the theory of tau functions.

The problem of quantum gravity is often viewed as the most pressing unresolved problem of modern physics: our theories of spacetime and matter, described respectively by general relativity (Einstein's theory of gravitation and spacetime) and quantum mechanics (our best theory of matter and the other forces of nature) resist unification. Covered with Deep Mist provides the first book-length treatment of the history of quantum gravity, focusing on its origins and earliest stages of development until the mid-1950s. Readers will be guided through the impacts on the problem of quantum gravity resulting from changes in the two ingredient theories, quantum theory and general relativity, which were themselves still under construction in the years studied. We examine how several of the core approaches of today were formed in an era when the field was highly unfashionable. The book aims to be accessible to a broad range of readers and goes beyond a merely technical examination to include social and cultural factors involved in the changing fortunes of the field. Suitable for both newcomers and seasoned quantum gravity professionals, the book will shine new light on this century-old, unresolved problem.

Describes the branch of astronomy in which processes in the universe are investigated with experimental methods employed in particle-physics experiments. After a historical introduction the basics of elementary particles, Explains particle interactions and the relevant detection techniques, while modern aspects of astroparticle physics are described in a chapter on cosmology. Provides an orientation in the field of astroparticle physics that many beginners might seek and appreciate because the underlying physics fundamentals are presented with little mathematics, and the results are illustrated by many diagrams. Readers have a chance to enter this field of astronomy with a book that closes the gap between expert and popular level.

With the aid of entertaining short stories, anecdotes, lucid explanations and straight-forward figures, this book challenges the perception that the world of physics is inaccessible to the non-expert. Beginning with Neanderthal man, it traces the evolution of human reason and understanding from paradoxes and optical illusions to gravitational waves, black holes and dark energy. On the way, it provides insights into the mind-boggling advances at the frontiers of physics and cosmology. Unsolved problems and contradictions are highlighted, and contentious issues in modern physics are discussed in a non-dogmatic way in a language comprehensible to the non-scientist. It has something for everyone.

Unlike most traditional introductory textbooks on relativity and cosmology that answer questions like "Does accelerated expansion pull our bodies apart?", "Does the presence of dark matter affect the classical tests of general relativity?" in a qualitative manner, the present text is intended as a foundation, enabling students to read and understand the textbooks and many of the scientific papers on the subject. And, above all, the readers are taught and encouraged to do their own calculations, check the numbers and answer the above and other questions regarding the most exciting discoveries and theoretical developments in general relativistic cosmology, which have occurred since the early 1980s. In comparison to these intellectual benefits the text is short. In fact, its brevity without neglect of scope or mathematical accessibility of key points is rather unique. The authors connect the necessary mathematical concepts and their reward, i.e. the understanding of an important piece of modern physics, along the shortest path. The unavoidable mathematical concepts and tools are presented in as straightforward manner as possible. Even though the mathematics is not very difficult, it certainly is beneficial to know some statistical thermodynamics as well as some quantum mechanics. Thus the text is suitable for the upper undergraduate curriculum.

This book presents a novel mathematical formalism, based on the tetrad formulation of differential geometry, for describing cosmological observables exactly and conveniently. It covers all the standard observables, i.e. distances, weak lensing, number counts and cosmic microwave background, and also includes a detailed derivation of general-relativistic matrix kinetic theory. All the fully nonlinear equations are derived in detail and the mathematical content is self-contained, so that readers require only a basic knowledge of general relativity. Moreover, the authors discuss several subtle issues that are usually overlooked in the literature and, in particular, issues that distinguish this formalism from the more approximative standard practice.

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.

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.

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.

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 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.

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 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.

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.