This introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. The exposition is driven by examples, and collects and extends many results scattered throughout the literature, in particular the Langlands constant term formula for Eisenstein series on G(A) as well as the Casselman-Shalika formula for the p-adic spherical Whittaker function. This book also covers more advanced topics such as spherical Hecke algebras and automorphic L-functions. Many of these mathematical results have natural interpretations in string theory, and so some basic concepts of string theory are introduced with an emphasis on connections with automorphic forms. Throughout the book special attention is paid to small automorphic representations, which are of particular importance in string theory but are also of independent mathematical interest. Numerous open questions and conjectures, partially motivated by physics, are included to prompt the reader's own research.

What happens when the country's greatest logician meets the century's greatest physicist? In the case of Kurt Godel and Albert Einstein the result in Godel's revolutioinary new model of the cosmos. In the 'Godel Universe' the philosophical fantasy of time travel becomes a scientific reality. For Godel, however, the reality of time travel signals the unreality of time. If Godel is right, the real meaning of the Einstein revolution had remained, for half a century, a secret. Now, half-century after Godel met Einstein, the real meaning of time travel in the Godel universe can be revealed.

This volume compiles notes from four mini courses given at the summer school on asymptotic analysis in general relativity, held at the Institut Fourier in Grenoble, France. It contains an up-to-date panorama of modern techniques in the asymptotic analysis of classical and quantum fields in general relativity. Accessible to graduate students, these notes gather results that were not previously available in textbooks or monographs and will be of wider interest to researchers in general relativity. The topics of these mini courses are: the geometry of black hole spacetimes; an introduction to quantum field theory on curved spacetimes; conformal geometry and tractor calculus; and microlocal analysis for wave propagation.

A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravities, and therefore providing graduates and researchers with an invaluable resource on this important topic in gravitational physics. Including contributions by David Chow, Christopher N. Pope and Ergin Sezgin (chapters 16-19).

Classical field theory, which concerns the generation and interaction of fields, is a logical precursor to quantum field theory, and can be used to describe phenomena such as gravity and electromagnetism. Written for advanced undergraduates, and appropriate for graduate level classes, this book provides a comprehensive introduction to field theories, with a focus on their relativistic structural elements. Such structural notions enable a deeper understanding of Maxwell's equations, which lie at the heart of electromagnetism, and can also be applied to modern variants such as Chern-Simons and Born-Infeld. The structure of field theories and their physical predictions are illustrated with compelling examples, making this book perfect as a text in a dedicated field theory course, for self-study, or as a reference for those interested in classical field theory, advanced electromagnetism, or general relativity. Demonstrating a modern approach to model building, this text is also ideal for students of theoretical physics.

This is the definitive popular exploration of what the fourth dimension means, both physically and spiritually. Mathematician and science-fiction novelist Rudy Rucker takes readers on a guided tour of a higher reality that explores what the fourth dimension is and what it's meant to generations of thinkers. The exciting and challenging journey is enhanced by more than 200 illustrations and a host of puzzles and problems (with answers).
"This is an invigorating book, a short but spirited slalom for the mind." -- Timothy Ferris, "The New York Times Book Review"
"Highly readable. One is reminded of the breadth and depth of Hofstadter's" G""o""del, Escher, Bach."" --" Science
""Anyone with even a minimal interest in mathematics and fantasy will find "The Fourth Dimension" informative and mind-dazzling... Rucker] plunges into spaces above three with a zest and energy that is breathtaking." -- Martin Gardner
"Those who think the fourth dimension is nothing but time should be encouraged to read"The Fourth Dimension, " along with anyone else who feels like opening the hinges of his mind and letting in a bit of fresh air." -- John Sladek, "Washington Post Book World
""A mine of mathematical insights and a thoroughly satisfying read." -- Paul Davies, "Nature Magazine"

Here is a self-contained exposition of the theory of gravitational solitons and provides a comprehensive review of exact soliton solutions to Einstein's equations. The text begins with a detailed discussion of the extension of the Inverse Scattering Method to the theory of gravitation, starting with pure gravity and then extending it to the coupling of gravity with the electromagnetic field. There follows a systematic review of the gravitational soliton solutions based on their symmetries. These solutions include some of the most interesting in gravitational physics such as those describing inhomogeneous cosmological models, cylindrical waves, the collision of exact gravity waves, and the Schwarzschild and Kerr black holes.

Relativity has much to offer for a well-rounded education. Yet books on relativity either assume a strong background in physics and math, aimed at advanced physics students, or, alternatively, offer a broad description with little intellectual challenge. This book bridges the gap. It aims at readers with essentially no physics or math background, who still find it rewarding to think rigorously. The book takes a "thinking tools" approach, by first making readers comfortable with a new thinking tool and then applying it to learn more about how nature works. By the end of the book, readers will have collected a versatile toolbox and will be comfortable using the tools to think about and really understand the intriguing phenomena they may have only heard about, including the twin paradox, black holes, and time travel. End-of-chapter exercises span a range of difficulty, allowing adventurous readers to stretch their understanding further as desired. Students who have studied, or are studying, relativity at a more mathematical level will also find the book useful for a more conceptual understanding.

This book presents a high-level study of cosmology with interacting dark energy and no additional fields. It is known that dark energy is not necessarily uniform when other sources of gravity are present: interaction with matter leads to its variation in space and time. The present text studies the cosmological implications of this circumstance by analyzing cosmological models in which the dark energy density interacts with matter and thus changes with the time. The book also includes a translation of a seminal article about the remarkable life and work of E.B. Gliner, the first person to suggest the concept of dark energy in 1965.

Following the approach of Lev Landau and Evgenii Lifshitz, this book introduces the theory of special and general relativity with the Lagrangian formalism and the principle of least action. This method allows the complete theory to be constructed starting from a small number of assumptions, and is the most natural approach in modern theoretical physics. The book begins by reviewing Newtonian mechanics and Newtonian gravity with the Lagrangian formalism and the principle of least action, and then moves to special and general relativity. Most calculations are presented step by step, as is done on the board in class. The book covers recent advances in gravitational wave astronomy and provides a general overview of current lines of research in gravity. It also includes numerous examples and problems in each chapter.

This book is devoted to a pedagogical introduction to supergravity from a practical perspective. As a particular feature of the book, the authors provide explicit details, which makes the computations easier to follow for the interested reader. Each chapter has summary tables, which contain the main results and, in addition, we have collected important or additional material in the appendix.In the first part of the book, the N=1 supergravity Lagrangian in four spacetime dimensions is derived. Closely following the reference of Wess and Bagger, we use the superspace approach. All steps, from the geometric principles of curved superspace to the field redefinition necessary to obtain a correctly normalised Lagrangian, are carefully analysed. Comparisons with other methods, such as conformal supergravity, are also given.In the second part of the book, we address more phenomenological aspects of supergravity such as supersymmetry breaking, no-scale supergravity, super-Higgs mechanism, etc. Finally, the relationship between supergravity and particle physics, and cosmology are analysed.

The idea of infinity plays a crucial role in our understanding of the universe, with the infinite spacetime continuum perhaps the best-known example - but is spacetime really continuous? Throughout the history of science, many have felt that the continuum model is an unphysical idealization, and that spacetime should be thought of as 'quantized' at the smallest of scales. Combining novel conceptual analysis, a fresh historical perspective, and concrete physical examples, this unique book tells the story of the search for the fundamental unit of length in modern physics, from early classical electrodynamics to current approaches to quantum gravity. Novel philosophical theses, with direct implications for theoretical physics research, are presented and defended in an accessible format that avoids complex mathematics. Blending history, philosophy, and theoretical physics, this refreshing outlook on the nature of spacetime sheds light on one of the most thought-provoking topics in modern physics.

This work is a detailed study of both the theoretical and phenomenological consequences of a massive graviton, within the ghost-free theory of massive gravity, the de Rham-Gabadadze-Tolley (dRGT) theory. Its aim is to test the physical viability of the theory. It begins by putting constraints on the parameters of the theory in the decoupling limit based on purely theoretical grounds, like classical stability in the cosmological evolution of self-accelerating and degravitating solutions. The author then constructs a proxy theory to massive gravity from the decoupling limit resulting in non-minimally coupled scalar-tensor interactions as an example of a subclass of Horndeski theories. Lastly, she addresses the natural question of whether the parameters introduced in the dRGT theory are subject to strong renormalization by quantum loops and shows how the non-renormalization theorem protects the graviton mass from quantum corrections. Beyond the decoupling limit the quantum corrections are found to be proportional to the graviton mass, proving its technical naturalness.

Tjonnie Li's thesis covers two applications of Gravitational Wave astronomy: tests of General Relativity in the strong-field regime and cosmological measurements. The first part of the thesis focuses on the so-called TIGER, i.e. Test Infrastructure for General Relativity, an innovative Bayesian framework for performing hypothesis tests of modified gravity using ground-based GW data. After developing the framework, Li simulates a variety of General Relativity deviations and demonstrates the ability of the aforementioned TIGER to measure them. The advantages of the method are nicely shown and compared to other, less generic methods. Given the extraordinary implications that would result from any measured deviation from General Relativity, it is extremely important that a rigorous statistical approach for supporting these results would be in place before the first Gravitational Wave detections begin. In developing TIGER, Tjonnie Li shows a large amount of creativity and originality, and his contribution is an important step in the direction of a possible discovery of a deviation (if any) from General Relativity. In another section, Li's thesis deals with cosmology, describing an exploratory study where the possibility of cosmological parameters measurement through gravitational wave compact binary coalescence signals associated with electromagnetic counterparts is evaluated. In particular, the study explores the capabilities of the future Einstein Telescope observatory. Although of very long term-only applicability, this is again a thorough investigation, nicely put in the context of the current and the future observational cosmology.

Originally published in 1921, this book presents a concise study of time and space relations by the renowned British physicist Alfred Robb (1873-1936). The text is one of a series of works on the topic of special relativity written by Robb from 1911 onwards. An appendix section is included. This book will be of value to anyone with an interest in special relativity, the development of physics and the history of science.

In early April 1911 Albert Einstein arrived in Prague to become full professor of theoretical physics at the German part of Charles University. It was there, for the first time, that he concentrated primarily on the problem of gravitation. Before he left Prague in July 1912 he had submitted the paper "Relativitat und Gravitation: Erwiderung auf eine Bemerkung von M. Abraham" in which he remarkably anticipated what a future theory of gravity should look like. At the occasion of the Einstein-in-Prague centenary an international meeting was organized under a title inspired by Einstein's last paper from the Prague period: "Relativity and Gravitation, 100 Years after Einstein in Prague". The main topics of the conference included: classical relativity, numerical relativity, relativistic astrophysics and cosmology, quantum gravity, experimental aspects of gravitation and conceptual and historical issues. The conference attracted over 200 scientists from 31 countries, among them a number of leading experts in the field of general relativity and its applications. This volume includes abstracts of the plenary talks and full texts of contributed talks and articles based on the posters presented at the conference. These describe primarily original results of the authors. Full texts of the plenary talks are included in the volume "General Relativity, Cosmology and Astrophysics--Perspectives 100 Years after Einstein in Prague", eds. J. Bicak and T. Ledvinka, published also by Springer Verlag.

Over the course of the last century it has become clear that both elementary particle physics and relativity theories are based on the notion of symmetries. These symmetries become manifest in that the "laws of nature" are invariant under spacetime transformations and/or gauge transformations. The consequences of these symmetries were analyzed as early as in 1918 by Emmy Noether on the level of action functionals. Her work did not receive due recognition for nearly half a century, but can today be understood as a recurring theme in classical mechanics, electrodynamics and special relativity, Yang-Mills type quantum field theories, and in general relativity. As a matter of fact, as shown in this monograph, many aspects of physics can be derived solely from symmetry considerations. This substantiates the statement of E.P. Wigner "... if we knew all the laws of nature, or the ultimate Law of nature, the invariance properties of these laws would not furnish us new information." Thanks to Wigner we now also understand the implications of quantum physics and symmetry considerations: Poincare invariance dictates both the characteristic properties of particles (mass, spin, ...) and the wave equations of spin 0, 1/2, 1, ... objects. Further, the work of C.N. Yang and R. Mills reveals the consequences of internal symmetries as exemplified in the symmetry group of elementary particle physics. Given this pivotal role of symmetries it is thus not surprising that current research in fundamental physics is to a great degree motivated and inspired by considerations of symmetry. The treatment of symmetries in this monograph ranges from classical physics to now well-established theories of fundamental interactions, to the latest research on unified theories and quantum gravity.

The effective theory of quantum gravity coupled to models of particle physics is being probed by cutting edge experiments in both high energy physics (searches for extra dimensions) and cosmology (testing models of inflation). This thesis derives new bounds that may be placed on these models both theoretically and experimentally. In models of extra dimensions, the internal consistency of the theories at high energies are investigated via perturbative unitarity bounds. Similarly it is shown that recent models of Higgs inflation suffer from a breakdown of perturbative unitarity during the inflationary period. In addition, the thesis uses the latest LHC data to derive the first ever experimental bound on the size of the Higgs boson's non-minimal coupling to gravity.

The search for gravitational radiation with optical interferometers is gaining momentum worldwide. Beside the VIRGO and GEO gravitational wave observatories in Europe and the two LIGOs in the United States, which have operated successfully during the past decade, further observatories are being completed (KAGRA in Japan) or planned (ILIGO in India). The sensitivity of the current observatories, although spectacular, has not allowed direct discovery of gravitational waves. The advanced detectors (Advanced LIGO and Advanced Virgo) at present in the development phase will improve sensitivity by a factor of 10, probing the universe up to 200 Mpc for signal from inspiraling binary compact stars. This book covers all experimental aspects of the search for gravitational radiation with optical interferometers. Every facet of the technological development underlying the evolution of advanced interferometers is thoroughly described, from configuration to optics and coatings and from thermal compensation to suspensions and controls. All key ingredients of an advanced detector are covered, including the solutions implemented in first-generation detectors, their limitations, and how to overcome them. Each issue is addressed with special reference to the solution adopted for Advanced VIRGO but constant attention is also paid to other strategies, in particular those chosen for Advanced LIGO.

This thesis explores the idea that the Higgs boson of the Standard Model and the cosmological inflation are just two manifestations of one and the same scalar field - the Higgs-inflation. By this unification two energy scales that are separated by many orders of magnitude are connected, thereby building a bridge between particle physics and cosmology. An essential ingredient for making this model consistent with observational data is a strong non-minimal coupling to gravity. Predictions for the value of the Higgs mass as well as for cosmological parameters are derived, and can be tested by future experiments. The results become especially exciting in the light of the recently announced discovery of the Higgs boson. The model of non-minimal Higgs inflation is also used in a quantum cosmological context to predict initial conditions for inflation. These results can in turn be tested by the detection of primordial gravitational waves. The presentation includes all introductory material about cosmology and the Standard Model that is essential for the further understanding. It also provides an introduction to the mathematical methods used to calculate the effective action by heat kernel methods.

This thesis presents theoretical and numerical studies on phenomenological description of the quark–gluon plasma (QGP), a many-body system of elementary particles. The author formulates a causal theory of hydrodynamics for systems with net charges from the law of increasing entropy and a momentum expansion method. The derived equation results can be applied not only to collider physics, but also to the early universe and ultra-cold atoms. The author also develops novel off-equilibrium hydrodynamic models for the longitudinal expansion of the QGP on the basis of these equations. Numerical estimations show that convection and entropy production during the hydrodynamic evolution are key to explaining excessive charged particle production, recently observed at the Large Hadron Collider. Furthermore, the analyses at finite baryon density indicate that the energy available for QGP production is larger than the amount conventionally assumed.

Pulsar timing is a promising method for detecting gravitational waves in the nano-Hertz band. In his prize winning Ph.D. thesis Rutger van Haasteren deals with how one takes thousands of seemingly random timing residuals which are measured by pulsar observers, and extracts information about the presence and character of the gravitational waves in the nano-Hertz band that are washing over our Galaxy. The author presents a sophisticated mathematical algorithm that deals with this issue. His algorithm is probably the most well-developed of those that are currently in use in the Pulsar Timing Array community. In chapter 3, the gravitational-wave memory effect is described. This is one of the first descriptions of this interesting effect in relation with pulsar timing, which may become observable in future Pulsar Timing Array projects. The last part of the work is dedicated to an effort to combine the European pulsar timing data sets in order to search for gravitational waves. This study has placed the most stringent limit to date on the intensity of gravitational waves that are produced by pairs of supermassive black holes dancing around each other in distant galaxies, as well as those that may be produced by vibrating cosmic strings. Rutger van Haasteren has won the 2011 GWIC Thesis Prize of the Gravitational Wave International Community for his innovative work in various directions of the search for gravitational waves by pulsar timing. The work is presented in this Ph.D. thesis.

Proceedings from the 2012 Fourth International Meeting on Gravitation and Cosmology, focusing on accelerated cosmic expansion This volume provides both an update and a review of the state of alternative theories of gravity in connection with the accelerated expansion of the universe issue. Different theoretical proposals exist to explain the acceleration in the cosmic expansion, generating the dark energy issue and opening the possibility to theories of gravity alternative to general relativity. Related issues such as the dark matter problem are also surveyed in order to give the readers profound insight on the subject from different points of view. Comprised of short talks and plenary lectures given by leading experts in the field, some of them with brilliant and historic contributions, the book allows the reader to find readable and referenced surveys in topics like f(R) theories, the dark matter and dark energy issues, Modified Newtonian Dynamics (MOND) scenarios, f(T) theories, scalar-tensor theories derived from non-Riemannian geometries, emergent universes, the cosmological constant and other topics of current interest for younger and senior physicists and graduate students. These proceedings are from the Fourth International Meeting on Gravitation and Cosmology, held in Guadalajara, Jalisco, México, from 20 - 25 May, 2012, was sponsored by ICTP- Trieste, Italy and COECyTJAL-Universidad de Guadalajara, México. This event is a series of scientific meetings started in 2004 in Cuba, focusing on current and selected topics in the fields of gravitation and cosmology.

This book contains contributions from the Spanish Relativity Meeting, ERE 2012, held in Guimaraes, Portugal, September 2012. It features more than 70 papers on a range of topics in general relativity and gravitation, from mathematical cosmology, numerical relativity and black holes to string theory and quantum gravity. Under the title "Progress in Mathematical Relativity, Gravitation and Cosmology," ERE 2012 was attended by an exceptional international list of over a hundred participants from the five continents and over forty countries. ERE is organized every year by one of the Spanish or Portuguese groups working in this area and is supported by the Spanish Society of Gravitation and Relativity (SEGRE). This book will be of interest to researchers in mathematics and physics.