This book provides an accessible, yet thorough, introduction to special and general relativity, crafted and class-tested over many years of teaching. Suitable for advanced undergraduate and graduate students, this book provides clear descriptions of how to approach the mathematics and physics involved. It is also contains the latest exciting developments in the field, including dark energy, gravitational waves, and frame dragging. The table of contents has been carefully developed in consultation with a large number of instructors teaching courses worldwide, to ensure its wide applicability to modules on relativity and gravitation. Features: A clear, accessible writing style, presenting a sophisticated approach to the subject, that remains suitable for advanced undergraduate students and above Class-tested over many years To be accompanied by a partner volume on 'Advanced Topics' for students to further extend their learning

In this short book, renowned theoretical physicist and author Carlo Rovelli gives a straightforward introduction to Einstein's General Relativity, our current theory of gravitation. Focusing on conceptual clarity, he derives all the basic results in the simplest way, taking care to explain the physical, philosophical and mathematical ideas at the heart of "the most beautiful of all scientific theories". Some of the main applications of General Relativity are also explored, for example, black holes, gravitational waves and cosmology, and the book concludes with a brief introduction to quantum gravity. Written by an author well known for the clarity of his presentation of scientific ideas, this concise book will appeal to university students looking to improve their understanding of the principal concepts, as well as science-literate readers who are curious about the real theory of General Relativity, at a level beyond a popular science treatment.

This thesis presents several significant new results that shed light on two major puzzles of modern cosmology: the nature of inflation, the very early phase of the universe that is thought to have given rise to the large-scale structures that we observe today; and that of the current accelerated expansion. In particular, it develops a clean method for characterizing linear cosmological perturbations for general theories where gravity is modified and/or affected by a new component, called dark energy, responsible for the accelerated expansion. It proposes a new extension to what were long thought to be the most general scalar field theories devoid of instabilities, and demonstrates the robustness of the relation between the energy scale of inflation and the predicted amplitude of gravitational waves. Finally, it consolidates a set of consistency relations between correlation functions of the cosmological density field and investigates the phenomenological consequences of their potential violation. Presented in a clear, succinct and rigorous style, each of these original results is both profound and important and will leave a deep mark on the field.

Ross P. Cameron argues that the flow of time is a genuine feature of reality. He suggests that the best version of the A-Theory is a version of the Moving Spotlight view, according to which past and future beings are real, but there is nonetheless an objectively privileged present. Cameron argues that the Moving Spotlight theory should be viewed as having more in common with Presentism (the view that reality is limited to the present) than with the B-Theory (the view that time is just another dimension like space through which things are spread out). The Moving Spotlight view, on this picture, agrees with Presentism that everything is the way it is now, it simply thinks that non-present beings are amongst the things that are now some way. Cameron argues that the Moving Spotlight theory provides the best account of truthmakers for claims about what was or will be the case, and he defends the view against a number of objections, including McTaggart's argument that the A-Theory is inconsistent, and the charge that if the A-Theory is true but presentism false then we could not know that we are present. The Moving Spotlight defends an account of the open future-that what will happen is, as yet, undetermined-Land argues that this is a better account than that available to the Growing Block theory.

All physicists would agree that one of the most fundamental problems of the 21st century physics is the dimensionality of the world. In the four-dimensional world of Minkowski (or Minkowski spacetime) the most challenging problem is the nature of the temporal dimension. In Minkowski spacetime it is merely one of the four dimensions, which means that it is entirely given like the other three spacial dimensions. If the temporal dimension were not given in its entirety and only one constantly changing moment of it existed, Minkowski spacetime would be reduced to the ordinary three-dimensional space. But if the physical world, represented by Minkowski spacetime, is indeed four-dimensional with time being the fourth dimension, then such a world is drastically different from its image based on our perceptions.

Bad Hofgastein who made the very successful Salzburger Abend with indi- nous music from Salzburg possible. Special thanks also to the former director of the Institute of Astronomy in Vienna, Prof. Paul Jackson for his generous private donation. We should not forget our hosts Mr. and Mrs. Winkler and their employees from the hotel who made the stay quite enjoyable. None of us will forget the very last evening, when the staff of kitchen under the le- ership of the cook himself came to offer us as farewell the famous Salzburger Nockerln, a traditional Austrian dessert. Everyone got a lot of scienti?c input during the lectures and the discussions and, to summarize, we all had a spl- did week in Salzburg in the Hotel Winkler. We all hope to come again in 2008 to discuss new results and new perspectives on a high level scienti?c standard in the Gasteinertal. Rudolf Dvorak and Sylvio Ferraz-Mello Celestial Mechanics and Dynamical Astronomy (2005) 92:1-18 (c) Springer 2005 DOI 10. 1007/s10569-005-3314-7 FROM ASTROMETRY TO CELESTIAL MECHANICS: ORBIT DETERMINATION WITH VERY SHORT ARCS (Heinrich K. Eichhorn Memorial Lecture) 1 2 ? ' ANDREA MILANI and ZORAN KNEZEVIC 1 Department of Mathematics, University of Pisa, via Buonarroti 2, 56127 Pisa, Italy, e-mail: milani@dm. unipi. it 2 Astronomical Observatory, Volgina 7, 11160 Belgrade 74, Serbia and Montenegro, e-mail: zoran@aob. bg. ac.

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.

This book provides an introduction to classical celestial mechanics. It is based on lectures delivered by the authors over many years at both Padua University (MC) and V.N. Karazin Kharkiv National University (EB). The book aims to provide a mathematical description of the gravitational interaction of celestial bodies. The approach to the problem is purely formal. It allows the authors to write equations of motion and solve them to the greatest degree possible, either exactly or by approximate techniques, when there is no other way. The results obtained provide predictions that can be compared with the observations. Five chapters are supplemented by appendices that review certain mathematical tools, deepen some questions (so as not to interrupt the logic of the mainframe with heavy technicalities), give some examples, and provide an overview of special functions useful here, as well as in many other fields of physics. The authors also present the original investigation of torus potential. This book is aimed at senior undergraduate students of physics or astrophysics, as well as graduate students undertaking a master's degree or Ph.D.

A IUTAM symposium on 'Waves in Liquid/Gas and Liquid/Vapor Two-Phase Systems' was held in Kyoto, Japan, 9-13 May 1994. Sixty-three scientists partici pated coming from ten countries, and forty-two lectures were presented. The list of participants and the program are included in this volume. The symposium was held in response to the request of the participants in the IUTAM symposium 'Adiabatic Waves in Liquid-Vapor System' held at Gottingen in 1989. At that time, the need for another symposium in about five years had been indicated by all the participants. This symposium intends to develop the subject of wave properties in more general liquid-gas two-phase systems. Topics in this symposium may be classified as (1) waves in liquid-gas bubble systems including interfacial effects, (2) waves in gas( vapor )-droplets systems, (3) waves in films or stratified systems, (4) waves with liquid-vapor transition, (5) waves with vapor-liquid transition, (6) wave propagation near the critical point and (7) waves with low pressure effect. As for topic (1), experiments, numerical simulations and analytical approaches to waves in bubly liquids were discussed. The importance of interbubble interactions through the liquid-field is now well established at least in terms of potential theory. There was also a progress concerning the well-posedness of governing equations for void waves. For pressure waves there were some new phenomena, such as bubble cluster formation and the occurrence of three-dimensional structures, in addition to a progress from more qualitative studies to quantitative ones."

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.

This volume is a collection of scholarly articles on the Mach Principle, the impact that this theory has had since the end of the 19th century, and its role in helping Einstein formulate the doctrine of general relativity. 20th-century physics is concerned with the concepts of time,space, motion, inertia and gravity. The documentation on all of these makes this book a reference for those who are interested in the history of science and the theory of general relativity.

This thesis sheds valuable new light on the second-order cosmological perturbation theory, extensively discussing it in the context of cosmic microwave background (CMB) fluctuations. It explores the observational consequences of the second-order vector mode, and addresses magnetic field generation and the weak lensing signatures, which are key phenomena of the vector mode. The author demonstrates that the second-order vector mode, which never appears at the linear-order level, naturally arises from the non-linear coupling of the first-order scalar modes. This leads to the remarkable statement that the vector-order mode clearly contributes to the generation of cosmological magnetic fields. Moreover, the weak lensing observations are shown to be accessible to the vector mode. On the basis of ongoing and forthcoming observations, the thesis concludes that the second-order vector mode is detectable.

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.

Devoted to the history of general relativity, this text provides reviews from scholars all over the world. Many of the papers originated at the Third International Conference on the History of General Relativity, held at the University of Pittsburgh in the summer of 1991. Topics covered include: disputes with Einstein; the empirical basis of general relativity; variational principles in general relativity; the reception and development of general relativity; and cosmology and general relativity.

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 thesis reports the discovery of relativistic stellar explosions outside of the gamma ray band, using optical time domain surveys. It is well known that some massive stars end their lives with the formation of a compact object (a neutron star or black hole) that launches a relativistic jet detectable from earth as a burst of gamma rays. It has long been suspected, however, that gamma ray bursts are only the tip of the iceberg in a broad landscape of relativistic explosions, and so the results presented in this thesis represent a major breakthrough. Highlights of this thesis include: characterization of the first major new class of relativistic explosions in a decade; the discovery of abrupt end-of-life mass-loss in a surprisingly diverse range of stars; and the routine discovery of afterglow emission and several events that may represent baryonically dirty jets or jets viewed slightly off axis. These discoveries necessitated the solution of difficult technical challenges such as the identification of rare and fleeting "needles" in a vast haystack of time-varying phenomena in the night sky, and responding to discoveries within hours to obtain data across the electromagnetic spectrum from X-rays to radio wavelengths.

This book offers a concise and coherent introduction to accelerator physics and technology at the fundamental level but still in connection to advanced applications ranging from high-energy colliders to most advanced light sources, i.e., Compton sources, storage rings and free-electron lasers. The book is targeted at accelerator physics students at both undergraduate and graduate levels, but also of interest also to Ph.D. students and senior scientists not specialized in beam physics and accelerator design, or at the beginning of their career in particle accelerators. The book introduces readers to particle accelerators in a logical and sequential manner, with paragraphs devoted to highlight the physical meaning of the presented topics, providing a solid link to experimental results, with a simple but rigorous mathematical approach. In particular, the book will turn out to be self-consistent, including for example basics of Special Relativity and Statistical Mechanics for accelerators. Mathematical derivations of the most important expressions and theorems are given in a rigorous manner, but with simple and immediate demonstration where possible. The understanding gained by a systematic study of the book will offer students the possibility to further specialize their knowledge through the wide and up-to-date bibliography reported. Both theoretical and experimental items are presented with reference to the most recent achievements in colliders and light sources. The author draws on his almost 20-years long experience in the design, commissioning and operation of accelerator facilities as well as on his 10-years long teaching experience about particle accelerators at the University of Trieste, Department of Engineering and of Physics, as well as at international schools on accelerator physics.

This thesis covers several theoretical aspects of WIMP (weakly interacting massive particles) dark matter searches, with a particular emphasis on colliders. It mainly focuses on the use of effective field theories as a tool for Large Hadron Collider (LHC) searches, discussing in detail the issue of their validity, and on simplified dark matter models, which are receiving a growing attention from the physics community. It highlights the theoretical consistency of simplified models, which is essential in order to correctly exploit their potential and for them to be a common reference when comparing results from different experiments. This thesis is of interest to researchers (both theorists and experimentalists) in the field of dark matter searches, and offers a comprehensive introduction to dark matter and to WIMP searches for students and non-experts.

Divided into four parts, this book covers recent developments in topics pertaining to gravity theories, including discussions on the presence of scalar fields. Part One is devoted to exact solutions in general relativity, and is mainly concerned with the results of rotating null dust beams and fluids. Also included is a panoramic vision of new research directions in this area, which would require revising certain theorems and their possible extensions within gravity theories, new aspects concerning the Ernst potentials, double Kerr spacetimes, and rotating configurations. In particular, there is a detailed discussion of totally symmetric and totally geodesic spaces, in which a method for generating (2+1)-dimensional solutions from (3+1)-dimensional solutions is given. Part Two deals with alternative theories of gravity, all of which include scalar fields and gauge fields. Here, quantum and cosmological effects, which arise from both gravity theories in four and higher dimensions and from metric-affine theories, are investigated. Part Three is devoted to cosmological and inflationary scenarios. Local effects, such as the influence of scalar fields in protogalactic interactions, numerical studies of the collapse of molecular cores, as well as the inverse inflationary problem and the blue eigenvalue spectrum of it, are considered. Moreover, the role of scalar fields as dark matter and quantum cosmology in the Bergman-Wagoner and Gowdy theories, together with the relation of the conformal symmetry and deflationary gas universe, are likewise presented. The last part of the book includes some mixed topics which are still in the experimental stage. Among them are the foundation of the Maxwell theory, a discussion on electromagnetic Thirring problems, a note on the staticity of black holes with non-minimally coupled scalar fields, and a study of the Lorentz force free charged fluids in general relativity. Thus, this book is the most up-to-date, comprehensive collection of papers on the subject of exact solutions and scalar fields in gravity and is a valuable tool for researchers in the area.

Three eminent scientists, each well known for the clarity of their writing, present for students and researchers what is known about the internal structure, origin and evolution of White Dwarfs, Neutron Stars and Black Holes, all objects at the final stage of stellar evolution. They cover fascinating topics such as pulsation of white dwarfs, millisecond pulsars or the dynamics around black holes. The book is written for graduate students in astrophysics, but is also of interest to professional astronomers and physicists.

Owing to the increased accuracy requirements in fields such as astrometry and geodesy the general theory of relativity must be taken into account for any mission requiring highly accurate orbit information and for practically all observation and measurement techniques. This book highlights the confluence of Applied Mathematics, Physics and Space Science as seen from Einstein's general theory of relativity and aims to bridge the gap between theoretical and applied domains. The book investigates three distinct areas of general relativity: Exact solutions of the Einstein field equations of gravitation. Dynamics of near-Earth objects and solar system bodies. Relativistic orbitography. This book is an updated and expanded version of the author's PhD thesis which was awarded the International Astronomical Union PhD prize in Division A: Fundamental Astronomy. Included is a new introduction aimed at graduate students of General Relativity and extended discussions and results on topics in post-Newtonian dynamics and general relativistic spacecraft propagation.

This book discusses the notion that quantum gravity may represent the "breakdown" of spacetime at extremely high energy scales. If spacetime does not exist at the fundamental level, then it has to be considered "emergent", in other words an effective structure, valid at low energy scales. The author develops a conception of emergence appropriate to effective theories in physics, and shows how it applies (or could apply) in various approaches to quantum gravity, including condensed matter approaches, discrete approaches, and loop quantum gravity.

This open access monograph offers a detailed study and a systematic defense of a key intuition we typically have, as human beings, with respect to the nature of time: the intuition that the future is open, whereas the past is fixed. For example, whereas it seems unsettled whether there will be a fourth world war, it is settled that there was a first world war. The book contributes, in particular, three major and original insights. First, it provides a coherent, non-metaphorical, and metaphysically illuminating elucidation of the intuition. Second, it determines which model of the temporal structure of the world is most appropriate to accommodate the intuition, and settles on a specific version of the Growing Block Theory of time (GBT). Third, it puts forward a naturalistic foundation for GBT, by exploiting recent results of our best physics (viz. General Relativity, Quantum Mechanics, and Quantum Gravity). Three main challenges are addressed: the dismissal of temporal asymmetries as non-fundamental phenomena only (e.g., thermodynamic or causal phenomena), the epistemic objection against GBT, and the apparent tension between GBT and relativistic physics. It is argued that the asymmetry between the open future and the fixed past must be grounded in the temporal structure of the world, and that this is neither precluded by our epistemic device, nor by the latest approaches to Quantum Gravity ( e.g., the Causal Set Theory). Aiming at reconciling time as we find it in ordinary experience and time as physics describes it, this innovative book will raise the interest of both academic researchers and graduate students working on the philosophy of time. More generally, it presents contents of interest for all metaphysicians and non-dogmatic philosophers of physics. This is an open access book.