This compact yet informative Guide presents an accessible route through Special Relativity, taking a modern axiomatic and geometrical approach. It begins by explaining key concepts and introducing Einstein's postulates. The consequences of the postulates - length contraction and time dilation - are unravelled qualitatively and then quantitatively. These strands are then tied together using the mathematical framework of the Lorentz transformation, before applying these ideas to kinematics and dynamics. This volume demonstrates the essential simplicity of the core ideas of Special Relativity, while acknowledging the challenges of developing new intuitions and dealing with the apparent paradoxes that arise. A valuable supplementary resource for intermediate undergraduates, as well as independent learners with some technical background, the Guide includes numerous exercises with hints and notes provided online. It lays the foundations for further study in General Relativity, which is introduced briefly in an appendix.

Black Holes are regions of space-time where the gravitational field is so strong that not even light can escape. There has been much written on black holes, however in most cases they are treated as isolated objects. The author has found a number of cases in which the interaction of a black hole with another strong-field system (such as the background universe or another black hole) could be treated analytically. This includes using the powerful method of matched asymptotic expansions. In this book the author considers these wider ranging problems and examples for the first time. This book will be widely read by all those working in gravitation, and PhD students in mathematical physics.

This book opens with an axiomatic description of Euclidean and non-Euclidean geometries. Euclidean geometry is the starting point to understand all other geometries and it is the cornerstone for our basic intuition of vector spaces. The generalization to non-Euclidean geometry is the following step to develop the language of Special and General Relativity. These theories are discussed starting from a full geometric point of view. Differential geometry is presented in the simplest way and it is applied to describe the physical world. The final result of this construction is deriving the Einstein field equations for gravitation and spacetime dynamics. Possible solutions, and their physical implications are also discussed: the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, the cosmological solutions like de Sitter, Friedmann-Lemaitre-Robertson-Walker, and Goedel ones. Some current problems like dark energy are also scketched. The book is self-contained and includes details of all proofs. It provides solutions or tips to solve problems and exercises. It is designed for undergraduate students and for all readers who want a first geometric approach to Special and General Relativity.

Based on lectures given at a summer school on computer algebra, the book provides a didactic description of the facilities available in three computor algebra systems - MAPLE, REDUCE and SHEEP - for performing calculations in the algebra-intensive field of general relativity. With MAPLE and REDUCE, two widespread great-purpose systems, the reader is shown how to use currently available packages to perform calculations with respect to tetrads, co-ordinate systems, and Poincare` gauge theory. The section on SHEEP and Stensor, being the first published book on these systems, explains how to use these systems to tackle a wide range of calculations with respect to tackle a wide range of calculations in general relativity, including the manipulation of indicial formulae. For the researcher in general relativity, the book therefore promises a wide overview of the facilities available in computer algebra to lessen the burden of the lengthy, error-prone calculations involved in their research.

Jayme Tiomno (1920-2011) was one of the most influential Brazilian physicists of the 20th century, interacting with many of the renowned physicists of his time, including John Wheeler and Richard Feynman, Eugene Wigner, Chen Ning Yang, David Bohm, Murray Gell-Mann, Remo Ruffini, Abdus Salam, and many others. This biography tells the sometimes romantic, often discouraging but finally optimistic story of a dedicated scientist and educator from a developing country who made important contributions to particle physics, gravitation, cosmology and field theory, and to the advancement of science and of scientific education, in many institutions in Brazil and elsewhere. Drawing on unpublished documents from archives in Brazil and the US as well as private sources, the book traces Tiomno's long life, following his role in the establishment of various research facilities and his tribulations during the Brazilian military dictatorship. It presents a story of progress and setbacks in advancing science in Brazil and beyond, and of the persistence and dedication of a talented physicist who spent his life in search of scientific truth.

In the late 20th and beginning 21st century high-precision astronomy, positioning and metrology strongly rely on general relativity. Supported by exercises and solutions this book offers graduate students and researchers entering those fields a self-contained and exhaustive but accessible treatment of applied general relativity. The book is written in a homogenous (graduate level textbook) style allowing the reader to understand the arguments step by step. It first introduces the mathematical and theoretical foundations of gravity theory and then concentrates on its general relativistic applications: clock rates, clock sychronization, establishment of time scales, astronomical references frames, relativistic astrometry, celestial mechanics and metrology. The authors present up-to-date relativistic models for applied techniques such as Satellite LASER Ranging (SLR), Lunar LASER Ranging (LLR), Globale Navigation Satellite Systems (GNSS), Very Large Baseline Interferometry (VLBI), radar measurements, gyroscopes and pulsar timing. A list of acronyms helps the reader keep an overview and a mathematical appendix provides required functions and terms.

Einstein's theories of special relativity and general relativity form a core part of today's undergraduate (or Masters-level) physics curriculum. This is a supplementary problem book or student's manual, consisting of 150 problems in each of special and general relativity. The problems, which have been developed, tested and refined by the authors over the past two decades, are a mixture of short-form and multi-part extended problems, with hints provided where appropriate. Complete solutions are elaborated for every problem, in a different section of the book; some solutions include brief discussions on their physical or historical significance. Designed as a companion text to complement a main relativity textbook, it does not assume access to any specific textbook. This is a helpful resource for advanced students, for self-study, a source of problems for university teaching assistants, or as inspiration for instructors and examiners constructing problems for their lectures, homework or exams.

Einstein's theories of special relativity and general relativity form a core part of today's undergraduate (or Masters-level) physics curriculum. This is a supplementary problem book or student's manual, consisting of 150 problems in each of special and general relativity. The problems, which have been developed, tested and refined by the authors over the past two decades, are a mixture of short-form and multi-part extended problems, with hints provided where appropriate. Complete solutions are elaborated for every problem, in a different section of the book; some solutions include brief discussions on their physical or historical significance. Designed as a companion text to complement a main relativity textbook, it does not assume access to any specific textbook. This is a helpful resource for advanced students, for self-study, a source of problems for university teaching assistants, or as inspiration for instructors and examiners constructing problems for their lectures, homework or exams.

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.

General relativity, which lies at the heart of contemporary physics, has recently become the focus of a number of lively theoretical, experimental, and computational research programs. As a result, undergraduates have become increasingly excited to learn about the subject. A General Relativity Workbook is a textbook intended to support a one-semester upper division undergraduate course on general relativity. Through its unique workbook-based design, it enables students to develop a solid mastery of both the physics and the supporting tensor calculus by pushing (and guiding) them to work through the implications. Each chapter, which is designed to correspond to one class session, involves a short overview of the concepts without obscuring derivations or details, followed by a series of boxes that guide students through the process of working things out for themselves. This active-learning approach enables students to develop a more secure mastery of the material than more traditional approaches. More than 350 homework problems support further learning. This book more strongly emphasizes the physics than many of its competitors, and while it provides students a full grounding in the supporting mathematics (unlike certain other competitors), it introduces the mathematics gradually and in a completely physical context. Ancillaries To facilitate self-study, a complimentary Online Student Manual with Hints and Answers for Selected Problems is available online. A detailed Instructor's Manual is available to adopting professors.

In this book, all physical laws are derived from a small number of invariant integrals which express the conservation of energy, mass, or momentum. This new approach allows us to unify the laws of theoretical physics, to simplify their derivation, and to discover some novel or more universal laws. Newton's Law of gravity is generalized to take into account cosmic forces of repulsion, Archimedes' principle of buoyancy is modified for account of the surface tension, and Coulomb's Laws for rolling friction and for the interaction of electric charges are substantially repaired and generalized. For postgraduate students, lecturers and researchers.

The wealth of recent cosmic microwave background and large-scale structure data has transformed the field of cosmology. These observations have not only become precise enough to answer questions about the universe on the largest scales, but also to address puzzles in the microscopic description of Nature. This thesis investigates new ways of probing the early universe, the properties of neutrinos and the possible existence of other light particles. In particular, based on detailed theoretical insights and novel analyses, new evidence for the cosmic neutrino background is found in the distribution of galaxies and in cosmic microwave background data. This tests the Standard Model of particle physics and the universe back to a time when it was about one second old. Furthermore, it is demonstrated that future observations will be capable of probing physics beyond the Standard Model since they can achieve a particular target which would either allow the detection of any light particles that have ever been in thermal equilibrium or imply strong bounds on their properties.

The natural generalization of the quantum-mechanical N-particle wave function to relativistic space-time is a function of N space-time points, and thus of N time variables. This book, based on a collection of lectures given at a spring school in Tubingen in 2019, provides an accessible and concise introduction to the recent development of the theory of multi-time wave functions, their use in quantum field theory, their relation to detection probabilities, and the mathematical question of consistency of their time evolution equations. The book is intended for advanced students and researchers with an interest in relativity and quantum physics.

This book presents the first English translation of the original French treatise "La Physique d'Einstein" written by the young Georges Lemai tre in 1922, only six years after the publication of Albert Einstein's theory of General Relativity. It includes an historical introduction and a critical edition of the original treatise in French supplemented by the author's own later additions and corrections. Monsignor Georges Lemai tre can be considered the founder of the "Big Bang Theory" and a visionary architect of modern Cosmology. The scientific community is only beginning to grasp the full extent of the legacy of this towering figure of 20th century physics. Against the best advice of the greatest names of his time, the young Lemai tre was convinced, solely through the study of Einstein's theory of General Relativity, that space and time must have had a beginning with a tremendous "Big Bang" from a "quantum primeval atom" resulting in an ever-expanding Universe with a positive cosmological constant. But how did the young Lemai tre, essentially on his own, come to grips with the physics of Einstein? A year before his ordination as a diocesan priest, he submitted the audacious treatise, published in this book, that was to earn him Fellowships to study at Cambridge, MIT and Harvard, and launched him on a scientific path of ground-breaking discoveries. Almost a century after Lemai tre's seminal publications of 1927 and 1931, this highly pedagogical treatise is still of timely interest to young minds and remains of great value from a history of science perspective.

This book is about the dark photon which is a new gauge boson whose existence has been conjectured. Due to its interaction with the ordinary, visible photon, such a particle can be experimentally detected via specific signatures. In this book, the authors review the physics of the dark photon from the theoretical and experimental point of view. They discuss the difference between the massive and the massless case, highlighting how the two phenomena arise from the same vector portal between the dark and the visible sector. A review of the cosmological and astrophysical observations is provided, together with the connection to dark matter physics. Then, a perspective on current and future experimental limits on the parameters of the massless and massive dark photon is given, as well as the related bounds on milli-charged fermions. The book is intended for graduate students and young researchers who are embarking on dark photon research, and offers them a clear and up-to-date introduction to the subject.

This unique textbook offers a mathematically rigorous presentation of the theory of relativity, emphasizing the need for a critical analysis of the foundations of general relativity in order to best study the theory and its implications. The transitions from classical mechanics to special relativity and then to general relativity are explored in detail as well, helping readers to gain a more profound and nuanced understanding of the theory as a whole. After reviewing the fundamentals of differential geometry and classical mechanics, the text introduces special relativity, first using the physical approach proposed by Einstein and then via Minkowski's mathematical model. The authors then address the relativistic thermodynamics of continua and electromagnetic fields in matter - topics which are normally covered only very briefly in other treatments - in the next two chapters. The text then turns to a discussion of general relativity by means of the authors' unique critical approach, underlining the difficulty of recognizing the physical meaning of some statements, such as the physical meaning of coordinates and the derivation of physical quantities from those of space-time. Chapters in this section cover the model of space-time proposed by Schwarzschild; black holes; the Friedman equations and the different cosmological models they describe; and the Fermi-Walker derivative. Well-suited for graduate students in physics and mathematics who have a strong foundation in real analysis, classical mechanics, and general physics, this textbook is appropriate for a variety of graduate-level courses that cover topics in relativity. Additionally, it will interest physicists and other researchers who wish to further study the subtleties of these theories and understand the contemporary scholarly discussions surrounding them.

This textbook offers a readily comprehensible introduction to classical Newtonian gravitation, which is fundamental for an understanding of classical mechanics and is particularly relevant to Astrophysics. The opening chapter recalls essential elements of vectorial calculus, especially to provide the formalism used in subsequent chapters. In chapter two Classical Newtonian gravity theory for one point mass and for a generic number N of point masses is then presented and discussed. The theory for point masses is naturally extended to the continuous case. The third chapter addresses the paradigmatic case of spherical symmetry in the mass density distribution (central force), with introduction of the useful tool of qualitative treatment of motion. Subsequent chapters discuss the general case of non-symmetric mass density distribution and develop classical potential theory, with elements of harmonic theory, which is essential to understand the potential development in series of the gravitational potential, the subject of the fourth chapter. Finally, in the last chapter the specific case of motion of a satellite around the earth is considered. Examples and exercises are presented throughout the book to clarify aspects of the theory. The book is aimed at those who wish to progress further beyond an initial bachelor degree, onward to a master degree, and a PhD. It is also a valuable resource for postgraduates and active researchers in the field.

Astrophysical observations implying the existence of Dark Matter and Dark Energy, which are not described by the Standard Model (SM) of particle physics, have led to extensions of the SM predicting new particles that could be directly produced at the Large Hadron Collider (LHC) at CERN. Based on 2015 and 2016 ATLAS proton-proton collision data, this thesis presents searches for the supersymmetric partner of the top quark, for Dark Matter, and for DarkEnergy, in signatures with jets and missing transverse energy. Muon detection is key to some of the most important LHC physics results, including the discovery of the Higgs boson and the measurement of its properties. The efficiency with which muons can be detected with the ATLAS detector is measured using Z boson decays. The performance of high-precision Monitored Drift Tube muon chambers under background rates similar to the ones expected for the High Luminosity-LHC is studied.

This book provides a pedagogical introduction to the rapidly growing field of reheating after inflation. It begins with a brief review of the inflationary paradigm and a motivation for why the reheating of the universe is an integral part of inflationary cosmology. It then goes on to survey different aspects of reheating in a chronological manner, starting from the young, empty and cold universe at the end of inflation, and going all the way to the hot and thermal universe at the beginning of the Big Bang nucleosynthesis epoch. Different particle production mechanisms are considered with a focus on the non-perturbative excitation of scalar fields at the beginning of reheating (fermionic and vector fields are also discussed). This is followed by a review of the subsequent non-linear dynamical processes, such as soliton formation and relativistic turbulence. Various thermalization processes are also discussed. High energy physics embeddings of phenomenological models as well as observational implications of reheating such as gravitational waves generation and imprints on the cosmic microwave background are also covered.

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.

Devised at the beginning of the 20th century by french physicists Charles Fabry and Alfred Perot, the Fabry-Perot optical cavity is perhaps the most deceptively simple setup in optics, and today a key resource in many areas of science and technology. This thesis delves deeply into the applications of optical cavities in a variety of contexts: from LIGO's 4-km-long interferometer arms that are allowing us to observe the universe in a new way by measuring gravitational waves, to the atomic clocks used to realise time with unprecedented accuracy which will soon lead to a redefinition of the second, and the matterwave interferometers that are enabling us to test and measure gravity in a new scale. The work presented accounts for the elegance and versatility of this setup, which today underpins much of the progress in the frontier of atomic and gravitational experimental physics.

Despite the success of general relativity in explaining classical gravitational phenomena, several problems at the interface between gravitation and high energy physics still remain open. The purpose of this thesis is to explore quantum gravity and its phenomenological consequences for dark matter, gravitational waves and inflation. A new formalism to classify gravitational theories based on their degrees of freedom is introduced and, in light of this classification, it is argued that dark matter is no different from modified gravity. Gravitational waves are shown to be damped due to quantum degrees of freedom. The consequences for gravitational wave events are also discussed. The non-minimal coupling of the Higgs boson to gravity is studied in connection with Starobinsky inflation and its implications for the vacuum instability problem is analyzed.

This book reports on the extraordinary observation of TeV gamma rays from the Crab Pulsar, the most energetic light ever detected from this type of object. It presents detailed information on the painstaking analysis of the unprecedentedly large dataset from the MAGIC telescopes, and comprehensively discusses the implications of pulsed TeV gamma rays for state-of-the-art pulsar emission models. Using these results, the book subsequently explores new testing methodologies for Lorentz Invariance Violation, in terms of a wavelength-dependent speed of light. The book also covers an updated search for Very-High-Energy (VHE), >100 GeV, emissions from millisecond pulsars using the Large Area Telescope on board the Fermi satellite, as well as a study on the promising Pulsar Wind Nebula candidate PSR J0631. The observation of VHE gamma rays is essential to studying the non-thermal sources of radiation in our Universe. Rotating neutron stars, also known as pulsars, are an extreme source class known to emit VHE gamma rays. However, to date only two pulsars have been detected with emissions above 100 GeV, and our understanding of their emission mechanism is still lacking.

The advent of high-precision antihydrogen spectroscopy has opened up the possibility of direct tests with unprecedented accuracy of some of the most fundamental principles of physics, notably Lorentz and CPT symmetry and the Einstein equivalence principle. This book reviews these principles, emphasising their interconnections in quantum field theory and general relativity and the special role of antimatter, and explores how they may be tested in current and forthcoming experiments on antihydrogen. Original research results relevant to the experimental programme of the ALPHA collaboration at CERN are presented, together with the implications for antihydrogen of proposed theories featuring novel `fifth-force' interactions.

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.