Gravitation

"The most trusted explainer of the most mind-boggling concepts pulls back the veil of mystery that has too long cloaked the most valuable building blocks of modern science. Sean Carroll, with his genius for making complex notions entertaining, presents in his uniquely lucid voice the fundamental ideas informing the modern physics of reality. Physics offers deep insights into the workings of the universe but those insights come in the form of equations that often look like gobbledygook. Sean Carroll shows that they are really like meaningful poems that can help us fly over sierras to discover a miraculous multidimensional landscape alive with radiant giants, warped space-time, and bewilderingly powerful forces. High school calculus is itself a centuries-old marvel as worthy of our gaze as the Mona Lisa. And it may come as a surprise the extent to which all our most cutting-edge ideas about black holes are built on the math calculus enables. No one else could so smoothly guide readers to grasping the very equation Einstein used to describe his theory of general relativity. In the tradition of the legendary Richard Feynman lectures presented sixty years ago, this book is an inspiring, dazzling introduction to a way of seeing that will resonate across cultural and generational boundaries for many years to come"--

This graduate textbook covers the basic formalism of supergravity, as well as its modern applications, suitable for a focused first course. Assuming a working knowledge of quantum field theory, Part I gives the basic formalism, including on- and off-shell supergravity, the covariant formulation, superspace and coset formulations, coupling to matter, higher dimensions and extended supersymmetry. A wide range of modern applications are introduced in Part II, including string theoretical (T- and U-duality, AdS/CFT, susy and sugra on the worldsheet, superembeddings), gravitational (p-brane solutions and their susy, attractor mechanism, Witten's positive energy theorem) and phenomenological (inflation in supergravity, supergravity no-go theorems, string theory constructions at low energies, minimal supergravity and its susy-breaking). The broader emphasis on applications than competing texts gives Ph.D. students the tools they need to do research that uses supergravity and benefits researchers already working in areas related to supergravity.

By the star physicist and author of multiple #1 Sunday Times bestsellers, a major and definitive narrative work on black holes and how they can help us understand the universe. At the heart of our galaxy lies a monster so deadly it can bend space, throwing vast jets of radiation millions of light years out into the cosmos. Its kind were the very first inhabitants of the universe, the black holes.Today, across the universe, at the heart of every galaxy, and dotted throughout, mature black holes are creating chaos. And in a quiet part of the universe, the Swift satellite has picked up evidence of a gruesome death caused by one of these dark powers. High energy X-ray flares shooting out from deep within the Draco constellation are thought to be the dying cries of a white dwarf star being ripped apart by the intense tides of a supermassive black hole ? heating it to millions of degrees as it is shredded at the event horizon.They have the power to wipe out any of the universe's other inhabitants, but no one has ever seen a black hole itself die. But 1.8 billion light years away, the LIGO instruments have recently detected something that could be the closest a black hole gets to death. Gravitational waves given off as two enormous black holes merge together. And now scientists think that these gravitational waves could be evidence of two black holes connecting to form a wormhole ? a link through space and time. It seems outlandish, but today's physicists are daring to think the unthinkable ? that black holes could connect us to another universe.At their very heart, black holes are also where Einstein's Theory of General Relativity is stretched in almost unimaginable ways, revealing black holes as the key to our understanding of the fundamentals of our universe and perhaps all other universes.Join Professors Brian Cox and Jeff Forshaw in exploring our universe's most mysterious inhabitants, how they are formed, why they are essential components of every galaxy, including our own, and what secrets they still hold, waiting to be discovered.

Principles of General Pharmacy: With Specific Reference to Systems of Weights and Measures, Specific Gravity and Its Uses, Pharmaceutical Manipulations (1886) by Adolphus Fennel is a comprehensive guide to the principles of pharmacy. The book covers various topics related to pharmacy, including the systems of weights and measures used in pharmacy, the specific gravity of pharmaceutical substances, and the various pharmaceutical manipulations used in the preparation of drugs. The author provides detailed explanations of each topic, along with examples and illustrations to help readers understand the concepts better. The book is a valuable resource for students of pharmacy and professionals in the field who need to refresh their knowledge of the fundamental principles of pharmacy. Published in 1886, the book also provides a historical perspective on the development of pharmacy as a profession.Pursuant To A Course Of Adolphus Fennel.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

Time, space and entanglement are the main characters in this book. Their nature is still a great mystery in physics and we study here the possibility that these three phenomena are closely connected, showing how entanglement can be at the basis of the emergence of time and space within closed quantum systems. We revisit and extend the Page and Wootters theory that was originally introduced in order to describe the emergence of time through entanglement between subsystems in a globally static, quantum Universe. In the book, after providing a complete review of the salient aspects of the theory, we establish a connection with recent research on the foundations of statistical mechanics and we provide a new understanding of the thermalization process. Furthermore, we generalize the framework in order describe the spatial degree of freedom and we provide a model of 3+1 dimensional, quantum spacetime emerging from entanglement among different subsystems in a globally "timeless" and "positionless" Universe. Finally, via the Page and Wootters theory, the evolution of quantum clocks within a gravitational field is treated and a time dilation effect is obtained in agreement with the Schwarzschild solution.

One of the main unanswered question of modern Physics is "How does gravity behave at small scales?". The aim of this thesis is to illustrate in a comprehensive but accessible way how to look for deviations from Einstein's theory of General Relativity in this regime, looking at the simplest celestial bodies: static and spherically symmetric ones.With a conservative and bottom-up approach, at smaller scales the first corrections to the action of General Relativity are generally considered to be terms quadratic in the curvature tensors; while these modifications do not cure the inconsistency between gravity and quantum mechanics, the solutions of this theory are plausible candidates to be the first-order corrections of the classical ones.Even with such simple modifications, a striking picture emerges from the study of isolated objects: the unique Schwarzschild solution of General Relativity is only a rare bird in the set of solutions, with non-Schwarzschild black holes, wormholes and naked singularities appearing as possible substitutes.Tailored to graduate students and researchers entering this field, this thesis shows how to construct these new solutions from action principles, how to characterize their metric, how to study their physical properties, such as their stability or Thermodynamics, and how to look for phenomenological signatures.

This concise book reviews methods used for gluing space-time manifolds together. It is therefore relevant to theorists working on branes, walls, domain walls, concepts frequently used in theoretical cosmology, astrophysics, and gravity theory. Nowadays, applications are also in theoretical condensed matter physics where Riemannian geometry appears. The book also reviews the history of matching conditions between two space-time manifolds from the early times of general relativity up to now.

Classical mechanics is the basis for any university-level study of technical-scientific disciplines. But most existing manuals use a technological and engineering approach, with basic aspects sometimes insufficiently highlighted. This book introduces the concepts and applications of classical mechanics into Newtonian formalism. Newtonian dynamics is useful for solving applied physics and engineering problems, but also a fascinating theory anchored in questions posed since the times of the Greek philosophers, regarding space, the flow of time, measurable physical quantities, the physical principles with the mathematical structure needed to describe the Universe, etc. The author aims to encourage students to think about these fundamental aspects and how they will be addressed in modern physics, including the successes and limitations of Newton's mechanics. The book is designed to mirror the progress of the students using it, with earlier chapters assuming nomore than basic high school instruction and later ones geared toward subsequent enhanced understanding. The book is designed for students of undergraduate programs in physics, mathematics, chemistry, and engineering who will deal with modern physics, as they will benefit from an approach in which the aspects of classical mechanics are introduced in a propaedeutic approach towards relativistic physics and quantum mechanics.

Black holes have been captivating the human imagination for centuries. These mysterious cosmic entities have served as a source of inspiration for scientists, philosophers, and science fiction writers alike. In this subchapter, we will delve into the fascination that black holes hold over our collective consciousness and explore the reasons behind their allure.One of the primary reasons for the fascination with black holes is their incredible and mind-boggling properties. These celestial objects are formed from the remnants of massive stars that have collapsed under their own gravity. The sheer density of a black hole is unfathomable, with all its mass concentrated into an infinitesimally small point called a singularity. The gravitational pull exerted by a black hole is so immense that nothing, not even light, can escape its clutches once it crosses the event horizon.This concept alone challenges our understanding of the laws of physics and prompts us to question the very fabric of the universe. The enigmatic nature of black holes, their ability to distort space and time, and the possibility of wormholes and parallel universes within them, all contribute to their allure.The implications of black holes extend beyond astrophysics and into the realms of philosophy and existentialism. They represent the ultimate unknown, the great void in our knowledge. They force us to ponder the nature of existence, the fate of matter, and the limits of our understanding. The mystery of what happens beyond the event horizon tantalizes our curiosity and pushes us to explore the boundaries of human knowledge and imagination.Furthermore, black holes offer a unique laboratory for studying the fundamental laws of physics. They provide opportunities to test Einstein's theory of general relativity and investigate the nature of spacetime. By analyzing the effects of black holes on surrounding matter and their influence on the cosmic landscape, scientists can gain insights into the fundamental nature of the universe.

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.

This textbook gradually introduces the reader to several topics related to black hole physics with a didactic approach. It starts with the most basic black hole solution, the Schwarzschild metric, and discusses the basic classical properties of black hole solutions as seen by different probes. Then it reviews various theorems about black hole properties as solutions to Einstein gravity coupled to matter fields, conserved charges associated with black holes, and laws of black hole thermodynamics. Next, it elucidates semiclassical and quantum aspects of black holes, which are relevant in ongoing and future research. The book is enriched with many exercises and solutions to assist in the learning.The textbook is designed for physics graduate students who want to start their research career in the field of black holes; postdocs who recently changed their research focus towards black holes and want to get up-to-date on recent and current research topics; advanced researchers intending to teach (or learn) basic and advanced aspects of black hole physics and the associated mathematical tools. Besides general relativity, the reader needs to be familiar with standard undergraduate physics, like thermodynamics, quantum mechanics, and statistical mechanics. Moreover, familiarity with basic quantum field theory in Minkowski space is assumed. The book covers the rest of the needed background material in the main text or the appendices.

Our vast Universe is filled with an enormous amount of matter and energy, which are the source of large gravitational potentials affecting all physical phenomena. Because this fact about the size and contents of the Universe was not known when our fundamental theories of dynamics and relativity were completed by the 1920s, the current theories - based as they are in empty space - fail to incorporate cosmic gravity. Though the current theories are consistent with the majority of empirical facts, there are some crucial discrepancies, which demand a drastic shift to a cosmic gravitational paradigm for the theories of relativity and dynamics. The book is a detailed and widely accessible account of this paradigm, called Cosmic Relativity, supported by ample empirical evidence. It is established that all motional relativistic effects are cosmic gravitational effects. The new theory of Cosmic Relativity solves and answers all outstanding questions and puzzles about dynamics and relativity.

This book addresses the pursuit and further investigation of experimental results by analyzing classic examples from physics. The authors concentrate on the investigation of experimental results by examining case studies from the history of 20th and 21st century physics. Discussions on the discovery of parity nonconservation, the rise and fall of the Fifth Force, the search for neutrinoless double decay, supersymmetry and the expansion of the Standard Model, and measurements of the anomalous magnetic moment of the muons are provided. Experimental results may achieve acceptance to the point that even well known principles, such as conservation of energy and quantization, lose their status as accepted. Such principles and their options are treated on an equal footing as being pursuit worthy even though there is no plausible explanation as to why and how they might have failed.

With a rare blend of scientific insight and writing as graceful as the theories it so deftly explains, The Elegant Universe remains the unrivaled account of the modern search for the deepest laws of nature: "a standard that will be hard to beat" (George Johnson, New York Times Book Review). In this new 25th anniversary edition, renowned physicist and author Brian Greene-"the single best explainer of abstruse concepts in the world today" (Washington Post)-updates his classic work with a new preface and epilogue summarizing the significant theoretical and experimental developments over the past quarter-century. From established science, including relativity and quantum mechanics, to the cutting edge of thinking on black holes, string theory, and quantum gravity, The Elegant Universe makes some of the most sophisticated concepts ever contemplated thoroughly accessible and entertaining, bringing us closer than ever to comprehending how the universe works.

Benjamin Franklin was a Founding Father of America and had an enormous impact on America as it is today. In addition to that, there are many little-known facts about the man that is Benjamin Franklin. Unlike many of the other Founding Fathers, he started out in humble circumstances. Franklin never finished college because his parents couldn't afford it. He hated his first job, and when he did get another one, he left without notice.From a young age, Benjamin Franklin fought for the rights of America at home and abroad. Yet, he bore the burdens of leadership and never shirked nor faltered in his mission. His greatest asset was his charm and friendliness, but he had his detractors as well, and felt the emotional impact of that. Inside you'll read aboutEarly lifePhiladelphia: The beginning of a Master MindNear and Far: Family Life with Benjamin FranklinScientist: A kite, Electricity and InventionsBits and Pieces: Other Pieces of Benjamin FranklinA Revolution: Benjamin Franklin and the American RevolutionThe End of an Era: Benjamin Franklin's Last ChapterIn this book, you will read about the Founding Fathers, their upbringings, personal lives, political careers, and the work they did to earn them their rightful place in American history.

Estas son algunas de las preguntas a las que responde este extraordinario libro sobre la manera en que las criaturas del mundo natural y los humanos hemos desafiado la gravedad a lo largo de la historia.

Microgravity is the condition in which people or objects appear to be weightless. The microgravity lab consisting of only-in-space conditions facilitates a wide range of investigations in various disciplines. This lab provides a platform with greatly reduced non-gravitational sources of noise, access to the vacuum conditions of space, extreme heat and cold, large distances, and high velocity that is beneficial for physics research. The concept of microgravity is used in advanced materials science research, because it changes the processes such as crystal growth, fluid mixing, separation between gases and liquids, heat transfer, solidification, and combustion. Access to microgravity is beneficial for biology and human health. Data about how different organisms react to a microgravity environment and the ways various biological functions change in the absence of gravity increase the understanding related to organisms. This book is a compilation of chapters that discuss the most vital concepts and emerging trends on the subject of microgravity. It aims to serve as a resource guide for students and researchers alike.

Einstein's field equations of gravitation are a core element of his general theory of relativity. In four short communications to the Prussian Academy of Sciences in Berlin in November 1015, we can follow the final steps toward these equations and the resulting theory's spectacular success in accounting for the anomalous motion of Mercury's perihelion. This source book provides an expert guide to these four groundbreaking papers. Following an introductory essay placing these papers in the context of the development of Einstein's theory, it presents and analyzes, in addition to the four papers of November 1915, a careful selection of (critical excerpts from) papers, letters, and manuscripts documenting the path that early on led Einstein to the field equations of the first November 1915 paper, but then took a turn away from them only to lead back to them in the end. Drawing on extensive research at the Einstein Papers Project and the Max Planck Institute for History of Science, this volume traces the intricate interplay between considerations of physics and considerations of mathematics that guided Einstein along this path. It thus presents a concise yet authoritative account of how Einstein found his field equations, affording readers who are prepared to immerse themselves in these intricacies a unique glimpse of Einstein at work at the height of his creative prowess. Highlights of this journey in Einstein's footsteps include the crucial pages (with detailed annotation) from the Zurich Notebook, the record of Einstein's early search for field equation with his mathematician friend Marcel Grossmann, and the Einstein-Besso manuscript, documenting Einstein's attempts with his friend and confidant Michele Besso to explain the Mercury anomaly on the basis of the equations that he and Grossmann had eventually settled on in the Zurich Notebook.

This book deals with theoretical mechanics. Newton published the "Philosophiæ Naturalis Principia Mathematica" in 1687. In it, he sets out the basic principles of physics that are required to understand the motion of the planets, their moons, and the comets in the solar system. It includes the gravitational (inverse square) law, the inertial principle, and the basic elements of mechanics. Since its publication, a large number of refinements and reformulations have been introduced, thereby adding enormous insight into the structure of mechanics, which is commonly known as ¿classical mechanics¿. All these have in common that by taking a suitable limit, Newton's original principles re-appear. Thus, physicists and mathematicians who work on the subject always have a notion that if their theories do not return to Newton's foundations, then there is something wrong. Newton himself acknowledged that 'if I have seen further (than others), it is by standing on the shoulders of giants'. One of these giants was undoubtedly Galileo who died in the year Newton was born. So, Newton himself adhered to the 'classical limit'.