This user-friendly self-study guide is aimed at the general reader who is motivated to tackle that not insignificant challenge. The book is written using straightforward and accessible language, with clear derivations and explanations as well as numerous fully solved problems. For those with minimal mathematical background, the first chapter provides a crash course in foundation mathematics. The reader is then taken gently by the hand and guided through a wide range of fundamental topics, including Newtonian mechanics; the Lorentz transformations; tensor calculus; the Einstein field equations; the Schwarzschild solution (which gives a good approximation of the spacetime of our Solar System); simple black holes and relativistic cosmology. Following the historic 2015 LIGO (Laser Interferometer Gravitational-Wave Observatory) detection, there is now an additional chapter on gravitational waves, ripples in the fabric of spacetime that potentially provide a revolutionary new way to study the universe. Special relativity helps explain a huge range of non-gravitational physical phenomena and has some strangely counter-intuitive consequences. These include time dilation, length contraction, the relativity of simultaneity, mass-energy equivalence and an absolute speed limit. General relativity, the leading theory of gravity, is at the heart of our understanding of cosmology and black holes.Understand even the basics of Einstein's amazing theory and the world will never seem the same again. ContentsPrefaceIntroduction1 Foundation mathematics2 Newtonian mechanics3 Special relativity4 Introducing the manifold5 Scalars, vectors, one-forms and tensors6 More on curvature7 General relativity8 The Newtonian limit9 The Schwarzschild metric10 Schwarzschild black holes11 Cosmology12 Gravitational wavesAppendix: The Riemann curvature tensorBibliographyAcknowledgementsJanuary 2019. This third edition has been revised to make the material even more accessible to the enthusiastic general reader who seeks to understand the mathematics of relativity.

    Although Einstein understood that black holes were mathematical solutions to his equations, he never accepted their physical reality--a viewpoint many shared. This all changed in the 1960s and 1970s, when a deeper conceptual understanding of black holes developed just as new observations revealed the existence of quasars and X-ray binary star systems, whose mysterious properties could be explained by the presence of black holes. Black holes have since been the subject of intense research--and the physics governing how they behave and affect their surroundings is stranger and more mind-bending than any fiction.After introducing the basics of the special and general theories of relativity, this book describes black holes both as astrophysical objects and theoretical "laboratories" in which physicists can test their understanding of gravitational, quantum, and thermal physics. From Schwarzschild black holes to rotating and colliding black holes, and from gravitational radiation to Hawking radiation and information loss, Steven Gubser and Frans Pretorius use creative thought experiments and analogies to explain their subject accessibly. They also describe the decades-long quest to observe the universe in gravitational waves, which recently resulted in the LIGO observatories' detection of the distinctive gravitational wave "chirp" of two colliding black holes--the first direct observation of black holes' existence.The Little Book of Black Holes takes readers deep into the mysterious heart of the subject, offering rare clarity of insight into the physics that makes black holes simple yet destructive manifestations of geometric destiny.

    Thoroughly updated, this edition offers new, faster techniques for solving differential equations generated by the emergence of high-speed computers.

    Its ability to target users who have provided real data about themselves and their interests makes Facebook the ideal platform for marketers, and marketers everywhere recognize the importance of Facebook and are eager to successfully tap Facebook's potential. This book shows you how.Quickly get up to speed on today's Facebook conventions and demographics, and then gain an understanding of the various strategic and implementation issues you must consider from start to finish.Guides you through crafting a successful presence on Facebook and takes you through each step for developing an overall marketing strategy Explains each step for setting realistic goals, defining metrics, developing reports, and acquiring corporate buy-in Shows how to execute your strategy while incorporating all of Facebook's relevant features Addresses Facebook's pay-per-click platform, Facebook Connect, and more Packed with tips and tactics not documented anywhere else, the book serves as the ultimate step-by-step guide to developing a winning Facebook marketing campaign.

    But what if, nonetheless, Einstein got it wrong?Since the 1930s, physicists have noticed an alarming discrepancy between the universe as we see it and the universe that Einstein's theory of relativity predicts. There just doesn't seem to be enough stuff out there for everything to hang together. Galaxies spin so fast that, based on the amount of visible matter in them, they ought to be flung to pieces, the same way a spinning yo-yo can break its string. Cosmologists tried to solve the problem by positing dark matter—a mysterious, invisible substance that surrounds galaxies, holding the visible matter in place—and particle physicists, attempting to identify the nature of the stuff, have undertaken a slew of experiments to detect it. So far, none have.Now, John W. Moffat, a physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada, offers a different solution to the problem. The cap­stone to a storybook career—one that began with a correspondence with Einstein and a conversation with Niels Bohr—Moffat's modified gravity theory, or MOG, can model the movements of the universe without recourse to dark matter, and his work chal­lenging the constancy of the speed of light raises a stark challenge to the usual models of the first half-million years of the universe's existence.This bold new work, presenting the entirety of Moffat's hypothesis to a general readership for the first time, promises to overturn everything we thought we knew about the origins and evolution of the universe.

    Challenge your preceptions of the universe and explore ideas as varied as superspace theater and zero-time ghosts and even explore a future where time travel is real and black holes are gateways rather than endings.

    Things can exist in two places at once and travel backwards and forwards in time. Waves and particles are one and the same, and objects change their behaviour according to whether they are being watched. This is not some alternative universe but the realm of the very small, where quantum mechanics rules. In this weird world of atoms and their constituents, our common sense understanding of reality breaks down - yet quantum mechanics has never failed an experimental test. What does it all mean? For all its weirdness, quantum mechanics has given us many practical technologies including lasers and the transistors that underlie computers and all digital technology. In the future, it promises computers more powerful than any built before, the ability to communicate with absolute privacy, and even quantum teleportation. The Quantum World explores the past, present and future of quantum science, its applications and mind-bending implications. Discover how ideas from quantum mechanics are percolating out into the vast scale of the cosmos - perhaps, in the future, to reveal a new understanding of the big bang and the nature of space and time.ABOUT THE SERIESNew Scientist Instant Expert books are definitive and accessible entry points to the most important subjects in science; subjects that challenge, attract debate, invite controversy and engage the most enquiring minds. Designed for curious readers who want to know how things work and why, the Instant Expert series explores the topics that really matter and their impact on individuals, society, and the planet, translating the scientific complexities around us into language that's open to everyone, and putting new ideas and discoveries into perspective and context.

    It's all too easy to ignore the fascinating possibilities of emptiness and non-existence, and we may well wonder what there is to say about nothing. But scientists have known for centuries that nothing is the key to understanding absolutely everything, from why particles have mass to the expansion of the universe - so without nothing we'd be precisely nowhere.Absolute zero (the coldest cold that can exist) and the astonishing power of placebos, light bulbs, superconductors, vacuums, dark energy, 'bed rest' and the birth of time - all are different aspects of the concept of nothing. The closer we look, the bigger the subject gets. Why do some animals spend all day doing nothing? What happens in our brains when we try to think about nothing? With chapters by 20 science writers, including top names such as Ian Stewart, Marcus Chown, Nigel Henbest, Michael Brooks, Paul Davies and David Fisher, this fascinating and intriguing book revels in a subject that has tantalised the finest minds for centuries, and shows there's more to nothing than meets the eye.

    Frank Wilczek has played a lead role in establishing the new paradigms. Transcending the clash and mismatch of older ideas about what matter is, and what space is, Wilczek presents here some brilliant and clear syntheses. Space is a dynamic material, the engine of reality; matter is a subtle pattern of disturbance in that material.Extraordinarily readable and authoritative, The Lightness of Being is the first book to unwrap these exciting new ideas for the general public. It explores their implications for basic questions about space, mass, energy, and the longed-for possibility of a fully unified theory of Nature. Along the way, Wilczek presents new perspectives on many strange aspects of our fantastic universe. Pointing toward new directions where the great discoveries in fundamental physics are likely to come, he envisions a new Golden Age in physics.

    Richard Gott was among the first cosmologists to propose that the structure of our universe is like a sponge made up of clusters of galaxies intricately connected by filaments of galaxies—a magnificent structure now called the "cosmic web" and mapped extensively by teams of astronomers. Here is his gripping insider's account of how a generation of undaunted theorists and observers solved the mystery of the architecture of our cosmos.The Cosmic Web begins with modern pioneers of extragalactic astronomy, such as Edwin Hubble and Fritz Zwicky. It goes on to describe how, during the Cold War, the American school of cosmology favored a model of the universe where galaxies resided in isolated clusters, whereas the Soviet school favored a honeycomb pattern of galaxies punctuated by giant, isolated voids. Gott tells the stories of how his own path to a solution began with a high-school science project when he was eighteen, and how he and astronomer Mario Jurič measured the Sloan Great Wall of Galaxies, a filament of galaxies that, at 1.37 billion light-years in length, is one of the largest structures in the universe.Drawing on Gott’s own experiences working at the frontiers of science with many of today’s leading cosmologists, The Cosmic Web shows how ambitious telescope surveys such as the Sloan Digital Sky Survey are transforming our understanding of the cosmos, and how the cosmic web holds vital clues to the origins of the universe and the next trillion years that lie ahead.

    Hazen writes of how the co-evolution of the geosphere and biosphere—of rocks and living matter—has shaped our planet into the only one of its kind in the Solar System, if not the entire cosmos.With an astrobiologist’s imagination, a historian’s perspective, and a naturalist’s passion for the ground beneath our feet, Hazen explains how changes on an atomic level translate into dramatic shifts in Earth’s makeup over its 4.567 billion year existence. He calls upon a flurry of recent discoveries to portray our planet’s many iterations in vivid detail. Through his theory of “co-evolution,” we learn how reactions between organic molecules and rock crystals may have generated Earth’s first organisms, which in turn are responsible for more than two-thirds of the mineral varieties on the planet.The Story of Earth is also the story of the pioneering men and women behind the sciences. Readers will meet black-market meteorite hawkers of the Sahara Desert, the gun-toting Feds who guarded the Apollo missions’ lunar dust, and the World War II Navy officer whose super-pressurized “bomb”—recycled from military hardware—first simulated the molten rock of Earth’s mantle. As a mentor to a new generation of scientists, Hazen introduces the intrepid young explorers whose dispatches from Earth’s harshest landscapes will revolutionize geology.

    . . full of intellectual treats and tricks, of whimsy and deep scientific philosophy. It is highbrow entertainment at its best, a teasing challenge to all who aspire to think about the universe." — New York Herald TribuneOne of the world's foremost nuclear physicists (celebrated for his theory of radioactive decay, among other accomplishments), George Gamow possessed the unique ability of making the world of science accessible to the general reader.He brings that ability to bear in this delightful expedition through the problems, pleasures, and puzzles of modern science. Among the topics scrutinized with the author's celebrated good humor and pedagogical prowess are the macrocosm and the microcosm, theory of numbers, relativity of space and time, entropy, genes, atomic structure, nuclear fission, and the origin of the solar system.In the pages of this book readers grapple with such crucial matters as whether it is possible to bend space, why a rocket shrinks, the "end of the world problem," excursions into the fourth dimension, and a host of other tantalizing topics for the scientifically curious. Brimming with amusing anecdotes and provocative problems, One Two Three . . . Infinity also includes over 120 delightful pen-and-ink illustrations by the author, adding another dimension of good-natured charm to these wide-ranging explorations.Whatever your level of scientific expertise, chances are you'll derive a great deal of pleasure, stimulation, and information from this unusual and imaginative book. It belongs in the library of anyone curious about the wonders of the scientific universe. "In One Two Three . . . Infinity, as in his other books, George Gamow succeeds where others fail because of his remarkable ability to combine technical accuracy, choice of material, dignity of expression, and readability." — Saturday Review of Literature

    Business-related applications are evident throughout, and the book is relevant for anyone seeking a solid grounding in NLP.Also included are are fascinating perspectives from leading NLP practitioners. A chapter on 'NLP in Action' gives you an overview of practical applications of NLP, featuring profiles and interviews with people involved in those disciplines, including NLP in sports, education, leadership, selling, health, relationships and personal development.NOT GOT MUCH TIME?One, five and ten-minute introductions to key principles to get you started.AUTHOR INSIGHTSLots of instant help with common problems and quick tips for success, based on the authors' many years of experience.TEST YOURSELFTests in the book and online to keep track of your progress.EXTEND YOUR KNOWLEDGEExtra online articles at www.teachyourself.com to give you a richer understanding of NLP.THINGS TO REMEMBERQuick refreshers to help you remember the key facts.TRY THISInnovative exercises illustrate what you've learnt and how to use it.

    Readers will find excerpts from bestsellers such as Douglas R. Hofstadter's Gödel, Escher, Bach, Francis Crick's Life Itself, Loren Eiseley's The Immense Journey, Daniel Dennett's Darwin's Dangerous Idea, and Rachel Carson's The Sea Around Us. There are classic essays ranging from J.B.S. Haldane's "On Being the Right Size" and Garrett Hardin's "The Tragedy of the Commons" to Alan Turing's "Computing Machinery and Intelligence" and Albert Einstein's famed New York Times article on "Relativity." And readers will also discover lesser-known but engaging pieces such as Lewis Thomas's "Seven Wonders of Science," J. Robert Oppenheimer on "War and Physicists," and Freeman Dyson's memoir of studying under Hans Bethe.A must-read volume for all science buffs, The Oxford Book of Modern Science Writing is a rich and vibrant anthology that captures the poetry and excitement of scientific thought and discovery.One of New Scientist's Editor's Picks for 2008.

    The planets were nothing like Earth, however: they were giant gas balls like Jupiter or Saturn. More than 500 planets have been found since then, yet none of them could support life. Now, armed with more powerful technology, planet hunters are racing to find a true twin of Earth. Science writer Michael Lemonick has unique access to these exoplaneteers, as they call themselves, and Mirror Earth unveils their passionate quest. Geoff Marcy, at the University of California, Berkeley, is the world's most successful planet hunter, having found two of the first three extra-solar planets. Bill Borucki, at the NASA Ames Research Center, struggled for more than a decade to launch the Kepler mission-the only planet finder, human or machine, to beat Marcy's record. David Charbonneau, at Harvard, realized that Earths would be much easier to find if he looked at tiny stars called M-dwarfs rather than stars like the Sun-and that he could use backyard telescopes to find them! Unlike those in other races, the competing scientists actually consult and cooperate with one another. But only one will be the first to find Earth's twin. Mirror Earth is poised narrate this historic event as the discovery is made.