Gravitation and spacetime.
01 Jan 1976-
TL;DR: Ohanian and Ruffini's Gravitation and Spacetime, Second Edition, the authors is the best book on the market today of 500 pages or less on gravitation and general relativity.
Abstract: Now more than ever, Gravitation and Spacetime, Second Edition, by Hans C. Ohanian and new coauthor Remo Ruffini, deserves John Wheeler's praise as "the best book on the market today of 500 pages or less on gravitation and general relativity." Gravitation and Spacetime has been thoroughly updated with the most exciting finds and hottest theoretical topics in general relativity and cosmology. Highlights of the revision include the rise and fall of the fifth force, principles and applications of gravitational lensing, COBE's spectacular confirmation of the blackbody spectrum of the cosmic thermal radiation, theories of dark matter and inflation, and the early universe as a testing ground for particle physicists' unification theories, and much, much more. The ideal choice for a graduate-level introduction to general relativity, Gravitation and Spacetime is also suitable for an advanced undergaduate course.
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TL;DR: The study of waves can be traced back to antiquity where philosophers, such as Pythagoras, studied the relation of pitch and length of string in musical instruments and the subject of classical acoustics was laid down and presented as a coherent whole by John William Strutt in his treatise Theory of Sound.
Abstract: The study of waves can be traced back to antiquity where philosophers, such as Pythagoras (c.560-480 BC), studied the relation of pitch and length of string in musical instruments. However, it was not until the work of Giovani Benedetti (1530-90), Isaac Beeckman (1588-1637) and Galileo (1564-1642) that the relationship between pitch and frequency was discovered. This started the science of acoustics, a term coined by Joseph Sauveur (1653-1716) who showed that strings can vibrate simultaneously at a fundamental frequency and at integral multiples that he called harmonics. Isaac Newton (1642-1727) was the first to calculate the speed of sound in his Principia. However, he assumed isothermal conditions so his value was too low compared with measured values. This discrepancy was resolved by Laplace (1749-1827) when he included adiabatic heating and cooling effects. The first analytical solution for a vibrating string was given by Brook Taylor (1685-1731). After this, advances were made by Daniel Bernoulli (1700-82), Leonard Euler (1707-83) and Jean d’Alembert (1717-83) who found the first solution to the linear wave equation, see section (3.2). Whilst others had shown that a wave can be represented as a sum of simple harmonic oscillations, it was Joseph Fourier (1768-1830) who conjectured that arbitrary functions can be represented by the superposition of an infinite sum of sines and cosines now known as the Fourier series. However, whilst his conjecture was controversial and not widely accepted at the time, Dirichlet subsequently provided a proof, in 1828, that all functions satisfying Dirichlet’s conditions (i.e. non-pathological piecewise continuous) could be represented by a convergent Fourier series. Finally, the subject of classical acoustics was laid down and presented as a coherent whole by John William Strutt (Lord Rayleigh, 1832-1901) in his treatise Theory of Sound. The science of modern acoustics has now moved into such diverse areas as sonar, auditoria, electronic amplifiers, etc.
1,428 citations
TL;DR: In this article, the authors argue that the generalized uncertainty principle may prevent black holes from total evaporation in exactly the same way that the uncertainty principle prevents the hydrogen atom from total collapse.
Abstract: In the current standard viewpoint small black holes are believed to emit black body radiation at the Hawking temperature, at least until they approach Planck size, after which their fate is open to conjecture A cogent argument against the existence of remnants is that, since no evident quantum number prevents it, black holes should radiate completely away to photons and other ordinary stable particles and vacuum, like any unstable quantum system Here we argue the contrary, that the generalized uncertainty principle may prevent their total evaporation in exactly the same way that the uncertainty principle prevents the hydrogen atom from total collapse: the collapse is prevented, not by symmetry, but by dynamics, as a minimum size and mass are approached
776 citations
TL;DR: In this paper, it was shown that there is an absolute minimum uncertainty in the position of any particle, of order of the Planck length, of a photon and a particle being observed.
Abstract: Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term. From the modified or gravitational uncertainty principle it follows that there is an absolute minimum uncertainty in the position of any particle, of order of the Planck length. A modified uncertainty relation of this form is a standard result of superstring theory, but the derivation given here is based on simpler and rather general considerations with either Newtonian gravitational theory or general relativity theory.
465 citations
Cites background or methods from "Gravitation and spacetime."
...In this section and the following we give a dimensional estimate and an approximate calculation based on general relativity theory, free of such drawbacks [6,2,4]....
[...]
...ciple: dimensional analysis in Newtonian theory, an approximate calculation in Newtonian theory, dimensional analysis in general relativity theory, and an approximate calculation in general relativity theory [4]....
[...]
...We first estimate the effects of gravity in a very rough and heuristic way using Newtonian gravitational theory, with the assumption that the photon behaves as a classical particle with an effective mass equal to its energy divided by c(2) [4]....
[...]
TL;DR: A review of the development of Einstein's thought on general covariance, its relation to the foundations of general relativity and the evolution of the continuing debate over his viewpoint can be found in this paper.
Abstract: Einstein offered the principle of general covariance as the fundamental physical principle of his general theory of relativity and as responsible for extending the principle of relativity to accelerated motion. This view was disputed almost immediately with the counter-claim that the principle was no relativity principle and was physically vacuous. The disagreement persists today. This article reviews the development of Einstein's thought on general covariance, its relation to the foundations of general relativity and the evolution of the continuing debate over his viewpoint.
407 citations
TL;DR: In this paper, the authors consider the evolution of planets, stars, stellar populations, galaxies, and the universe itself over time scales that greatly exceed the current age of the universe and derive scaling relations that describe how the range of stellar masses and lifetimes depends on forthcoming increases in metallicity.
Abstract: This paper outlines astrophysical issues related to the long-term fate of the universe. The authors consider the evolution of planets, stars, stellar populations, galaxies, and the universe itself over time scales that greatly exceed the current age of the universe. Their discussion starts with new stellar evolution calculations which follow the future evolution of the low-mass (M-type) stars that dominate the stellar mass function. They derive scaling relations that describe how the range of stellar masses and lifetimes depends on forthcoming increases in metallicity. They then proceed to determine the ultimate mass distribution of stellar remnants, i.e., the neutron stars, white dwarfs, and brown dwarfs remaining at the end of stellar evolution; this aggregate of remnants defines the 'final stellar mass function.' At times exceeding \ensuremath{\sim}1--10 trillion years, the supply of interstellar gas will be exhausted, yet star formation will continue at a highly attenuated level via collisions between brown dwarfs. This process tails off as the galaxy gradually depletes its stars by ejecting the majority and driving a minority toward eventual accretion onto massive black holes. As the galaxy disperses, stellar remnants provide a mechanism for converting the halo dark matter into radiative energy. Posited weakly interacting massive particles are accreted by white dwarfs, where they subsequently annihilate with each other. Thermalization of the decay products keeps the old white dwarfs much warmer than they would otherwise be. After accounting for the destruction of the galaxy, the authors consider the fate of the expelled degenerate objects (planets, white dwarfs, and neutron stars) within the explicit assumption that proton decay is a viable process. The evolution and eventual sublimation of these objects is dictated by the decay of their constituent nucleons, and this evolutionary scenario is developed in some detail. After white dwarfs and neutron stars have disappeared, galactic black holes slowly lose their mass as they emit Hawking radiation. This review finishes with an evaluation of cosmological issues that arise in connection with the long-term evolution of the universe. Special attention is devoted to the relation between future density fluctuations and the prospects for continued large-scale expansion. The authors compute the evolution of the background radiation fields of the universe. After several trillion years, the current cosmic microwave background will have redshifted into insignificance; the dominant contribution to the radiation background will arise from other sources, including stars, dark-matter annihilation, proton decay, and black holes. Finally, the authors consider the dramatic possible effects of a nonzero vacuum energy density.
275 citations
References
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TL;DR: The principle of relativity Relativistic mechanics Electromagnetic fields electromagnetic waves as discussed by the authors The propagation of light The field of moving charges Radiation of electromagnetic waves Particle in a gravitational field The gravitational field equation
Abstract: The principle of relativity Relativistic mechanics Electromagnetic fields Electromagnetic waves The propagation of light The field of moving charges Radiation of electromagnetic waves Particle in a gravitational field The gravitational field equation The field of gravitational bodies Gravitational waves Relativistic cosmology Index.
9,047 citations
Book•
01 Jan 1973
TL;DR: In this paper, the authors discuss the General Theory of Relativity in the large and discuss the significance of space-time curvature and the global properties of a number of exact solutions of Einstein's field equations.
Abstract: Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.
8,932 citations
TL;DR: The present edition of this now classic text offers substantial refinements and improvements over the first edition and includes some new material as mentioned in this paper, including an improved derivation of the macroscopic equations, monopoles, causality and dispersion relations, signal propagation in a dispersive media.
Abstract: J D Jackson Chichester: J Wiley 1975 pp xxii + 848 price £10.75 The present edition of this now classic text offers substantial refinements and improvements over the first edition and includes some new material. New topics on electromagnetism include an improved derivation of the macroscopic equations, monopoles, causality and dispersion relations, signal propagation in a dispersive media.
2,786 citations
TL;DR: The study of waves can be traced back to antiquity where philosophers, such as Pythagoras, studied the relation of pitch and length of string in musical instruments and the subject of classical acoustics was laid down and presented as a coherent whole by John William Strutt in his treatise Theory of Sound.
Abstract: The study of waves can be traced back to antiquity where philosophers, such as Pythagoras (c.560-480 BC), studied the relation of pitch and length of string in musical instruments. However, it was not until the work of Giovani Benedetti (1530-90), Isaac Beeckman (1588-1637) and Galileo (1564-1642) that the relationship between pitch and frequency was discovered. This started the science of acoustics, a term coined by Joseph Sauveur (1653-1716) who showed that strings can vibrate simultaneously at a fundamental frequency and at integral multiples that he called harmonics. Isaac Newton (1642-1727) was the first to calculate the speed of sound in his Principia. However, he assumed isothermal conditions so his value was too low compared with measured values. This discrepancy was resolved by Laplace (1749-1827) when he included adiabatic heating and cooling effects. The first analytical solution for a vibrating string was given by Brook Taylor (1685-1731). After this, advances were made by Daniel Bernoulli (1700-82), Leonard Euler (1707-83) and Jean d’Alembert (1717-83) who found the first solution to the linear wave equation, see section (3.2). Whilst others had shown that a wave can be represented as a sum of simple harmonic oscillations, it was Joseph Fourier (1768-1830) who conjectured that arbitrary functions can be represented by the superposition of an infinite sum of sines and cosines now known as the Fourier series. However, whilst his conjecture was controversial and not widely accepted at the time, Dirichlet subsequently provided a proof, in 1828, that all functions satisfying Dirichlet’s conditions (i.e. non-pathological piecewise continuous) could be represented by a convergent Fourier series. Finally, the subject of classical acoustics was laid down and presented as a coherent whole by John William Strutt (Lord Rayleigh, 1832-1901) in his treatise Theory of Sound. The science of modern acoustics has now moved into such diverse areas as sonar, auditoria, electronic amplifiers, etc.
1,428 citations