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Libros sobre el tema "Einstein metric"

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Publicado: 4 de junio de 2021
Última modificación: 21 de febrero de 2023

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1

Asymptotically symmetric Einstein metrics. Providence, R.I: American Mathematical Society, 2006.

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2

Siu, Yum-Tong. Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics. Basel: Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-7486-1.

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3

Kähler-Einstein metrics and integral invariants. Berlin: Springer-Verlag, 1988.

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4

Futaki, Akito. Kähler-Einstein Metrics and Integral Invariants. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0078084.

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5

Biquard, Olivier, ed. AdS/CFT Correspondence: Einstein Metrics and Their Conformal Boundaries. Zuerich, Switzerland: European Mathematical Society Publishing House, 2005. http://dx.doi.org/10.4171/013.

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6

Siu, Yum-Tong. Lectures on Hermitian-Einstein metrics for stable bundles and Kähler-Einstein metrics: Delivered at the German Mathematical Society Seminar in Düsseldorf in June, 1986. Basel: Birkhäuser Verlag, 1987.

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7

Wentworth, Richard A., Duong H. Phong, Paul M. N. Feehan, Jian Song y Ben Weinkove. Analysis, complex geometry, and mathematical physics: In honor of Duong H. Phong : May 7-11, 2013, Columbia University, New York, New York. Providence, Rhode Island: American Mathematical Society, 2015.

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8

Siu, Yum-Tong. Lectures on Hermitian-Einstein Metric for Stable Bundles and Kahler-Einstein Metrics (DMV Seminar). Birkhauser Verlag AG, 1989.

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9

Deruelle, Nathalie y Jean-Philippe Uzan. The Kerr solution. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0048.

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This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals. Finally, the chapter turns to the Kerr black hole, as well as its curvature singularity, horizons, static limit, and maximal extension.
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10

Wittman, David M. General Relativity and the Schwarzschild Metric. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199658633.003.0018.

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Previously, we saw that variations in the time part of the spacetime metric cause free particles to accelerate, thus unifying gravity and relativity; and that orbits trace those accelerations, which follow the inverse‐square law around spherical source masses. But a metric that empirically models orbits is not enough; we want to understand how any arrangement of mass determines the metric in the surrounding spacetime. This chapter describes thinking tools, especially the frame‐independent idea of spacetime curvature, that helped Einstein develop general relativity. We describe the Einstein equation, which determines the metric given a source or set of sources. Solving that equation for the case of a static spherical mass (such as the Sun) yields the Schwarzschild metric. We compare Schwarzschild and Newtonian predictions for precession, the deflection of light, and time delay of light; and we contrast the effects of variations in the time and space parts of the metric.
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11

Deruelle, Nathalie y Jean-Philippe Uzan. The Schwarzschild solution. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0046.

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This chapter deals with the Schwarzschild metric. To find the gravitational potential U produced by a spherically symmetric object in the Newtonian theory, it is necessary to solve the Poisson equation Δ‎U = 4π‎Gρ‎. Here, the matter density ρ‎ and U depend only on the radial coordinate r and possibly on the time t. Outside the source the solution is U = –GM/r, where M = 4π‎ ∫ ρ‎r2dr is the source mass. In general relativity the problem is to find the ‘spherically symmetric’ spacetime solutions of the Einstein equations, and the analog of the vacuum solution U = –GM/r is the Schwarzschild metric.
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12

Deruelle, Nathalie y Jean-Philippe Uzan. Riemannian manifolds. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0064.

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This chapter is about Riemannian manifolds. It first discusses the metric manifold and the Levi-Civita connection, determining if the metric is Riemannian or Lorentzian. Next, the chapter turns to the properties of the curvature tensor. It states without proof the intrinsic versions of the properties of the Riemann–Christoffel tensor of a covariant derivative already given in Chapter 2. This chapter then performs the same derivation as in Chapter 4 by obtaining the Einstein equations of general relativity by varying the Hilbert action. However, this will be done in the intrinsic manner, using the tools developed in the present and the preceding chapters.
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13

Deruelle, Nathalie y Jean-Philippe Uzan. Gravitational radiation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0054.

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This chapter attempts to calculate the radiated energy of a source in the linear approximation of general relativity to infinity in the lowest order. For this, the chapter first expands the Einstein equations to quadratic order in metric perturbations. It reveals that the radiated energy is then given by the (second) quadrupole formula, which is the gravitational analog of the dipole formula in Maxwell theory. This formula is a priori valid only if the motion of the source is due to forces other than gravity. Finally, this chapter shows that, to prove this formula for the case of self-gravitating systems, the Einstein equations to quadratic order must be solved, and the radiative field in the post-linear approximation of general relativity obtained.
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14

Deruelle, Nathalie y Jean-Philippe Uzan. The physics of black holes I. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0049.

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This chapter describes two physical processes related to the Schwarzschild and Kerr solutions which can be induced by the gravitational field of a black hole. The first is the Penrose process, which suggests that rotating black holes are large energy reservoirs. Next is superradiance, which is the first step in the study of black-hole stability. The study of the stability of black holes involves the linearization of the Einstein equations about the Schwarzschild or Kerr solution. As this chapter shows, the equations of motion for perturbations of the metric are wave equations. The problem then is to determine whether or not these solutions are bounded.
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15

Mabuchi, Toshiki. Einstein Metrics and Yang-Mills Connections. Taylor & Francis Group, 2020.

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16

Mabuchi, Toshiki. Einstein Metrics and Yang-Mills Connections. Taylor & Francis Group, 2020.

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17

Mabuchi, Toshiki. Einstein Metrics and Yang-Mills Connections. Taylor & Francis Group, 2017.

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18

Mabuchi, Toshiki. Einstein Metrics and Yang-Mills Connections. Taylor & Francis Group, 2020.

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19

Mabuchi, Toshiki. Einstein Metrics and Yang-Mills Connections. Taylor & Francis Group, 2020.

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20

Futaki, Akito. Kähler-Einstein Metrics and Integral Invariants. Springer London, Limited, 2006.

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21

Deruelle, Nathalie y Jean-Philippe Uzan. Riemannian manifolds. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0042.

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This chapter introduces the Riemann tensor characterizing curved spacetimes, and then the metric tensor, which allows lengths and durations to be defined. As shown in the preceding chapter, ‘absolute, true, and mathematical’ spacetimes representing ‘relative, apparent, and common’ space and time in Einstein’s theory are Riemannian manifolds supplied with a metric and its associated Levi-Civita connection. Moreover, this metric simultaneously describes the coordinate system chosen to reference the events. The chapter begins with a study of connections, parallel transport, and curvature; the commutation of derivatives, torsion, and curvature; geodesic deviation and curvature; the metric tensor and the Levi-Civita connection; and locally inertial frames. Finally, it discusses Riemannian manifolds.
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22

Futaki, Akito. Kähler-Einstein Metrics and Integral Invariants (Lecture Notes in Mathematics). Springer, 1988.

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23

Siu, Y. T. Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics: Delivered at the German Mathematical Society Seminar in düsseldorf in June 1986. Birkhauser Verlag, 2012.

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24

Chruściel, Piotr T. Geometry of Black Holes. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198855415.001.0001.

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There exists a large scientific literature on black holes, including many excellent textbooks of various levels of difficulty. However, most of these prefer physical intuition to mathematical rigour. The object of this book is to fill this gap and present a detailed, mathematically oriented, extended introduction to the subject. The first part of the book starts with a presentation, in Chapter 1, of some basic facts about Lorentzian manifolds. Chapter 2 develops those elements of Lorentzian causality theory which are key to the understanding of black-hole spacetimes. We present some applications of the causality theory in Chapter 3, as relevant for the study of black holes. Chapter 4, which opens the second part of the book, constitutes an introduction to the theory of black holes, including a review of experimental evidence, a presentation of the basic notions, and a study of the flagship black holes: the Schwarzschild, Reissner–Nordström, Kerr, and Majumdar–Papapetrou solutions of the Einstein, or Einstein–Maxwell, equations. Chapter 5 presents some further important solutions: the Kerr–Newman–(anti-)de Sitter black holes, the Emperan–Reall black rings, the Kaluza–Klein solutions of Rasheed, and the Birmingham family of metrics. Chapters 6 and 7 present the construction of conformal and projective diagrams, which play a key role in understanding the global structure of spacetimes obtained by piecing together metrics which, initially, are expressed in local coordinates. Chapter 8 presents an overview of known dynamical black-hole solutions of the vacuum Einstein equations.
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25

Saha, Prasenjit y Paul A. Taylor. Schwarzschild’s Spacetime. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198816461.003.0003.

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The concept of a metric is motivated and introduced, along with the introduction of relativistic quantities of spacetime, proper time, and Einstein’s field equations. Geodesics are cast in basic form as a Hamiltonian dynamical problem, which readers are guided towards exploring numerically themselves. The specific case of the Schwarzschild metric is presented, which is applicable to space around non-rotating black holes, and orbital motion around such objects is contrasted with that of Newtonian systems. Some well-known formulas for black hole phenomena are derived, such as those for light deflection (also known as gravitational lensing) and the innermost stable orbit, and their consequences discussed.
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26

Siu, Yum-Tong. Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kahler-Einstein Metrics: Delivered at the German Mathematical Society Seminar in Dusseldorf in June, 1986 (D M V Seminar). Birkhauser, 1989.

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27

1950-, Mabuchi Toshiki, Mukai Shigeru 1953- y International Tanaguchi Symposium (27th : 1990 : Sanda-shi, Japan), eds. Einstein metrics and Yang-Mills connections: Proceedings of the 27th Taniguchi international symposium. New York: M. Dekker, 1993.

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28

Steane, Andrew M. Relativity Made Relatively Easy Volume 2. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895646.001.0001.

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This is a textbook on general relativity and cosmology for a physics undergraduate or an entry-level graduate course. General relativity is the main subject; cosmology is also discussed in considerable detail (enough for a complete introductory course). Part 1 introduces concepts and deals with weak-field applications such as gravitation around ordinary stars, gravimagnetic effects and low-amplitude gravitational waves. The theory is derived in detail and the physical meaning explained. Sources, energy and detection of gravitational radiation are discussed. Part 2 develops the mathematics of differential geometry, along with physical applications, and discusses the exact treatment of curvature and the field equations. The electromagnetic field and fluid flow are treated, as well as geodesics, redshift, and so on. Part 3 then shows how the field equation is solved in standard cases such as Schwarzschild-Droste, Reissner-Nordstrom, Kerr, and internal stellar structure. Orbits and related phenomena are obtained. Black holes are described in detail, including horizons, wormholes, Penrose process and Hawking radiation. Part 4 covers cosmology, first in terms of metric, then dynamics, structure formation and observational methods. The meaning of cosmic expansion is explained at length. Recombination and last scattering are calculated, and the quantitative analysis of the CMB is sketched. Inflation is introduced briefly but quantitatively. Part 5 is a brief introduction to classical field theory, including spinors and the Dirac equation, proceeding as far as the Einstein-Hilbert action. Throughout the book the emphasis is on making the mathematics as clear as possible, and keeping in touch with physical observations.
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29

Park, Jihun, Xiuxiong Chen, Ivan Cheltsov y Ludmil Katzarkov. Birational Geometry, Kähler-Einstein Metrics and Degenerations: Moscow, Shanghai and Pohang, June-November 2019. Springer International Publishing AG, 2022.

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30

Fredholm Operators And Einstein Metrics on Conformally Compact Manifolds (Memoirs of the American Mathematical Society). American Mathematical Society, 2006.

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31

An Introduction to Extremal Kahler Metrics. Providence, Rhode Island: Springer, 2014.

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32

AdS/CFT correspondence: Einstein metrics and their conformal boundaries : 73rd meeting of theoretical physicists and mathematicians, Strasbourg, September 11-13, 2003. Zürich: European Mathematical Society, 2005.

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33

Silberstein, Michael, W. M. Stuckey y Timothy McDevitt. Resolving Puzzles, Problems, and Paradoxes from General Relativity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198807087.003.0004.

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The main thread of chapter 3 introduces general relativity (GR), Big Bang cosmology, and closed timelike curves, showing how the ant’s-eye view leads to the puzzle of the creation of the universe, the horizon problem, the flatness problem, the low entropy problem, and the paradoxes of closed time-like curves. All these puzzles, problems, and paradoxes of the dynamical universe are resolved using the God’s-eye view of the adynamical block universe. Accordingly, Einstein’s equations of GR are not understood dynamically, but rather adynamically, that is, as a global self-consistency constraint between the spacetime metric and stress–energy tensor throughout the spacetime manifold. This is “spatiotemporal ontological contextuality” as applied to GR. The philosophical nuances such as the status of the block universe argument in GR and debates about the Past Hypothesis have been placed in Philosophy of Physics for Chapter 3. The associated formalism and computations are in Foundational Physics for Chapter 3.
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34

Ads/Cft Correspondence: Einstein Metrics and Their Conformal Boundaries: 73rd Meeting of Theoretical Physicists and Mathematicians .. (IRMA Lectures in Mathematics & Theoretical Physics). A S M International, Incorporated, 2005.

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