廣義相對論基礎教程

內容概要

　　《廣義相對論基礎教程(第2版)(英文影印版)》是一部教程，這是第二版，用盡可能少的數(shù)學背景，清晰，易懂，簡明地介紹了廣義相對論。在相對論的框架內盡可能全面的包括更多的內容，從黑洞到引力透視，脈沖星到整個宇宙學的研究，形成一個有機的整體。書中包括了天體學家的很多重大發(fā)現(xiàn)，增加了一章講述相對論星體，包括了有關脈沖星的最新知識，有關宇宙學的一章完全更新，全面，綜合的講述了現(xiàn)代發(fā)展和預期前景。300多道練習題，許多是這本書中新增加的，這讓學生有足夠的信心學習好廣義相對論和必需的數(shù)學知識，本書的寫作風格更加使得這門科目更加容易理解。目次：狹義相對論；狹義相對論中的向量分析；狹義相對論中的張量分析；狹義相對論中的完全流；曲率介紹；彎曲流形；彎曲時空中的物理學；einstein場方程；引力輻射；星體的球面解；schwarzschild幾何和黑洞；宇宙學。
　　讀者對象：適用于高年級本科生及更層次的，對宇宙學，天體物理學，以及引力物理實驗感興趣的科研人員。

作者簡介

作者：(英國)舒茨 (Bernard F.Schutz)

書籍目錄

preface to the second edition
preface to the first edition
1 special relativity
1.1 fundamental principles of special relativity (sr) theory
1.2 definition of an inertial observer in sr
1.3 new units
1.4 spacetime diagrams
1.5 construction of the coordinates used by another observer
1.6 invariance of the interval
1.7 invariant hyperbolae
1.8 particularly important results
1.9 the lorentz transformation
1.10 the velocity-composition law
1.11 paradoxes and physical intuition
1.12 further reading
1.13 appendix: the twin 'paradox' dissected
1.14 exercises
2 vector analysis in special relativity
2.1 definition of a vector
2.2 vector algebra
2.3 the four-velocity
2.4 the four-momentum
2.5 scalar product
2.6 applications
2.7 photons
2.8 further reading
2.9 exercises
3 tensor analysis in special relativity
3.1 the metric tensor
3.2 definition of tensors
3.3 the tensors: one-forms
3.4 the tensors
3.5 metric as a mapping of vectors into one-forms
3.6 finally: (m)tensors
3.7 index 'raising' and 'lowering'
3.8 differentiation of tensors
3.9 further reading
3.10 exercises
4 perfect fluids in special relativity
4.1 fluids
4.2 dust: the number-flux vector
4.3 one-forms and surfaces
4.4 dust again: the stress--energy tensor
4.5 general fluids
4.6 perfect fluids
4.7 importance for general relativity
4.8 gauss' law
4.9 further reading
4.10 exercises
5 preface to curvature
5.1 on the relation of gravitation to curvature
5.2 tensor algebra in polar coordinates
5.3 tensor calculus in polar coordinates
5.4 christoffel symbols and the metric
5.5 noncoordinate bases
5.6 looking ahead
5.7 further reading
5.8 exercises
6 curved manifolds
6.1 differentiable manifolds and tensors
6.2 riemannian manifolds
6.3 covariant differentiation
6.4 parallel-transport, geodesics, and curvature
6.5 the curvature tensor
6.6 bianchi identities: ricci and einstein tensors
6.7 curvature in perspective
6.8 further reading
6.9 exercises
7 physics in a curved spacetime
7.1 the transition from differential geometry to gravity
7.2 physics in slightly curved spacetimes
7.3 curved intuition
7.4 conserved quantities
7.5 further reading
7.6 exercises
8 the einstein field equations
8.1 purpose and justification of the field equations
8.2 einstein's equations
8.3 einstein's equations for weak gravitational fields
8.4 newtonian gravitational fields
8.5 further reading
8.6 exercises
9 gravitational radiation
9.1 the propagation of gravitational waves
9.2 the detection of gravitational waves
9.3 the generation of gravitational waves
9.4 the energy carried away by gravitational waves
9.5 astrophysical sources of gravitational waves
9.6 further reading
9.7 exercises
10 spherical solutions for stars
10.1 coordinates for spherically symmetric spacetimes
10.2 static spherically symmetric spacetimes
10.3 static perfect fluid einstein equations
10.4 the exterior geometry
10.5 the interior structure of the star
10.6 exact interior solutions
10.7 realistic stars and gravitational collapse
10.8 further reading
10.9 exercises
11 schwarzschild geometry and black holes
11.1 trajectories in the schwarzschild spacetime
11.2 nature of the surface r = 2m
11.3 general black holes
11.4 real black holes in astronomy
11.5 quantum mechanical emission of radiation by black holes: the
hawking process
11.6 further reading
11.7 exercises
12 cosmology
12.1 what is cosmology?
12.2 cosmological kinematics: observing the expanding
universe
12.3 cosmological dynamics: understanding the expanding
universe
12.4 physical cosmology: the evolution of the universe we
observe
12.5 further reading
12.6 exercises
appendix a summary of linear algebra
references
index

章節(jié)摘錄

版權頁：插圖：Although stationary black holes are simple, there are situations where black holes areexpected to be highly dynamical, and these are more difficult to treat analytically. When ablack hole is formed, any initial asymmetry （such as quadrupole moments） must be radi-ated away in gravitational wave.s, until finally only the mass and angular momentum areleft behind. This generally happens quickly: studies oflinear perturbations of black holesshow that black holes have a characteristic spectrum of oscillations, but that they typicallydamp out （ring down） exponentially after only a few cycles （Kokkotas and Schmidt 1999）.The Kerr metric takes over very quickly.   Even more dynamical are black holes in collision, either with other black holes or withstars. As described in Ch. 9. binary systems involving black holes will eventually merge,and black holes in the centers of galaxies can merge with other massive holes when galax-ies merge. These situations can only be studied numerically, by using computers to solveEinstein's equations and perform a dynamical simulation.Numerical techniques for GR have been developed over a period of sevefal decades, butprogress initially was slow. The coordinate freedom of general relativity, coupled with thecomplexity of the Einstein equations, means that there is no unique way to formulate asystem of equations for the computer. Most formulations have turned out to lead to intrin-sically unstable numerical schemes, and finding a stable scheme took much trial and error.Moreover, when black holes are invoved the full metric has a singularity where its com-ponents diverge: this has someho\x, to be removed from the numerical domain, becausecomputers can work only to a finite precision, See Bona and Palenzuela-Luque （2005） andAlcubierre （2008） for surveys of these problems and their solutions.

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