作者︰(英國)舒茨 (Bernard F.Schutz)
preface to the second editionpreface to the first edition1 special relativity1.1 fundamental principles of special relativity (sr) theory1.2 definition of an inertial observer in sr1.3 new units1.4 spacetime diagrams1.5 construction of the coordinates used by another observer1.6 invariance of the interval1.7 invariant hyperbolae1.8 particularly important results1.9 the lorentz transformation1.10 the velocity-composition law1.11 paradoxes and physical intuition1.12 further reading1.13 appendix: the twin 'paradox' dissected1.14 exercises2 vector analysis in special relativity2.1 definition of a vector2.2 vector algebra2.3 the four-velocity2.4 the four-momentum2.5 scalar product2.6 applications2.7 photons2.8 further reading2.9 exercises3 tensor analysis in special relativity3.1 the metric tensor3.2 definition of tensors3.3 the tensors: one-forms3.4 the tensors3.5 metric as a mapping of vectors into one-forms3.6 finally: (m)tensors3.7 index 'raising' and 'lowering'3.8 differentiation of tensors3.9 further reading3.10 exercises4 perfect fluids in special relativity4.1 fluids4.2 dust: the number-flux vector4.3 one-forms and surfaces4.4 dust again: the stress--energy tensor4.5 general fluids4.6 perfect fluids4.7 importance for general relativity4.8 gauss' law4.9 further reading4.10 exercises5 preface to curvature5.1 on the relation of gravitation to curvature5.2 tensor algebra in polar coordinates5.3 tensor calculus in polar coordinates5.4 christoffel symbols and the metric5.5 noncoordinate bases5.6 looking ahead5.7 further reading5.8 exercises6 curved manifolds6.1 differentiable manifolds and tensors6.2 riemannian manifolds6.3 covariant differentiation6.4 parallel-transport, geodesics, and curvature6.5 the curvature tensor6.6 bianchi identities: ricci and einstein tensors6.7 curvature in perspective6.8 further reading6.9 exercises7 physics in a curved spacetime7.1 the transition from differential geometry to gravity7.2 physics in slightly curved spacetimes7.3 curved intuition7.4 conserved quantities7.5 further reading7.6 exercises8 the einstein field equations8.1 purpose and justification of the field equations8.2 einstein's equations8.3 einstein's equations for weak gravitational fields8.4 newtonian gravitational fields8.5 further reading8.6 exercises9 gravitational radiation9.1 the propagation of gravitational waves9.2 the detection of gravitational waves9.3 the generation of gravitational waves9.4 the energy carried away by gravitational waves9.5 astrophysical sources of gravitational waves9.6 further reading9.7 exercises10 spherical solutions for stars10.1 coordinates for spherically symmetric spacetimes10.2 static spherically symmetric spacetimes10.3 static perfect fluid einstein equations10.4 the exterior geometry10.5 the interior structure of the star10.6 exact interior solutions10.7 realistic stars and gravitational collapse10.8 further reading10.9 exercises11 schwarzschild geometry and black holes11.1 trajectories in the schwarzschild spacetime11.2 nature of the surface r = 2m11.3 general black holes11.4 real black holes in astronomy11.5 quantum mechanical emission of radiation by black holes: thehawking process11.6 further reading11.7 exercises12 cosmology12.1 what is cosmology?12.2 cosmological kinematics: observing the expandinguniverse12.3 cosmological dynamics: understanding the expandinguniverse12.4 physical cosmology: the evolution of the universe weobserve12.5 further reading12.6 exercisesappendix a summary of linear algebrareferencesindex
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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