舒茨编著的《广义相对论基础教程(第2版)》用尽可能少的数学背景，清晰、易懂、简明地介绍了广义相对论。在相对论的框架内尽可能全面的包括更多的内容，从黑洞到引力透视，脉冲星到整个宇宙学的研究，形成一个有机的整体。书中包括了天体学家的很多重大发现，在第一版的基础上增加了一章讲述相对论星体，包括了有关脉冲星的最新知识，有关宇宙学的一章完全更新，全面，综合的讲述了现代发展和预期前景。300多道练习题，许多是这本书中新增加的，这让学生有足够的信心学习好广义相对论和必需的数学知识。本书的写作风格更加使得这门科目更加容易理解。目次：狭义相对论；狭义相对论中的向量分析；狭义相对论中的张量分析；狭义相对论中的完全流；曲率介绍；弯曲流形；弯曲时空中的物理学；einstein场方程；引力辐射；星体的球面解；schwarzschild几何和黑洞；宇宙学。

本书适用于高年级本科生及更层次的，对宇宙学，天体物理学，以及引力物理实验感兴趣的科研人员。

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