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书名 引力--基础与前沿(影印版)/引进系列/中外物理学精品书系
分类 科学技术-自然科学-物理
作者 (印度)帕德马纳班
出版社 北京大学出版社
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简介
目录

List of exercises

List of projects

Preface

How to use this book

1 Special relativity

 1.1 Introduction

 1.2 The principles of special relativity

 1.3 Transformation of coordinates and velocities

  1.3.1 Lorentz transformation

  1.3.2 Transformation of velocities

  1.3.3 Lorentz boost in an arbitrary direction

 1.4 Four-vectors

  1.4.1 Four-velocity and acceleration

 1.5 Tensors

 1.6 Tensors as geometrical objects

 1.7 Volume and surface integrals in four dimensions

 1.8 Particle dynamics

 1.9 The distribution function and its moments

 1.10 The Lorentz group and Pauli matrices

2 Scalar and electromagnetic fields in special relativity

 2.1 Introduction

 2.2 External fields of force

 2.3 Classical scalar field

  2.3.1 Dynamics of a particle interacting with a scalarfield

  2.3.2 Action and dynamics of the scalar field

  2.3.3 Energy-momentum tensor for the scalar field

  2.3.4 Free field and the wave solutions

  2.3.5 Why does the scalar field lead to an attractiveforce?

 2.4 Electromagnetic field

  2.4.1 Charged particle in an electromagnetic field

  2.4.2 Lorentz transformation of electric and magneticfields

  2.4.3 Current vector

 2.5 Motion in the Coulomb field

 2.6 Motion in a constant electric field

 2.7 Action principle for the vector field

 2.8 Maxwell's equations

 2.9 Energy and momentum of the electromagnetic field

 2.10 Radiation from an accelerated charge

 2.11 Larmor formula and radiation reaction

3 Gravity and spaeetime geometry: the inescapable connection

 3.1 Introduction

 3.2 Field theoretic approaches to gravity

 3.3 Gravity as a scalar field

 3.4 Second rank tensor theory of gravity

 3.5 The principle of equivalence and the geometricaldescription of gravity

   3.5.1 Uniformly accelerated observer

   3.5.2 Gravity and the flow of time

4 Metric tensor, geodesics and covariant derivative

  4.1 Introduction

  4.2 Metric tensor and gravity

  4.3 Tensor algebra in curved spacetime

  4.4 Volume and surface integrals

  4.5 Geodesic curves

   4.5.1 Properties of geodesic curves

   4.5.2 Affine parameter and null geodesics

  4.6 Covariant derivative

   4.6.1 Geometrical interpretation of the covariantderivative

   4.6.2 Manipulation of covariant derivatives

  4.7 Parallel transport

  4.8 Lie transport and Killing vectors

  4.9 Fermi-Walker transport

5 Curvature of spaeetime

  5.1 Introduction

  5.2 Three perspectives on the spacetimecurvature

   5.2.1 Parallel transport around a closed curve

   5.2.2 Non-commutativity of covariant derivatives

5.2.3 Tidal acceleration produced by gravity

 5.3 Properties of the curvature tensor

5.3.1 Algebraic properties

5.3.2 Bianchi identity

5.3.3 Ricci tensor, Weyl tensor and conformal transformations

 5.4 Physics in curved spacetime

5.4.1 Particles and photons in curved spacetime

5.4.2 Ideal fluid in curved spacetime

5.4.3 Classical field theory in curved spacetime

5.4.4 Geometrical optics in curved spacetime

 5.5 Geodesic congruence and Raychaudhuri's equation

5.5.1 Timelike congruence

5.5.2 Null congruence

5.5.3 Integration on null surfaces

 5.6 Classification of spacetime curvature

5.6.1 Curvature in two dimensions

5.6.2 Curvature in three dimensions

5.6.3 Curvature in four dimensions

6 Einstein's field equations and gravitational dynamics

 6.1 Introduction

 6.2 Action and gravitational field equations

6.2.1 Properties of the gravitational action

6.2.2 Variation of the gravitational action

6.2.3 A digression on an alternative form of action functional

6.2.4 Variation of the matter action

6.2.5 Gravitational field equations

 6.3 General properties of gravitational field equations

 6.4 The weak field limit of gravity

6.4.1 Metric of a stationary source in linearized theory

6.4.2 Metric of a light beam in linearized theory

 6.5 Gravitational energy-momentum pseudo-tensor

7 Spherically symmetric geometry

 7.1 Introduction

 7.2 Metric of a spherically symmetric spacetime

7.2.1 Static geometry and Birkoff's theorem

7.2.2 Interior solution to the Schwarzschild metric

7.2.3 Embedding diagrams to visualize geometry

 7.3 Vaidya metric of a radiating source

 7.4 Orbits in the Schwarzschild metric

7.4.1 Precession of the perihelion

7.4.2 Deflection of an ultra-relativistic particle

7.4.3 Precession of a gyroscope

 7.5 Effective potential for orbits in the Schwarzschild metric

 7.6 Gravitational collapse of a dust sphere

8 Black holes

 8.1 Introduction

 8.2 Horizons in spherically symmetric metrics

 8.3 Kruskal-Szekeres coordinates

8.3.1 Radial infall in different coordinates

8.3.2 General properties of maximal extension

 8.4 Penrose-Carter diagrams

 8.5 Rotating black holes and the Kerr metric

8.5.1 Event horizon and infinite redshift surface

8.5.2 Static limit

8.5.3 Penrose process and the area of the event horizon

8.5.4 Particle orbits in the Kerr metric

 8.6 Super-radiance in Kerr geometry

 8.7 Horizons as null surfaces

9 Gravitational waves

 9.1 Introduction

 9.2 Propagating modes of gravity

 9.3 Gravitational waves in a flat spacetime background

9.3.1 Effect of the gravitational wave on a system of particles

 9.4 Propagation of gravitational waves in the curved spacetime

 9.5 Energy and momentum of the gravitational wave

 9.6 Generation of gravitational waves

9.6.1 Quadrupole formula for the gravitational radiation

9.6.2 Back reaction due to the emission of gravitational waves

  9.7 General relativistic effects in binary systems

9.7.1 Gravitational radiation from binary pulsars

9.7.2 Observational aspects of binary pulsars

9.7.3 Gravitational radiation from coalescing binaries

10 Relativistic cosmology

 10.1 Introduction

 10.2 The Friedmann spacetime

 10.3 Kinematics of the Friedmann model

10.3.1 The redshifting of the momentum

10.3.2 Distribution functions for particles and photons

10.3.3 Measures of distance

 10.4 Dynamics of the Friedmann model

 10.5 The de Sitter spacetime

 10.6 Brief thermal history of the universe

10.6.1 Decoupling of matter and radiation

 10.7 Gravitational lensing

 10.8 Killing vectors and the symmetries of the space

10.8.1 Maximally symmetric spaces

10.8.2 Homogeneous spaces

11 Differential forms and exterior calculus

 11.1 Introduction

 11.2 Vectors and 1-forms

 11.3 Differential forms

 11.4 Integration of forms

 11.5 The Hodge duality

 11.6 Spin connection and the curvature 2-forms

11.6.1 Einstein-Hilbert action and curvature 2-forms

11.6.2 Gauge theories in the language of forms

12 Hamiltoulan structure of general relativity

 12.1 Introduction

 12.2 Einstein's equations in (1+3)-form

 12.3 Gauss--Codazzi equations

 12.4 Gravitational action in (l+3)-form

12.4.1 The Hamiltonian for general relativity

12.4.2 The surface term and the extrinsic curvature

12.4.3 Variation of the action and canonical momenta

 12.5 Junction conditions

12.5.1 Collapse of a dust sphere and thin-shell

13 Evolution of cosmological perturbations

 13.1 Introduction

 13.2 Structure formation and linear perturbation theory

 13.3 Perturbation equations and gauge transformations

13.3.1 Evolution equations for the source

 13.4 Perturbations in dark matter and radiation

13.4.1 Evolution of modes with A >> dH

13.4.2 Evolution of modes with A << dH in the radiation dominated phase

13.4.3 Evolution in the matter dominated phase

13.4.4 An alternative description of the matter-radiation system

 13.5 Transfer function for the matter perturbations

 13.6 Application: temperature anisotropies of CMBR

13.6.1 The Sachs-Wolfe effect

14 Quantum field theory in curved spaeetime

 14.1 Introduction

 14.2 Review of some key results in quantum field theory

14.2.1 Bogolyubov transformations and the particle concept

14.2.2 Path integrals and Euclidean time

 14.3 Exponential redshift and the thermal spectrum

 14.4 Vacuum state in the presence of horizons

 14.5 Vacuum functional from a path integral

 14.6 Hawking radiation from black holes

 14.7 Quantum field theory in a Friedmann universe

14.7.1 General formalism

14.7.2 Application: power law expansion

 14.8 Generation of initial perturbations from inflation

14.8.1 Background evolution

14.8.2 Perturbations in the inflationary models

15 Gravity in higher and lower dimensions

 15.1 Introduction

 15.2 Gravity in lower dimensions

15.2.1 Gravity and black hole solutions in (1 + 2) dimensions

15.2.2 Gravity in two dimensions

 15.3 Gravity in higher dimensions

15.3.1 Black holes in higher dimensions

15.3.2 Brane world models

 15.4 Actions with holography

 15.5 Surface term and the entropy of the horizon

16 Gravity as an emergent phenomenon

 16.1 Introduction

 16.2 The notion of an emergent phenomenon

 16.3 Some intriguing features of gravitational dynamics

16.3.1 Einstein's equations as a thermodynamic identity

16.3.2 Gravitational entropy and the boundary term in the action

16.3.3 Horizon thermodynamics and Lanczos-Lovelock theories

 16.4 An alternative perspective on gravitational dynamics

Notes

Index

编辑推荐

帕德马纳班编著的这本《引力--基础与前沿》覆盖了当代引力理论的方方面面。在基础部分,本书首先介绍了引力理论的一些基本的概念、方法和公式。之后,本书进而对引力理论在球对称时空、黑洞、引力波和宇宙学领域的应用做了系统而深入的介绍。在前沿部分,本书讨论了宇宙微扰论、弯曲时空量子场论和广义相对论的Hamiltonian结构等当前很受关注的重要问题。本书适合理论物理所有领域的研究者和研究生阅读。

内容推荐
本书覆盖了当代引力理论的方方面面。首先介绍了引力理论的一些基本的概念、方法和公式。进而对引力理论在球对称时空、黑洞、引力波和宇宙学领域的应用做了系统而深入的介绍。
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