广义相对论简明教程(第2版)


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收藏	广义相对论简明教程(第2版) 作者:Foster,JD,JFoster,Nightingale, 分类:逻辑学人气: 装帧:平装 / 32开 / 230页 / 0字 ISBN(10位/13位):7506236265 出版:世界图书出版公司于1998-03- 1出版定价:¥40元标签(Tags):哲学物理学逻辑学收藏人数：

简介:

Contents

Preface

Introduction

1 Vector and tensor fields

1.0 Introduction

1.1 Coordinate systems in Euclidean space

1.2 Suffix notation

1.3 Tangents and gradients

1.4 Coordinate transfonnations in Euclidean space

1.5 Tensor fields in Euclidean space

1.6 Surfaces in Euclidean space

1.7 Manifolds

1.8 Tensor fields on manifolds

1.9 Metric properties

1.10 What and where are the bases?

Problems 1

2.The spacetime of general relativity and paths of particles

2.0 Introduction

2.1 Geodesics

2.2 Parallel vectors along a curve

2.3 Absolute and covariant differentiation

2.4 Geodesic coordinates

2.5 The spacetime of general relativity

2.6 Newton's laws of motion

2.7 Gravitational potential and the geodesic

2.8 Newton's law of universal gravitation

2.9 A rotating reference system

Problems 2

3.Field equations and curvature

3.0 Introduction

3.1 The stress tensor and fluid motion

3.2 The curvature tensor and related tensors

3.3 Curvature and parallel transport

3.4 Geodesic deviation

3.5 Einstein's field equations

3.6 Einstein's equation comparedwith Poisson's equation

3.7 The Schwarzschild solution

Problems 3

4. Physics in the vicinity of a massive object

4.0 Introduction

4.1 Length and time

4.2 Radar sounding

4.3 Spectral shift

4.4 General particle motion (including photons)

4.5 Perihelion advance

4.6 Bending of light

4.7 Geodesic effect

4.8 Blackholes

4.9 Other coordinate systems

Problems 4

5.Gravitational radiation

5.0 Introduction

5.1 What wiggles?

5.2 Two polarizations

5.3 Simple generation and detection

Problems 5

6.Elements of cosmology

6.0 Introduction

6.1 Robertson-Walker line element

6.2 Field equations

6.3 The Friedmann models

6.4 Comment on Einstein's models

6.5 Newtonian dust

Problems 6

A.Special relativity review

A.O Introduction

A.l Lorentz transfonnations

A.2 Relativistic addition of velocities

A.3 Simultaneity

A.4 Time dilation, length contraction

A.5 Spacetime diagrams

A.6 Some standard 4vectors

A.7 Doppler effect

A.8 Electromagnetism

Problems A

B.Tbe Chinese connection

B.O Background

B.l Lanchester's transporter on a plane

B.2 Lanchester's transporter on a surface

B.3 A trip at constant latitude

References

Index

内容摘要:

Introduction

The originator of the general theory of relativity was Einstein, and in 1919

he wrotel: The special theory, on which the general theory rests, applies to

all physical phenomena with the exception of gravitation; the general theory

provides the law of gravitation and its relation to the otherforces ofnature.

The claim that the general theory provides the law of gravitation does

not mean that H.G. Wells' Mr Cavor could now introduce an antigravity

material and glide up to the Moon, nor, for example, that we might produce

intense pennanent gravitational fields in the laboratory, as we can electric

fields. It means only that all the properties of gravity of which we are aware

are explicable by the theory, and that gravity is essentially a matter of

geometry. Before saying how we get to the general from the special theory,

we must first discuss the principle of equivalence.

In electrostatics, when a test particle of charge q and inertial mass m,

is placed in a static field E, it experiences a force qE and undergoes an

acceleration a given by

a = (qlm)E. (0.1)

In contrast, a test particle of gravitational mass mg and inertial mass mi,

placed in a gravitational field g expenences a force mgg and undergoes an

acceleration a given by

a = (mg/m)g. (0.2),

It.is an experimental fact (known since Galileo's time) that different parti-

cles placed in the same gravitational field acquire the same acceleration (see

Fig. 0.1). This implies that the ratio mg/mi appearing in equation (0.2)

is the same for all particles, and by an appropriate choice of units this

ratio may be taken to be unity. This equivalence of gravitational and in-

ertial mass (which allows us to drop the qualification, and simply refer to

mass) has been checked experimentally by Eotvos (in 1889 and 1922), and

more recently and more accurately (to one part in 10) by Dicke and his

co-workers (in the 1960s). In contrast, the ratio q/mi occurring in equa-

tion (0.1) is not the same for all particles (see Fig. 0.1).

Let us now consider the principle of equivalence, which it is instructive

to do from the point of view of Einstein's freely faUing elevator. If we

consider a projectile shot from one side of the elevator cabin to the other,

the projectile appears to go in a straight line (the elevator cable being cut)

rather than in the usual curved trajectory. Projectiles that are released

from rest relative to the cabin remain floating weightless in the cabin. Of

course, if the cabin is left to fall for a long time, the particles gradually draw

closer together, since they are falling down radial lines towards a common

point which is the center of the Earth. However, if we make the proviso

that the cabin is in this state for a short time, as well as being spatially

small enough for the neglect of tidal forces in general, then the freely falling

cabin (which may have X, Y, Z coordinates chalked on its walls, as well as

a cabin clock measuring time T) looks remarkably like an inertial frame of

reference, and therefore the laws of special relativity hold sway inside the

cabin. (The cabin must not only occupy a small region of spacetime, it must

also be nonrotating with respect to distant matter in the universe) All

this follows from the fact that the acceleration of any particle relative to the

cabin is zero because they both have the same acceleration relative to the

Earth, and we see that the equivalence of inertial and gravitational mass is

an essential feature of the discussion. We may incorporate these ideas into

the principle of equivalence, which is this: in a freely falling (no'nrotating)

laboratory occupying a small region of spacetime, the laws of physics are

the laws of special relativity.

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