General Relativistic Dynamics

The following sections are included:

• Contents

One often reads about the beauty and importance of general relativity (GR). It is viewed almost universally as our premier theory of gravity, superseding Newton's theory of gravity in a profound way. We share this view whole-heartedly. However, while there have been a very large number of papers written in the field, it is disconcerting to note how little there is in the way of a connection of this large accumulated effort with the great body of the world's physicists and astronomers. Many of these papers are of great mathematical complexity, decipherable only by the experts in the field. Even when decoded, many, if not most, have little relevance to the important issues of physics and astronomy. This is unfortunate as gravity is assuming a greater role of significance in science and the best theory of gravity should be readily accessible to the non-experts…

The following sections are included:

• Basic principles

• The spacetime interval and the Lorentz transformation

• Lorentz contraction and time dilation

• Causality

• Transformation of velocity and the aberration of light

• Four-vectors and four-tensors

• Special relativistic dynamics

• Relativistic Doppler shift

The following sections are included:

• Introduction

• Velocity–Doppler factor connection

• Composition law for velocities and Doppler factors

• Derivation of the Lorentz transformation

• The twin or clock paradox

The following sections are included:

• The need for a new theory of gravity

• The Principle of Equivalence

• The metric tensor

• Basic tensor calculus–introduction

• Parallel transport, spacetime curvature and the Riemann tensor

• Geodesics

• Covariant conservation laws and the Einstein field equations

• Einstein–Maxwell equations and motion of a charged body in general relativity

• Summary of the steps from Newtonian gravity to Einstein's general relativity

The following sections are included:

• The metric

• The measurement of distance and time in general relativity

• The event horizon, black holes and singularities

• The tests of general relativity

The following sections are included:

• Introduction

• Linearized field equations

• The energy issue and the pseudotensor

• The energy localization hypothesis

The following sections are included:

• The hierarchy of scales

• The fundamental interactions of nature

• The Planck scale and the issue of the quantization of gravity

• Adding spin and charge to the Planck scale

• Quantum limits, spectra, the value of α

The following sections are included:

• Sizes of astronomical elements

• Early ideas about cosmology

• Friedmann universes

• The cosmological term

The following sections are included:

• Introduction

• General relativistic effects on the stellar motions in galaxies

• Modeling the observed galactic rotation curves

• A velocity dispersion test for the presence of extra matter

• Summary comments on rotation velocities of galaxies

The following sections are included:

• Preliminary comments

• Spherical dust collapse

• Velocity of particles falling in vacuum toward a spherical concentration of mass

• The velocity of dust in collapse

• Observing an idealized galactic cluster

• Current evidence for dark matter

The following sections are included:

• The background

• Creating closed timelike curves and Gödel's spacetime

• Re-examining the standard closed timelike curve interpretation

• The role of our experience in nature

• Gott's moving cosmic strings

In a very interesting recent book The Trouble With Physics [98], the author, L. Smolin provides his views on the misdirection of current physics research. His delineation of the sociology of theoretical physics research is astute and insightful, delivered with great panache. After a particularly scathing assessment of the string theory community and what is in his view a rather limited set of achievements, he leans towards his own favored directions in quantum gravity, decrying the dearth of revolutionary fervor in the physics community. Ironically, from our perspective, what is particularly valuable about this work is that it encapsulates the commonality of mind sets of what has become the dominant string theory group “A” and the supposed independents “B”…

We focused on various goals in this book. We wished to present the reader with a simple introduction to the basics of special and general relativity, theories that have changed our view of the physical world in the most profound ways. As for special relativity developed in Chapter 2, the very solidly supported Einstein theory of spacetime exempting gravity that reveals its correctness on a daily basis in laboratories throughout the world, our presentation had two foci. There was the standard approach of most texts but the best thus far in our opinion, the classical treatise of Landau and Lifshitz [3], is beyond the level of probably most general scientifically inclined readers. It is also somewhat terse in its presentation. The aim was to simplify this kind of treatment and expand upon parts that require more explanation…

The following sections are included:

• Appendix A: Critical Challenges and Our Replies Critical Challenges and Our Replies

• Appendix B: Radial Velocity Derivation Details

• Bibliography

• Acknowledgements

• Index