Preface
In our experience, while students may initially be attracted to general relativity by
the fact that it is the area of theoretical physics that predicts the existence of black
holes, gravitational waves and the big-bang beginning of the universe, and that all
three of these phenomena are currently being confirmed by observations, students
are attracted to the theory of these phenomena because general relativity provides a
framework for modelling them using abstract mathematics. When such students are
beginning research and looking around for ways to “get involved”, we envisage that
this book might possibly provide what they are looking for. Our approach is strongly
geometrical. Even the speculative explicit models which we describe in order to
stimulate further ideas and research are geometrically motivated. These include a
model of the gravitational field of a Kerr black hole incorporating matter escaping
at the speed of light and diminishing the mass and angular momentum; a light-like
charge in electromagnetic theory whose Maxwell field is a light-like analogue of the
Liénard-Wiechert field; a magnetic black hole; the analogue in general relativity of
a magnetic monopole, moving in external gravitational and electromagnetic fields;
run-away motion of Reissner-Nordström particles in the absence of external fields;
and a model of colliding gravitational waves leading to a de Sitter or an anti-de
Sitter universe. None of these examples could be claimed to be “fully understood”
and thereby leave room for development.
We assume a strong mathematical background in differential geometry (and
thus in tensor calculus); although we only occasionally refer to it, knowledge of
the powerful Cartan calculus is very useful for carrying out some of the involved
explicit calculations referred to in the text. Photons and material particles play
important roles in general relativity, and this fact is strongly represented in the
topics described in this book. Such objects are involved in analysing and measuring
gravitational fields and in constructing mathematical models of gravitational fields
of various types. This means that from the space-time geometry point of view, the
study of congruences of world lines, both time-like and light-like, are of paramount
importance in general relativity. For this reason, the book begins with a standard
description of both types of congruence. A key role in measuring a gravitational
field is played by the time-like congruences and, in particular, the use of deviation
equations in this context. These are therefore discussed at the beginning of the
book making use of Synge’s world function in the process. With an emphasis
v
In our experience, while students may initially be attracted to general relativity by
the fact that it is the area of theoretical physics that predicts the existence of black
holes, gravitational waves and the big-bang beginning of the universe, and that all
three of these phenomena are currently being confirmed by observations, students
are attracted to the theory of these phenomena because general relativity provides a
framework for modelling them using abstract mathematics. When such students are
beginning research and looking around for ways to “get involved”, we envisage that
this book might possibly provide what they are looking for. Our approach is strongly
geometrical. Even the speculative explicit models which we describe in order to
stimulate further ideas and research are geometrically motivated. These include a
model of the gravitational field of a Kerr black hole incorporating matter escaping
at the speed of light and diminishing the mass and angular momentum; a light-like
charge in electromagnetic theory whose Maxwell field is a light-like analogue of the
Liénard-Wiechert field; a magnetic black hole; the analogue in general relativity of
a magnetic monopole, moving in external gravitational and electromagnetic fields;
run-away motion of Reissner-Nordström particles in the absence of external fields;
and a model of colliding gravitational waves leading to a de Sitter or an anti-de
Sitter universe. None of these examples could be claimed to be “fully understood”
and thereby leave room for development.
We assume a strong mathematical background in differential geometry (and
thus in tensor calculus); although we only occasionally refer to it, knowledge of
the powerful Cartan calculus is very useful for carrying out some of the involved
explicit calculations referred to in the text. Photons and material particles play
important roles in general relativity, and this fact is strongly represented in the
topics described in this book. Such objects are involved in analysing and measuring
gravitational fields and in constructing mathematical models of gravitational fields
of various types. This means that from the space-time geometry point of view, the
study of congruences of world lines, both time-like and light-like, are of paramount
importance in general relativity. For this reason, the book begins with a standard
description of both types of congruence. A key role in measuring a gravitational
field is played by the time-like congruences and, in particular, the use of deviation
equations in this context. These are therefore discussed at the beginning of the
book making use of Synge’s world function in the process. With an emphasis
v