COSMIC STRINGS IN THE WIRE APPROXIMATION

This free book is a comprehensive survey of the current state of knowledge about the
dynamics and gravitational properties of cosmic strings treated in the idealized
classical approximation as line singularities described by the Nambu-Goto
action. The author’s purpose is to provide a standard reference to all work that
has been published since the mid-1970s and to link this work together in a
single conceptual framework and a single notational formalism. A working
knowledge of basic general relativity is assumed. The ebook will be essential
reading for researchers and postgraduate students in mathematics, theoretical
physics, and astronomy interested in cosmic strings.

One of the most striking successes of modern science has been to reduce the
complex panoply of dynamical phenomena we observe in the world around usfrom
the build-up of rust on a car bumper to the destructive effects of cyclonic
winds-to the action of only four fundamental forces: gravity, electromagnetism,
and the strong and weak nuclear forces. This simple picture of four fundamental
forces, which became evident only after the isolation of the strong and weak
nuclear forces in the 1930s, was simplified even further when Steven Weinberg in
1967 and Abdus Salam in 1968 independently predicted that the electromagnetic
and weak forces would merge at high temperatures to form a single electroweak
force.
The Weinberg-Salam model of electroweak unification was the first practical
realization of the Higgs mechanism, a theoretical device whereby a system of
initially massless particles and fields can be given a spectrum of masses by
coupling it to a massive scalar field. The model has been extremely successful
not only in describing the known weak reactions to high accuracy, but also in
predicting the masses of the carriers of the weak force, the W± and ZO bosons,
which were experimentally confirmed on their discovery in 1982-83.

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Complete, detailed instructions and numerous diagrams for constructing a do-it-
yourself telescope. No complicated mathematics are involved, and no prior
knowledge of optics or astronomy is needed to follow the text’s step-by-step
directions. Contents cover, among other topics, materials and equipment; tube
parts and alignment; eyepieces, and related problems; setting circles; and
optical principles. 1973 ed. Appendixes. Index. 6 plates. 100 figures.

PRIOR TO THE TIME of the telescope, man’s view of the celestial
universe was woefully restricted when compared with what
now can be enjoyed on any clear evening with ordinary binoculars.
There were visible to him then only the naked-eye objects, the sun
and the moon, five of the planets, and on a clear night stars down to
Ilbout the 6th magnitude, some 2,000 in all.1 A few hazy spots
could also be seen, and there would be an occasional comet. Completely
unknown were the outer planets, satellites of the planets,
Saturn’s rings, and infinite numbers of stars and galaxies.
Yet, working without optical aid, early observers managed to
make some amazingly accurate charts of the visible stars, and
amassed the observations from which the laws of planetary motion
were deduced. The principal instrument used in establishing star
and planet positions was the quadrant, a device having a graduated
are, and a pointer that pivoted about its center. With it Tycho
Brahe (1546-1601), Danish astronomer, and one of the keenest of
all observers, was able to record the positions of stars to within
one minute of arc - about 1/30 the diameter of the moon. This
was an amazing feat, wilen it is considered that olle minute of arc
is about the limit of visual acuity.
Then, in 1608, seven years after Tycho’s death, the telescope
brought upon the scene by a Dutch spectacle maker, Jan Lippershey,
to whom its invention is credited.2 The invention marked one of
the great progressive triumphs of man, enabling him to reach farther
and ever farther out into space. It was not much of a telescope,
this first refractor, con’Jisting of two spectacle lenses perhaps an
inch in diameter, one convex and the other concave, and magnifying
possibly two or three times. Lippershey, whose name historians
spell in various ways, managed to combine two such instruments
inlo a unit, and thus also made the first binocular telescope.

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The development of cosmology will no doubt be seen as one of the scientific
triumphs of the twentieth century. At its beginning, cosmology hardly existed as
a scientific discipline. By its end, the Hot Big Bang cosmology stood secure as
the accepted description of the Universe as a whole. Telescopes such as the
Hubble Space Telescope are capable of seeing light from galaxies so distant that
the light has been travelling towards us for most of the lifetime of the
Universe. The cosmic microwave background, a fossil relic of a time when
the Universe was both denser and hotter, is routinely detected and its
properties examined. That our Universe is presently expanding is established
without doubt.

The cornerstone of modem cosmology is the belief that the place which we occupy in the
Universe is in no way special. This is known as the cosmological principle, and it is
an idea which is both powerful and simple. It is intriguing, then, that for the bulk of the
history of civilization it was believed that we occupy a very special location, usually the
centre, in the scheme of things.
The ancient Greeks, in a model further developed by the Alexandrian Ptolemy, believed
that the Earth must lie at the centre of the cosmos. It would be circled by the Moon,
the Sun and the planets, and then the ‘fixed’ stars would be yet further away. A complex
combination of circular motions, Ptolemy’s Epicycles, was devised in order to explain the
motions of the planets, especially the phenomenon of retrograde motion where planets
appear to temporarily reverse their direction of motion. It was not until the early 1500s
that Copernicus stated forcefully the view, initiated nearly two thousand years before by
Aristarchus, that one should regard the Earth, and the other planets, as going around the
Sun. By ensuring that the planets moved at different speeds, retrograde motion could easily
be explained by this theory. However, although Copernicus is credited with removing
the anthropocentric view of the Universe, which placed the Earth at its centre, he in fact
believed that the Sun was at the centre.
Newton’s theory of gravity put what had been an empirical science (Kepler’s discovery
that the planets moved on elliptical orbits) on a solid footing, and it appears that Newton
believed that the stars were also suns pretty much like our own, distributed evenly throughout
infinite space, in a static configuration. However it seems that Newton was aware that
such a static configuration is unstable.
Over the next two hundred years, it became increasingly understood that the nearby
stars are not evenly distributed, but rather are located in a disk-shaped assembly which we
now know as the Milky Way galaxy. The Herschels were able to identify the disk structure
in the late 1700s, but their observations were not perfect and they wrongly concluded that
the solar system lay at its centre. Only in the early 1900s was this convincingly overturned,
by Shapley, who realised that we are some two-thirds of the radius away from the centre
of the galaxy. Even then, he apparently still believed our galaxy to be at the centre of the
Universe. Only in 1952 was it finally demonstrated, by Baade, that the Milky Way is a
fairly typical galaxy, leading to the modem view, known as the cosmological principle
(or sometimes the Copernican principle) that the Universe looks the same whoever and
wherever you are.
lt is important to stress that the cosmological principle isn’t exact. For example, no
one thinks that sitting in a lecture theatre is exactly the same as sitting in a bar, and the
interior of the Sun is a very different environment from the interstellar regions. Rather, it
is an approximation which we believe holds better and better the larger the length scales
we consider. Even on the scale of individual galaxies it is not very good, but once we take
very large regions (though still much smaller than the Universe itself), containing say a
million galaxies, we expect every such region to look more or less like every other one.
The cosmological principle is therefore a property of the global Universe, breaking down
if one looks at local phenomena.
The cosmological principle is the basis of the Big Bang Cosmology. The Big Bang is
the best description we have of our Universe, and the aim of this book is to explain why.
The Big Bang is a picture ofour Universe as an evolving entity, which was very different in
the past as compared to the present. Originally, it was forced to compete with a rival idea,
the Steady State Universe, which holds that the Universe does not evolve but rather has
looked the same forever, with new material being created to fill the gaps as the Universe
expands. However, the observations I will describe now support the Big Bang so strongly
that the Steady State theory is almost never considered.

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The present work covers practically all aspects of black hole physics and its
astrophysical applications. Among the topics treated in depth are: space-time of
stationary black holes, general theory of black holes, black hole perturbations,
black hole numerics, black hole electrodynamics, black holes in unified theories
of gravity, quantum black holes, final states of evaporating black holes and the
information loss puzzle. Special attention is paid to the role of black holes in
astrophysics and observational evidence of black hole existence. Many exotic
subjects linked with black holes, such as white holes, wormholes, and time
machines are discussed in detail. Numerous appendices cover mathematical aspects
of general relativity and black holes and quantum field theory in curved
spacetime. This makes the book practically self-contained. Extensive references
provide the reader with a guide to the literature in this field. Audience: This
book will be of interest to researchers and postgraduate students whose work
involves relativity and gravitation, statistical physics, thermo-dynamics,
active galactic nuclei and stellar physics.

A black hole is, by definition, a region in spacetime in which the gravitational
field is so strong that it precludes even light from escaping to infinity.
A black hole is formed when a body of mass M contracts to a size less than the
socalled gravitational radius rg = 2GM/c2 (G is Newton’s gravitational constant,
and c is the speed of light). The velocity required to leave the boundary of the
black hole and move away to infinity (the escape velocity) equals the speed of
light. ne easily concludes then that neither signals nor particles can escape
from the region inside the black hole since the speed of light is the limiting
propagation velocity for physical signals. This conclusion is of absolute nature
in Einstein’s theory of gravitation because the gravitational interaction is
universal. The role of gravitational charge is played by mass whose value is
proportional to the total energy of the system. Hence, all objects with nonzero
energy participate in the gravitational interaction. Einstein’s theory of gravitation,
alias general relativity, is employed to the full in the description of black holes.
It may appear at first glance that one cannot hope to obtain an acceptably complete
description of black holes, owing to the complexity of the equations involved and,
among other factors, their essential nonlinearity. Fortunately, it was found that
shortly after its formation, any black hole becomes stationary, and its field is
determined in a unique manner by a small number of parameters; namely, its mass and
angular momentum, and its electric charge (if it is charged). The physical reason
for this striking property of black holes is the fact that in the extremely strong
field of a black hole in empty space, only very special types of configuration of
physical fields (including the gravitational field) can be stationary.

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