20,633 research outputs found
Exact Solution for the Metric and the Motion of Two Bodies in (1+1) Dimensional Gravity
We present the exact solution of two-body motion in (1+1) dimensional dilaton
gravity by solving the constraint equations in the canonical formalism. The
determining equation of the Hamiltonian is derived in a transcendental form and
the Hamiltonian is expressed for the system of two identical particles in terms
of the Lambert function. The function has two real branches which join
smoothly onto each other and the Hamiltonian on the principal branch reduces to
the Newtonian limit for small coupling constant. On the other branch the
Hamiltonian yields a new set of motions which can not be understood as
relativistically correcting the Newtonian motion. The explicit trajectory in
the phase space is illustrated for various values of the energy. The
analysis is extended to the case of unequal masses. The full expression of
metric tensor is given and the consistency between the solution of the metric
and the equations of motion is rigorously proved.Comment: 34 pages, LaTeX, 16 figure
Quality determination of liquid-solid hydrogen mixtures
Quality determinations of liquid-solid hydrogen mixtures from mass fraction of vapor pumped off in freeze-thaw proces
Chaos in an Exact Relativistic 3-body Self-Gravitating System
We consider the problem of three body motion for a relativistic
one-dimensional self-gravitating system. After describing the canonical
decomposition of the action, we find an exact expression for the 3-body
Hamiltonian, implicitly determined in terms of the four coordinate and momentum
degrees of freedom in the system. Non-relativistically these degrees of freedom
can be rewritten in terms of a single particle moving in a two-dimensional
hexagonal well. We find the exact relativistic generalization of this
potential, along with its post-Newtonian approximation. We then specialize to
the equal mass case and numerically solve the equations of motion that follow
from the Hamiltonian. Working in hexagonal-well coordinates, we obtaining
orbits in both the hexagonal and 3-body representations of the system, and plot
the Poincare sections as a function of the relativistic energy parameter . We find two broad categories of periodic and quasi-periodic motions that we
refer to as the annulus and pretzel patterns, as well as a set of chaotic
motions that appear in the region of phase-space between these two types.
Despite the high degree of non-linearity in the relativistic system, we find
that the the global structure of its phase space remains qualitatively the same
as its non-relativisitic counterpart for all values of that we could
study. However the relativistic system has a weaker symmetry and so its
Poincare section develops an asymmetric distortion that increases with
increasing . For the post-Newtonian system we find that it experiences a
KAM breakdown for : above which the near integrable regions
degenerate into chaos.Comment: latex, 65 pages, 36 figures, high-resolution figures available upon
reques
Higher Gauge Theory and Gravity in (2+1) Dimensions
Non-abelian higher gauge theory has recently emerged as a generalization of
standard gauge theory to higher dimensional (2-dimensional in the present
context) connection forms, and as such, it has been successfully applied to the
non-abelian generalizations of the Yang-Mills theory and 2-form
electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a
fertile testing ground for many concepts related to classical and quantum
gravity, and it is therefore only natural to investigate whether we can find an
application of higher gauge theory in this latter context. In the present paper
we investigate the possibility of applying the formalism of higher gauge theory
to gravity in (2+1) dimensions, and we show that a nontrivial model of
(2+1)-dimensional gravity coupled to scalar and tensorial matter fields - the
model - can be formulated both as a standard gauge theory and
as a higher gauge theory. Since the model has a very rich structure - it admits
as solutions black-hole BTZ-like geometries, particle-like geometries as well
as Robertson-Friedman-Walker cosmological-like expanding geometries - this
opens a wide perspective for higher gauge theory to be tested and understood in
a relevant gravitational context. Additionally, it offers the possibility of
studying gravity in (2+1) dimensions coupled to matter in an entirely new
framework.Comment: 22 page
New Types of Thermodynamics from -Dimensional Black Holes
For normal thermodynamic systems superadditivity , homogeneity \H and
concavity \C of the entropy hold, whereas for -dimensional black holes
the latter two properties are violated. We show that -dimensional black
holes exhibit qualitatively new types of thermodynamic behaviour, discussed
here for the first time, in which \C always holds, \H is always violated
and may or may not be violated, depending of the magnitude of the black
hole mass. Hence it is now seen that neither superadditivity nor concavity
encapsulate the meaning of the second law in all situations.Comment: WATPHYS-TH93/05, Latex, 10 pgs. 1 figure (available on request), to
appear in Class. Quant. Gra
Quasiclassical Coarse Graining and Thermodynamic Entropy
Our everyday descriptions of the universe are highly coarse-grained,
following only a tiny fraction of the variables necessary for a perfectly
fine-grained description. Coarse graining in classical physics is made natural
by our limited powers of observation and computation. But in the modern quantum
mechanics of closed systems, some measure of coarse graining is inescapable
because there are no non-trivial, probabilistic, fine-grained descriptions.
This essay explores the consequences of that fact. Quantum theory allows for
various coarse-grained descriptions some of which are mutually incompatible.
For most purposes, however, we are interested in the small subset of
``quasiclassical descriptions'' defined by ranges of values of averages over
small volumes of densities of conserved quantities such as energy and momentum
and approximately conserved quantities such as baryon number. The
near-conservation of these quasiclassical quantities results in approximate
decoherence, predictability, and local equilibrium, leading to closed sets of
equations of motion. In any description, information is sacrificed through the
coarse graining that yields decoherence and gives rise to probabilities for
histories. In quasiclassical descriptions, further information is sacrificed in
exhibiting the emergent regularities summarized by classical equations of
motion. An appropriate entropy measures the loss of information. For a
``quasiclassical realm'' this is connected with the usual thermodynamic entropy
as obtained from statistical mechanics. It was low for the initial state of our
universe and has been increasing since.Comment: 17 pages, 0 figures, revtex4, Dedicated to Rafael Sorkin on his 60th
birthday, minor correction
Chaos in a Relativistic 3-body Self-Gravitating System
We consider the 3-body problem in relativistic lineal gravity and obtain an
exact expression for its Hamiltonian and equations of motion. While
general-relativistic effects yield more tightly-bound orbits of higher
frequency compared to their non-relativistic counterparts, as energy increases
we find in the equal-mass case no evidence for either global chaos or a
breakdown from regular to chaotic motion, despite the high degree of
non-linearity in the system. We find numerical evidence for a countably
infinite class of non-chaotic orbits, yielding a fractal structure in the outer
regions of the Poincare plot.Comment: 9 pages, LaTex, 3 figures, final version to appear in Phys. Rev. Let
Gauge Formulation of the Spinning Black Hole in (2+1)-Dimensional Anti-de Sitter Space
We compute the group element of SO(2,2) associated with the spinning black
hole found by Ba\~nados, Teitelboim and Zanelli in (2+1)-dimensional anti-de
Sitter space-time. We show that their metric is built with SO(2,2) gauge
invariant quantities and satisfies Einstein's equations with negative
cosmological constant everywhere except at . Moreover, although the metric
is singular on the horizons, the group element is continuous and possesses a
kink there.Comment: 10 page
Distortion of Schwarzschild-anti-de Sitter black holes to black strings
Motivated by the existence of black holes with various topologies in
four-dimensional spacetimes with a negative cosmological constant, we study
axisymmetric static solutions describing any large distortions of
Schwarzschild-anti-de Sitter black holes parametrized by the mass . Under
the approximation such that is much larger than the anti-de Sitter radius,
it is found that a cylindrically symmetric black string is obtained as a
special limit of distorted spherical black holes. Such a prolonged distortion
of the event horizon connecting a Schwarzschild-anti-de Sitter black hole to a
black string is allowed without violating both the usual black hole
thermodynamics and the hoop conjecture for the horizon circumference.Comment: 13 pages, accepted for publication in Physical Review
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