17,513 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
Conservation Laws and 2D Black Holes in Dilaton Gravity
A very general class of Lagrangians which couple scalar fields to gravitation
and matter in two spacetime dimensions is investigated. It is shown that a
vector field exists along whose flow lines the stress-energy tensor is
conserved, regardless of whether or not the equations of motion are satisfied
or if any Killing vectors exist. Conditions necessary for the existence of
Killing vectors are derived. A new set of 2D black hole solutions is obtained
for one particular member within this class of Lagrangians. One such solution
bears an interesting resemblance to the 2D string-theoretic black hole, yet
contains markedly different thermodynamic properties.Comment: 11 pgs. WATPHYS-TH92/0
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
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
Warming of the Antarctic ice-sheet surface since the 1957 International Geophysical Year
Assessments of Antarctic temperature change have emphasized the contrast between strong warming of the Antarctic Peninsula and slight cooling of the Antarctic continental interior in recent decades. This pattern of temperature change has been attributed to the increased strength of the circumpolar westerlies, largely in response to changes in stratospheric ozone. This picture, however, is substantially incomplete owing to the sparseness and short duration of the observations. Here we show that significant warming extends well beyond the Antarctic Peninsula to cover most of West Antarctica, an area of warming much larger than previously reported. West Antarctic warming exceeds 0.1 °C per decade over the past 50 years, and is strongest in winter and spring. Although this is partly offset by autumn cooling in East Antarctica, the continent-wide average near-surface temperature trend is positive. Simulations using a general circulation model reproduce the essential features of the spatial pattern and the long-term trend, and we suggest that neither can be attributed directly to increases in the strength of the westerlies. Instead, regional changes in atmospheric circulation and associated changes in sea surface temperature and sea ice are required to explain the enhanced warming in West Antarctica
Escort mean values and the characterization of power-law-decaying probability densities
Escort mean values (or -moments) constitute useful theoretical tools for
describing basic features of some probability densities such as those which
asymptotically decay like {\it power laws}. They naturally appear in the study
of many complex dynamical systems, particularly those obeying nonextensive
statistical mechanics, a current generalization of the Boltzmann-Gibbs theory.
They recover standard mean values (or moments) for . Here we discuss the
characterization of a (non-negative) probability density by a suitable set of
all its escort mean values together with the set of all associated normalizing
quantities, provided that all of them converge. This opens the door to a
natural extension of the well known characterization, for the instance,
of a distribution in terms of the standard moments, provided that {\it all} of
them have {\it finite} values. This question would be specially relevant in
connection with probability densities having {\it divergent} values for all
nonvanishing standard moments higher than a given one (e.g., probability
densities asymptotically decaying as power-laws), for which the standard
approach is not applicable. The Cauchy-Lorentz distribution, whose second and
higher even order moments diverge, constitutes a simple illustration of the
interest of this investigation. In this context, we also address some
mathematical subtleties with the aim of clarifying some aspects of an
interesting non-linear generalization of the Fourier Transform, namely, the
so-called -Fourier Transform.Comment: 20 pages (2 Appendices have been added
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
Mass Inflation in the Loop Black Hole
In classical general relativity the Cauchy horizon within a two-horizon black
hole is unstable via a phenomenon known as mass inflation, in which the mass
parameter (and the spacetime curvature) of the black hole diverges at the
Cauchy horizon. Here we study this effect for loop black holes -- quantum
gravitationally corrected black holes from loop quantum gravity -- whose
construction alleviates the singularity present in their classical
counterparts. We use a simplified model of mass inflation, which makes use of
the generalized DTR relation, to conclude that the Cauchy horizon of loop black
holes indeed results in a curvature singularity similar to that found in
classical black holes. The DTR relation is of particular utility in the loop
black hole because it does not directly rely upon Einstein's field equations.
We elucidate some of the interesting and counterintuitive properties of the
loop black hole, and corroborate our results using an alternate model of mass
inflation due to Ori.Comment: Latex 20 pages, 7 figure
U(1)' solution to the mu-problem and the proton decay problem in supersymmetry without R-parity
The Minimal Supersymmetric Standard Model (MSSM) is plagued by two major
fine-tuning problems: the mu-problem and the proton decay problem. We present a
simultaneous solution to both problems within the framework of a U(1)'-extended
MSSM (UMSSM), without requiring R-parity conservation. We identify several
classes of phenomenologically viable models and provide specific examples of
U(1)' charge assignments. Our models generically contain either lepton number
violating or baryon number violating renormalizable interactions, whose
coexistence is nevertheless automatically forbidden by the new U(1)' gauge
symmetry. The U(1)' symmetry also prohibits the potentially dangerous and often
ignored higher-dimensional proton decay operators such as QQQL and UUDE which
are still allowed by R-parity. Thus, under minimal assumptions, we show that
once the mu-problem is solved, the proton is sufficiently stable, even in the
presence of a minimum set of exotics fields, as required for anomaly
cancellation. Our models provide impetus for pursuing the collider
phenomenology of R-parity violation within the UMSSM framework.Comment: Version published in Phys. Rev.
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