31,442 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
Statistical Mechanics of Relativistic One-Dimensional Self-Gravitating Systems
We consider the statistical mechanics of a general relativistic
one-dimensional self-gravitating system. The system consists of -particles
coupled to lineal gravity and can be considered as a model of
relativistically interacting sheets of uniform mass. The partition function and
one-particle distitrubion functions are computed to leading order in
where is the speed of light; as results for the
non-relativistic one-dimensional self-gravitating system are recovered. We find
that relativistic effects generally cause both position and momentum
distribution functions to become more sharply peaked, and that the temperature
of a relativistic gas is smaller than its non-relativistic counterpart at the
same fixed energy. We consider the large-N limit of our results and compare
this to the non-relativistic case.Comment: latex, 60 pages, 22 figure
Exact Solutions of Relativistic Two-Body Motion in Lineal Gravity
We develop the canonical formalism for a system of bodies in lineal
gravity and obtain exact solutions to the equations of motion for N=2. The
determining equation of the Hamiltonian is derived in the form of a
transcendental equation, which leads to the exact Hamiltonian to infinite order
of the gravitational coupling constant. In the equal mass case explicit
expressions of the trajectories of the particles are given as the functions of
the proper time, which show characteristic features of the motion depending on
the strength of gravity (mass) and the magnitude and sign of the cosmological
constant. As expected, we find that a positive cosmological constant has a
repulsive effect on the motion, while a negative one has an attractive effect.
However, some surprising features emerge that are absent for vanishing
cosmological constant. For a certain range of the negative cosmological
constant the motion shows a double maximum behavior as a combined result of an
induced momentum-dependent cosmological potential and the gravitational
attraction between the particles. For a positive cosmological constant, not
only bounded motions but also unbounded ones are realized. The change of the
metric along the movement of the particles is also exactly derived.Comment: 37 pages, Latex, 24 figure
Entropy and Mass Bounds of Kerr-de Sitter Spacetimes
We consider Kerr-de Sitter spacetimes and evaluate their mass, angular
momentum and entropy according to the boundary counterterm prescription. We
provide a physicall interpretation for angular velocity and angular momentum at
future/past infinity. We show that the entropy of the four-dimensional Kerr-de
Sitter spacetimes is less than of pure de Sitter spacetime in agreement to the
entropic N-bound. Moreover, we show that maximal mass conjecture which states
any asymptotically de Sitter spacetime with mass greater than de Sitter has a
cosmological singularity is respected by asymptotically de Sitter spacetimes
with rotation. We furthermore consider the possibility of strengthening the
conjecture to state that any asymptotically dS spacetime will have mass greater
than dS if and only if it has a cosmological singularity and find that Kerr-de
Sitter spacetimes do not respect this stronger statement. We investigate the
behavior of the c-function for the Kerr-de Sitter spacetimes and show that it
is no longer isotropic. However an average of the c-function over the angular
variables yields a renormalization group flow in agreement with the expansion
of spacetime at future infinity.Comment: 13 pages, 3 figures, one figure added, typos correcte
Action, Mass and Entropy of Schwarzschild-de Sitter black holes and the de Sitter/CFT Correspondence
We investigate a recent proposal for defining a conserved mass in
asymptotically de Sitter spacetimes that is based on a conjectured holographic
duality between such spacetimes and Euclidean conformal field theory. We show
that an algorithm for deriving such terms in asymptotically anti de Sitter
spacetimes has an asymptotically de Sitter counterpart, and derive the explicit
form for such terms up to 9 dimensions. We show that divergences of the
on-shell action for de Sitter spacetime are removed in any dimension in
inflationary coordinates, but in covering coordinates a linear divergence
remains in odd dimensions that cannot be cancelled by local terms that are
polynomial in boundary curvature invariants. We show that the class of
Schwarzschild-de Sitter black holes up to 9 dimensions has finite action and
conserved mass, and construct a definition of entropy outside the cosmological
horizon by generalizing the Gibbs-Duhem relation in asymptotically dS
spacetimes. The entropy is agreement with that obtained from CFT methods in
. In general our results provide further supporting evidence for a dS/CFT
correspondence, although some important interpretive problems remain.Comment: 16 pages, LaTeX, typos correcte
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
Pair Production of Topological anti de Sitter Black Holes
The pair creation of black holes with event horizons of non-trivial topology
is described. The spacetimes are all limiting cases of the cosmological
metric. They are generalizations of the dimensional black hole and have
asymptotically anti de Sitter behaviour. Domain walls instantons can mediate
their pair creation for a wide range of mass and charge.Comment: 4 pages, uses late
Quasiclassical Equations of Motion for Nonlinear Brownian Systems
Following the formalism of Gell-Mann and Hartle, phenomenological equations
of motion are derived from the decoherence functional formalism of quantum
mechanics, using a path-integral description. This is done explicitly for the
case of a system interacting with a ``bath'' of harmonic oscillators whose
individual motions are neglected. The results are compared to the equations
derived from the purely classical theory. The case of linear interactions is
treated exactly, and nonlinear interactions are compared using classical and
quantum perturbation theory.Comment: 24 pages, CALT-68-1848 (RevTeX 2.0 macros
Research and development at ORNL/CESAR towards cooperating robotic systems for hazardous environments
One of the frontiers in intelligent machine research is the understanding of how constructive cooperation among multiple autonomous agents can be effected. The effort at the Center for Engineering Systems Advanced Research (CESAR) at the Oak Ridge National Laboratory (ORNL) focuses on two problem areas: (1) cooperation by multiple mobile robots in dynamic, incompletely known environments; and (2) cooperating robotic manipulators. Particular emphasis is placed on experimental evaluation of research and developments using the CESAR robot system testbeds, including three mobile robots, and a seven-axis, kinematically redundant mobile manipulator. This paper summarizes initial results of research addressing the decoupling of position and force control for two manipulators holding a common object, and the path planning for multiple robots in a common workspace
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