23,618 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
Low thrust interplanetary trajectory open loop error analysis, volume 1 Final report
Computer program for open-loop error analysis of low thrust interplanetary trajectorie
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
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
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
Coupling of a high-energy excitation to superconducting quasiparticles in a cuprate from Coherent Charge Fluctuation Spectroscopy
Dynamical information on spin degrees of freedom of proteins or solids can be
obtained by Nuclear Magnetic Resonance (NMR) and Electron Spin Resonance (ESR).
A technique with similar versatility for charge degrees of freedom and their
ultrafast correlations could move forward the understanding of systems like
unconventional superconductors. By perturbing the superconducting state in a
high-Tc cuprate using a femtosecond laser pulse, we generate coherent
oscillations of the Cooper pair condensate which can be described by an NMR/ESR
formalism. The oscillations are detected by transient broad-band reflectivity
and found to resonate at the typical scale of Mott physics (2.6 eV), suggesting
the existence of a non-retarded contribution to the pairing interaction, as in
unconventional (non Migdal-Eliashberg) theories.Comment: Accepted for publication in the Proceedings of the National Academy
of Sciences of the U.S.A. (PNAS
Cosmological Models in Two Spacetime Dimensions
Various physical properties of cosmological models in (1+1) dimensions are
investigated. We demonstrate how a hot big bang and a hot big crunch can arise
in some models. In particular, we examine why particle horizons do not occur in
matter and radiation models. We also discuss under what circumstances
exponential inflation and matter/radiation decoupling can happen. Finally,
without assuming any particular equation of state, we show that physical
singularities can occur in both untilted and tilted universe models if certain
assumptions are satisfied, similar to the (3+1)-dimensional cases.Comment: 22 pgs., 2 figs. (available on request) (revised version contains
`paper.tex' macro file which was omitted in earlier version
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
Dirac neutrino mass from the beta decay end-point modified by the dynamics of a Lorentz-violating equation of motion
Using a generalized procedure for obtaining the equation of motion of a
propagating fermionic particle, we examine previous claims for a lightlike
preferred axis embedded in the framework of Lorentz-invariance violation with
preserved algebra. In a high energy scale, the corresponding equation of motion
is reduced to a conserving lepton number chiral (VSR) equation, and in a low
energy scale, the Dirac equation for a free is recovered. The new dynamics
introduces some novel ingredients (modified cross section) to the phenomenology
of the tritium beta decay end-point.Comment: 11 pages, 4 figure
Probing minimal supergravity in the type-I seesaw mechanism with lepton flavour violation at the CERN LHC
The most general supersymmetric seesaw mechanism has too many parameters to
be predictive and thus can not be excluded by any measurements of lepton
flavour violating (LFV) processes. We focus on the simplest version of the
type-I seesaw mechanism assuming minimal supergravity boundary conditions. We
compute branching ratios for the LFV scalar tau decays, , as well as loop-induced LFV decays at low energy, such as
and , exploring their sensitivity to the
unknown seesaw parameters. We find some simple, extreme scenarios for the
unknown right-handed parameters, where ratios of LFV branching ratios correlate
with neutrino oscillation parameters. If the overall mass scale of the left
neutrinos and the value of the reactor angle were known, the study of LFV
allows, in principle, to extract information about the so far unknown
right-handed neutrino parameters.Comment: 29 pages, 27 figures; added explanatory comments, corrected typos,
final version for publicatio
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