16,003 research outputs found
Innermost stable circular orbits around relativistic rotating stars
We investigate the innermost stable circular orbit (ISCO) of a test particle
moving on the equatorial plane around rotating relativistic stars such as
neutron stars. First, we derive approximate analytic formulas for the angular
velocity and circumferential radius at the ISCO making use of an approximate
relativistic solution which is characterized by arbitrary mass, spin, mass
quadrupole, current octapole and mass -pole moments. Then, we show that
the analytic formulas are accurate enough by comparing them with numerical
results, which are obtained by analyzing the vacuum exterior around numerically
computed geometries for rotating stars of polytropic equation of state. We
demonstrate that contribution of mass quadrupole moment for determining the
angular velocity and, in particular, the circumferential radius at the ISCO
around a rapidly rotating star is as important as that of spin.Comment: 12 pages, 2 figures, accepted for publication in Phys. Rev.
Phase transition and landscape statistics of the number partitioning problem
The phase transition in the number partitioning problem (NPP), i.e., the
transition from a region in the space of control parameters in which almost all
instances have many solutions to a region in which almost all instances have no
solution, is investigated by examining the energy landscape of this classic
optimization problem. This is achieved by coding the information about the
minimum energy paths connecting pairs of minima into a tree structure, termed a
barrier tree, the leaves and internal nodes of which represent, respectively,
the minima and the lowest energy saddles connecting those minima. Here we apply
several measures of shape (balance and symmetry) as well as of branch lengths
(barrier heights) to the barrier trees that result from the landscape of the
NPP, aiming at identifying traces of the easy/hard transition. We find that it
is not possible to tell the easy regime from the hard one by visual inspection
of the trees or by measuring the barrier heights. Only the {\it difficulty}
measure, given by the maximum value of the ratio between the barrier height and
the energy surplus of local minima, succeeded in detecting traces of the phase
transition in the tree. In adddition, we show that the barrier trees associated
with the NPP are very similar to random trees, contrasting dramatically with
trees associated with the spin-glass and random energy models. We also
examine critically a recent conjecture on the equivalence between the NPP and a
truncated random energy model
Mapping spacetimes with LISA: inspiral of a test-body in a `quasi-Kerr' field
The future LISA detector will constitute the prime instrument for
high-precision gravitational wave observations.LISA is expected to provide
information for the properties of spacetime in the vicinity of massive black
holes which reside in galactic nuclei.Such black holes can capture stellar-mass
compact objects, which afterwards slowly inspiral,radiating gravitational
waves.The body's orbital motion and the associated waveform carry information
about the spacetime metric of the massive black hole,and it is possible to
extract this information and experimentally identify (or not!) a Kerr black
hole.In this paper we lay the foundations for a practical `spacetime-mapping'
framework. Our work is based on the assumption that the massive body is not
necessarily a Kerr black hole, and that the vacuum exterior spacetime is
stationary axisymmetric,described by a metric which deviates slightly from the
Kerr metric. We first provide a simple recipe for building such a `quasi-Kerr'
metric by adding to the Kerr metric the deviation in the value of the
quadrupole moment. We then study geodesic motion in this metric,focusing on
equatorial orbits. We proceed by computing `kludge' waveforms which we compare
with their Kerr counterparts. We find that a modest deviation from the Kerr
metric is sufficient for producing a significant mismatch between the
waveforms, provided we fix the orbital parameters. This result suggests that an
attempt to use Kerr waveform templates for studying EMRIs around a non-Kerr
object might result in serious loss of signal-to-noise ratio and total number
of detected events. The waveform comparisons also unveil a `confusion' problem,
that is the possibility of matching a true non-Kerr waveform with a Kerr
template of different orbital parameters.Comment: 19 pages, 6 figure
Spin effects in gravitational radiation backreaction II. Finite mass effects
A convenient formalism for averaging the losses produced by gravitational
radiation backreaction over one orbital period was developed in an earlier
paper. In the present paper we generalize this formalism to include the case of
a closed system composed from two bodies of comparable masses, one of them
having the spin S.
We employ the equations of motion given by Barker and O'Connell, where terms
up to linear order in the spin (the spin-orbit interaction terms) are kept. To
obtain the radiative losses up to terms linear in the spin, the equations of
motion are taken to the same order. Then the magnitude L of the angular
momentum L, the angle kappa subtended by S and L and the energy E are
conserved. The analysis of the radial motion leads to a new parametrization of
the orbit.
From the instantaneous gravitational radiation losses computed by Kidder the
leading terms and the spin-orbit terms are taken. Following Apostolatos,
Cutler, Sussman and Thorne, the evolution of the vectors S and L in the
momentary plane spanned by these vectors is separated from the evolution of the
plane in space. The radiation-induced change in the spin is smaller than the
leading-order spin terms in the momentary angular momentum loss. This enables
us to compute the averaged losses in the constants of motion E, L and L_S=L cos
kappa. In the latter, the radiative spin loss terms average to zero. An
alternative description using the orbital elements a,e and kappa is given.
The finite mass effects contribute terms, comparable in magnitude, to the
basic, test-particle spin terms in the averaged losses.Comment: 12 pages, 1 figure, Phys.Rev.D15, March, 199
Relativistic Wavepackets in Classically Chaotic Quantum Cosmological Billiards
Close to a spacelike singularity, pure gravity and supergravity in four to
eleven spacetime dimensions admit a cosmological billiard description based on
hyperbolic Kac-Moody groups. We investigate the quantum cosmological billiards
of relativistic wavepackets towards the singularity, employing flat and
hyperbolic space descriptions for the quantum billiards. We find that the
strongly chaotic classical billiard motion of four-dimensional pure gravity
corresponds to a spreading wavepacket subject to successive redshifts and
tending to zero as the singularity is approached. We discuss the possible
implications of these results in the context of singularity resolution and
compare them with those of known semiclassical approaches. As an aside, we
obtain exact solutions for the one-dimensional relativistic quantum billiards
with moving walls.Comment: 18 pages, 10 figure
Quasi-Elastic Scattering in the Inclusive (He, t) Reaction
The triton energy spectra of the charge-exchange C(He,t) reaction
at 2 GeV beam energy are analyzed in the quasi-elastic nucleon knock-out
region. Considering that this region is mainly populated by the charge-exchange
of a proton in He with a neutron in the target nucleus and the final proton
going in the continuum, the cross-sections are written in the distorted-wave
impulse approximation. The t-matrix for the elementary exchange process is
constructed in the DWBA, using one pion- plus rho-exchange potential for the
spin-isospin nucleon- nucleon potential. This t-matrix reproduces the
experimental data on the elementary pn np process. The calculated
cross-sections for the C(He,t) reaction at to triton
emission angle are compared with the corresponding experimental data, and are
found in reasonable overall accord.Comment: 19 pages, latex, 11 postscript figures available at
[email protected], submitted to Phy.Rev.
From the discrete to the continuous - towards a cylindrically consistent dynamics
Discrete models usually represent approximations to continuum physics.
Cylindrical consistency provides a framework in which discretizations mirror
exactly the continuum limit. Being a standard tool for the kinematics of loop
quantum gravity we propose a coarse graining procedure that aims at
constructing a cylindrically consistent dynamics in the form of transition
amplitudes and Hamilton's principal functions. The coarse graining procedure,
which is motivated by tensor network renormalization methods, provides a
systematic approximation scheme towards this end. A crucial role in this coarse
graining scheme is played by embedding maps that allow the interpretation of
discrete boundary data as continuum configurations. These embedding maps should
be selected according to the dynamics of the system, as a choice of embedding
maps will determine a truncation of the renormalization flow.Comment: 22 page
Threshold meson production and cosmic ray transport
An interesting accident of nature is that the peak of the cosmic ray
spectrum, for both protons and heavier nuclei, occurs near the pion production
threshold. The Boltzmann transport equation contains a term which is the cosmic
ray flux multiplied by the cross section. Therefore when considering pion and
kaon production from proton-proton reactions, small cross sections at low
energy can be as important as larger cross sections at higher energy. This is
also true for subthreshold kaon production in nuclear collisions, but not for
subthreshold pion production.Comment: 9 pages, 1 figur
Intravenous Prenatal Nicotine Exposure Alters METH-Induced Hyperactivity, Conditioned Hyperactivity, and BDNF in Adult Rat Offspring
In the USA, approximately 15% of women smoke tobacco cigarettes during pregnancy. In utero tobacco smoke exposure produces somatic growth deficits like intrauterine growth restriction and low birth w
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