13,305 research outputs found

### The Loudest Event Statistic: General Formulation, Properties and Applications

The use of the loudest observed event to generate statistical statements
about rate and strength has become standard in searches for gravitational waves
from compact binaries and pulsars. The Bayesian formulation of the method is
generalized in this paper to allow for uncertainties both in the background
estimate and in the properties of the population being constrained. The method
is also extended to allow rate interval construction. Finally, it is shown how
to combine the results from multiple experiments and a comparison is drawn
between the upper limit obtained in a single search and the upper limit
obtained by combining the results of two experiments each of half the original
duration. To illustrate this, we look at an example case, motivated by the
search for gravitational waves from binary inspiral.Comment: 11 pages, 8 figure

### Cosmic Censorship: As Strong As Ever

Spacetimes which have been considered counter-examples to strong cosmic
censorship are revisited. We demonstrate the classical instability of the
Cauchy horizon inside charged black holes embedded in de Sitter spacetime for
all values of the physical parameters. The relevant modes which maintain the
instability, in the regime which was previously considered stable, originate as
outgoing modes near to the black hole event horizon. This same mechanism is
also relevant for the instability of Cauchy horizons in other proposed
counter-examples of strong cosmic censorship.Comment: 4 pages RevTeX style, 1 figure included using epsfi

### Stability of degenerate Cauchy horizons in black hole spacetimes

In the multihorizon black hole spacetimes, it is possible that there are
degenerate Cauchy horizons with vanishing surface gravities. We investigate the
stability of the degenerate Cauchy horizon in black hole spacetimes. Despite
the asymptotic behavior of spacetimes (flat, anti-de Sitter, or de Sitter), we
find that the Cauchy horizon is stable against the classical perturbations, but
unstable quantum mechanically.Comment: Revtex, 4 pages, no figures, references adde

### Characteristics of magnetoacoustic sausage modes

Aims: We perform an advanced study of the fast magnetoacoustic sausage oscillations of coronal loops in the context of MHD coronal seismology to establish the dependence of the sausage mode period and cut-off wavenumber on the plasma-$\beta$ of the loop-filling plasma. A parametric study of the ratios for different harmonics of the mode is also carried out.
Methods: Full magnetohydrodynamic numerical simulations were performed using Lare2d, simulating hot, dense loops in a magnetic slab environment. The symmetric Epstein profile and a simple step-function profile were both used to model the density structure of the simulated loops. Analytical expressions for the cut-off wavenumber and the harmonic ratio between the second longitudinal harmonic and the fundamental were also examined.
Results: It was established that the period of the global sausage mode is only very weakly dependent on the value of the plasma-$\beta$ inside a coronal loop, which justifies the application of this model to hot flaring loops. The cut-off wavenumber kc for the global mode was found to be dependent on both internal and external values of the plasma-$\beta$, again only weakly. By far the most important factor in this case was the value of the density contrast ratio between the loop and the surroundings. Finally, the deviation of the harmonic ratio P1/2P2 from the ideal non-dispersive case was shown to be considerable at low k, again strongly dependent on plasma density. Quantifying the behaviour of the cut-off wavenumber and the harmonic ratio has significant applications to the field of coronal seismology

### Anisotropic Diffusion Limited Aggregation

Using stochastic conformal mappings we study the effects of anisotropic
perturbations on diffusion limited aggregation (DLA) in two dimensions. The
harmonic measure of the growth probability for DLA can be conformally mapped
onto a constant measure on a unit circle. Here we map $m$ preferred directions
for growth of angular width $\sigma$ to a distribution on the unit circle which
is a periodic function with $m$ peaks in $[-\pi, \pi)$ such that the width
$\sigma$ of each peak scales as $\sigma \sim 1/\sqrt{k}$, where $k$ defines the
``strength'' of anisotropy along any of the $m$ chosen directions. The two
parameters $(m,k)$ map out a parameter space of perturbations that allows a
continuous transition from DLA (for $m=0$ or $k=0$) to $m$ needle-like fingers
as $k \to \infty$. We show that at fixed $m$ the effective fractal dimension of
the clusters $D(m,k)$ obtained from mass-radius scaling decreases with
increasing $k$ from $D_{DLA} \simeq 1.71$ to a value bounded from below by
$D_{min} = 3/2$. Scaling arguments suggest a specific form for the dependence
of the fractal dimension $D(m,k)$ on $k$ for large $k$, form which compares
favorably with numerical results.Comment: 6 pages, 4 figures, submitted to Phys. Rev.

### Spacetime structure of static solutions in Gauss-Bonnet gravity: charged case

We have studied spacetime structures of static solutions in the
$n$-dimensional Einstein-Gauss-Bonnet-Maxwell-$\Lambda$ system. Especially we
focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet
coefficient $\alpha$ is non-negative and $4{\tilde \alpha}/\ell^2\leq 1$ in
order to define the relevant vacuum state. Solutions have the
$(n-2)$-dimensional Euclidean sub-manifold whose curvature is $k=1,~0$, or -1.
In Gauss-Bonnet gravity, solutions are classified into plus and minus branches.
In the plus branch all solutions have the same asymptotic structure as those in
general relativity with a negative cosmological constant. The charge affects a
central region of the spacetime. A branch singularity appears at the finite
radius $r=r_b>0$ for any mass parameter. There the Kretschmann invariant
behaves as $O((r-r_b)^{-3})$, which is much milder than divergent behavior of
the central singularity in general relativity $O(r^{-4(n-2)})$. Some charged
black hole solutions have no inner horizon in Gauss-Bonnet gravity. Although
there is a maximum mass for black hole solutions in the plus branch for $k=-1$
in the neutral case, no such maximum exists in the charged case. The solutions
in the plus branch with $k=-1$ and $n\geq6$ have an "inner" black hole, and
inner and the "outer" black hole horizons. Considering the evolution of black
holes, we briefly discuss a classical discontinuous transition from one black
hole spacetime to another.Comment: 20 pages, 10 figure

### Integrability of the Minimal Strain Equations for the Lapse and Shift in 3+1 Numerical Relativity

Brady, Creighton and Thorne have argued that, in numerical relativity
simulations of the inspiral of binary black holes, if one uses lapse and shift
functions satisfying the ``minimal strain equations'' (MSE), then the
coordinates might be kept co-rotating, the metric components would then evolve
on the very slow inspiral timescale, and the computational demands would thus
be far smaller than for more conventional slicing choices. In this paper, we
derive simple, testable criteria for the MSE to be strongly elliptic, thereby
guaranteeing the existence and uniqueness of the solution to the Dirichlet
boundary value problem. We show that these criteria are satisfied in a test-bed
metric for inspiraling binaries, and we argue that they should be satisfied
quite generally for inspiraling binaries. If the local existence and uniqueness
that we have proved holds globally, then, for appropriate boundary values, the
solution of the MSE exhibited by Brady et. al. (which tracks the inspiral and
keeps the metric evolving slowly) will be the unique solution and thus should
be reproduced by (sufficiently accurate and stable) numerical integrations.Comment: 6 pages; RevTeX; submitted to Phys. Rev. D15. Technical issue of the
uniqueness of the solution to the Dirichlet problem clarified. New subsection
on the nature of the boundary dat

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