10,501 research outputs found
Vacuum Polarisation and the Black Hole Singularity
In order to investigate the effects of vacuum polarisation on mass inflation
singularities, we study a simple toy model of a charged black hole with cross
flowing radial null dust which is homogeneous in the black hole interior. In
the region we find an approximate analytic solution to the
classical field equations. The renormalized stress-energy tensor is evaluated
on this background and we find the vacuum polarisation backreaction corrections
to the mass function . Asymptotic analysis of the semiclassical mass
function shows that the mass inflation singularity is much stronger in the
presence of vacuum polarisation than in the classical case.Comment: 12 pages, RevTe
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
Numerical investigation of black hole interiors
Gravitational perturbations which are present in any realistic stellar
collapse to a black hole, die off in the exterior of the hole, but experience
an infinite blueshift in the interior. This is believed to lead to a slowly
contracting lightlike scalar curvature singularity, characterized by a
divergence of the hole's (quasi-local) mass function along the inner horizon.
The region near the inner horizon is described to great accuracy by a plane
wave spacetime. While Einstein's equations for this metric are still too
complicated to be solved in closed form it is relatively simple to integrate
them numerically.
We find for generic regular initial data the predicted mass inflation type
null singularity, rather than a spacelike singularity. It thus seems that mass
inflation indeed represents a generic self-consistent picture of the black hole
interior.Comment: 6 pages LaTeX, 3 eps figure
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
A nonlinear detection algorithm for periodic signals in gravitational wave detectors
We present an algorithm for the detection of periodic sources of
gravitational waves with interferometric detectors that is based on a special
symmetry of the problem: the contributions to the phase modulation of the
signal from the earth rotation are exactly equal and opposite at any two
instants of time separated by half a sidereal day; the corresponding is true
for the contributions from the earth orbital motion for half a sidereal year,
assuming a circular orbit. The addition of phases through multiplications of
the shifted time series gives a demodulated signal; specific attention is given
to the reduction of noise mixing resulting from these multiplications. We
discuss the statistics of this algorithm for all-sky searches (which include a
parameterization of the source spin-down), in particular its optimal
sensitivity as a function of required computational power. Two specific
examples of all-sky searches (broad-band and narrow-band) are explored
numerically, and their performances are compared with the stack-slide technique
(P. R. Brady, T. Creighton, Phys. Rev. D, 61, 082001).Comment: 9 pages, 3 figures, to appear in Phys. Rev.
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
Spacetime structure of static solutions in Gauss-Bonnet gravity: charged case
We have studied spacetime structures of static solutions in the
-dimensional Einstein-Gauss-Bonnet-Maxwell- system. Especially we
focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet
coefficient is non-negative and in
order to define the relevant vacuum state. Solutions have the
-dimensional Euclidean sub-manifold whose curvature is , 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 for any mass parameter. There the Kretschmann invariant
behaves as , which is much milder than divergent behavior of
the central singularity in general relativity . 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
in the neutral case, no such maximum exists in the charged case. The solutions
in the plus branch with and 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
Breast Cancer: Modelling and Detection
This paper reviews a number of the mathematical models used in cancer modelling and then chooses a specific cancer, breast carcinoma, to illustrate how the modelling can be used in aiding detection. We then discuss mathematical models that underpin mammographic image analysis, which complements models of tumour growth and facilitates diagnosis and treatment of cancer. Mammographic images are notoriously difficult to interpret, and we give an overview of the primary image enhancement technologies that have been introduced, before focusing on a more detailed description of some of our own recent work on the use of physics-based modelling in mammography. This theoretical approach to image analysis yields a wealth of information that could be incorporated into the mathematical models, and we conclude by describing how current mathematical models might be enhanced by use of this information, and how these models in turn will help to meet some of the major challenges in cancer detection
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