1,494 research outputs found
Interior design of a two-dimensional semiclassical black hole: Quantum transition across the singularity
We study the internal structure of a two-dimensional dilatonic evaporating
black hole, based on the CGHS model. At the semiclassical level, a (weak)
spacelike singularity was previously found to develop inside the black hole. We
employ here a simplified quantum formulation of spacetime dynamics in the
neighborhood of this singularity, using a minisuperspace-like approach. Quantum
evolution is found to be regular and well-defined at the semiclassical
singularity. A well-localized initial wave-packet propagating towards the
singularity bounces off the latter and retains its well-localized form. Our
simplified quantum treatment thus suggests that spacetime may extend
semiclassically beyond the singularity, and also signifies the specific
extension.Comment: Accepted to Phys. Rev.
Outgoing gravitational shock-wave at the inner horizon: The late-time limit of black hole interiors
We investigate the interiors of 3+1 dimensional asymptotically flat charged
and rotating black holes as described by observers who fall into the black
holes at late times, long after any perturbations of the exterior region have
decayed. In the strict limit of late infall times, the initial experiences of
such observers are precisely described by the region of the limiting stationary
geometry to the past of its inner horizon. However, we argue that late
infall-time observers encounter a null shockwave at the location of the
would-be outgoing inner horizon. In particular, for spherically symmetric black
hole spacetimes we demonstrate that freely-falling observers experience a
metric discontinuity across this shock, that is, a gravitational shock-wave.
Furthermore, the magnitude of this shock is at least of order unity. A similar
phenomenon of metric discontinuity appears to take place at the inner horizon
of a generically-perturbed spinning black hole. We compare the properties of
this null shockwave singularity with those of the null weak singularity that
forms at the Cauchy horizon.Comment: 23 pages, 4 figures, minor change
Ground States of S-duality Twisted N=4 Super Yang-Mills Theory
We study the low-energy limit of a compactification of N=4 U(n) super
Yang-Mills theory on with boundary conditions modified by an S-duality
and R-symmetry twist. This theory has N=6 supersymmetry in 2+1D. We analyze the
compactification of this 2+1D theory by identifying a dual weakly coupled
type-IIA background. The Hilbert space of normalizable ground states is
finite-dimensional and appears to exhibit a rich structure of sectors. We
identify most of them with Hilbert spaces of Chern-Simons theory (with
appropriate gauge groups and levels). We also discuss a realization of a
related twisted compactification in terms of the (2,0)-theory, where the recent
solution by Gaiotto and Witten of the boundary conditions describing D3-branes
ending on a (p,q) 5-brane plays a crucial role.Comment: 104 pages, 5 figures. Revisions to subsection (6.6) and other minor
corrections included in version
Are physical objects necessarily burnt up by the blue sheet inside a black hole?
The electromagnetic radiation that falls into a Reissner-Nordstrom black hole
develops a ``blue sheet'' of infinite energy density at the Cauchy horizon. We
consider classical electromagnetic fields (that were produced during the
collapse and then backscattered into the black hole), and investigate the
blue-sheet effects of these fields on infalling objects within a simplified
model. These effects are found to be finite and even negligible for typical
parameters.Comment: 13 pages, ordinary LaTex. Accepted for Physical Review Letters
A new time-machine model with compact vacuum core
We present a class of curved-spacetime vacuum solutions which develope closed
timelike curves at some particular moment. We then use these vacuum solutions
to construct a time-machine model. The causality violation occurs inside an
empty torus, which constitutes the time-machine core. The matter field
surrounding this empty torus satisfies the weak, dominant, and strong energy
conditions. The model is regular, asymptotically-flat, and
topologically-trivial. Stability remains the main open question.Comment: 7 page
The Ori-Soen time machine
Ori and Soen have proposed a spacetime which has closed causal curves on the
boundary of a region of normal causality, all within a region where the weak
energy condition (positive energy density) is satisfied. I analyze the causal
structure of this spacetime in some simplified models, show that the Cauchy
horizon is compactly generated, and argue that any attempt to build such a
spacetime with normal matter might lead to singular behavior where the
causality violation would otherwise take place.Comment: 5 pages, RevTeX, 7 figures with epsf, miscellaneous clarifications in
v2, minor updates to correspond to version to appear in PR
The late-time singularity inside non-spherical black holes
It was long believed that the singularity inside a realistic, rotating black
hole must be spacelike. However, studies of the internal geometry of black
holes indicate a more complicated structure is typical. While it seems likely
that an observer falling into a black hole with the collapsing star encounters
a crushing spacelike singularity, an observer falling in at late times
generally reaches a null singularity which is vastly different in character to
the standard Belinsky, Khalatnikov and Lifschitz (BKL) spacelike singularity.
In the spirit of the classic work of BKL we present an asymptotic analysis of
the null singularity inside a realistic black hole. Motivated by current
understanding of spherical models, we argue that the Einstein equations reduce
to a simple form in the neighborhood of the null singularity. The main results
arising from this approach are demonstrated using an almost plane symmetric
model. The analysis shows that the null singularity results from the blueshift
of the late-time gravitational wave tail; the amplitude of these gravitational
waves is taken to decay as an inverse power of advanced time as suggested by
perturbation theory. The divergence of the Weyl curvature at the null
singularity is dominated by the propagating modes of the gravitational field.
The null singularity is weak in the sense that tidal distortion remains bounded
along timelike geodesics crossing the Cauchy horizon. These results are in
agreement with previous analyses of black hole interiors. We briefly discuss
some outstanding problems which must be resolved before the picture of the
generic black hole interior is complete.Comment: 16 pages, RevTeX, 3 figures included using psfi
Evaporation of a two-dimensional charged black hole
We construct a dilatonic two-dimensional model of a charged black hole. The
classical solution is a static charged black hole, characterized by two
parameters, and , representing the black hole's mass and charge. Then we
study the semiclassical effects, and calculate the evaporation rate of both
and , as a function of these two quantities. Analyzing this dynamical
system, we find two qualitatively different regimes, depending on the
electromagnetic coupling constant . If the latter is greater than a
certain critical value, the charge-to-mass ratio decays to zero upon
evaporation. On the other hand, for smaller than the critical value,
the charge-to-mass ratio approaches a non-zero constant that depends on
but not on the initial values of and .Comment: Latex, 30 pages, accepted for publication in Phys. Rev.
Conditional Spectral Analysis of Replicated Multiple Time Series with Application to Nocturnal Physiology
This article considers the problem of analyzing associations between power
spectra of multiple time series and cross-sectional outcomes when data are
observed from multiple subjects. The motivating application comes from sleep
medicine, where researchers are able to non-invasively record physiological
time series signals during sleep. The frequency patterns of these signals,
which can be quantified through the power spectrum, contain interpretable
information about biological processes. An important problem in sleep research
is drawing connections between power spectra of time series signals and
clinical characteristics; these connections are key to understanding biological
pathways through which sleep affects, and can be treated to improve, health.
Such analyses are challenging as they must overcome the complicated structure
of a power spectrum from multiple time series as a complex positive-definite
matrix-valued function. This article proposes a new approach to such analyses
based on a tensor-product spline model of Cholesky components of
outcome-dependent power spectra. The approach flexibly models power spectra as
nonparametric functions of frequency and outcome while preserving geometric
constraints. Formulated in a fully Bayesian framework, a Whittle likelihood
based Markov chain Monte Carlo (MCMC) algorithm is developed for automated
model fitting and for conducting inference on associations between outcomes and
spectral measures. The method is used to analyze data from a study of sleep in
older adults and uncovers new insights into how stress and arousal are
connected to the amount of time one spends in bed
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