231 research outputs found
Schwarzschild-de Sitter Spacetimes, McVittie Coordinates, and Trumpet Geometries
Trumpet geometries play an important role in numerical simulations of black
hole spacetimes, which are usually performed under the assumption of asymptotic
flatness. Our Universe is not asymptotically flat, however, which has motivated
numerical studies of black holes in asymptotically de Sitter spacetimes. We
derive analytical expressions for trumpet geometries in Schwarzschild-de Sitter
spacetimes by first generalizing the static maximal trumpet slicing of the
Schwarzschild spacetime to static constant mean curvature trumpet slicings of
Schwarzschild-de Sitter spacetimes. We then switch to a comoving isotropic
radial coordinate which results in a coordinate system analogous to McVittie
coordinates. At large distances from the black hole the resulting metric
asymptotes to a Friedmann-Lemaitre-Robertson-Walker metric with an
exponentially-expanding scale factor. While McVittie coordinates have another
asymptotically de Sitter end as the radial coordinate goes to zero, so that
they generalize the notion of a "wormhole" geometry, our new coordinates
approach a horizon-penetrating trumpet geometry in the same limit. Our
analytical expressions clarify the role of time-dependence, boundary conditions
and coordinate conditions for trumpet slices in a cosmological context, and
provide a useful test for black hole simulations in asymptotically de Sitter
spacetimes.Comment: 7 pages, 3 figures, added referenc
Approximate initial data for binary black holes
We construct approximate analytical solutions to the constraint equations of
general relativity for binary black holes of arbitrary mass ratio in
quasicircular orbit. We adopt the puncture method to solve the constraint
equations in the transverse-traceless decomposition and consider perturbations
of Schwarzschild black holes caused by boosts and the presence of a binary
companion. A superposition of these two perturbations then yields approximate,
but fully analytic binary black hole initial data that are accurate to first
order in the inverse of the binary separation and the square of the black
holes' momenta.Comment: 13 pages, 4 figures, added comparison to numerical calculations,
accepted to PR
Trumpet Slices in Kerr Spacetimes
We introduce a new time-independent family of analytical coordinate systems
for the Kerr spacetime representing rotating black holes. We also propose a
(2+1)+1 formalism for the characterization of trumpet geometries. Applying this
formalism to our new family of coordinate systems we identify, for the first
time, analytical and stationary trumpet slices for general rotating black
holes, even for charged black holes in the presence of a cosmological constant.
We present results for metric functions in this slicing and analyze the
geometry of the rotating trumpet surface.Comment: 5 pages, 2 figures; version published in PR
Trumpet slices of the Schwarzschild-Tangherlini spacetime
We study families of time-independent maximal and 1+log foliations of the
Schwarzschild-Tangherlini spacetime, the spherically-symmetric vacuum black
hole solution in D spacetime dimensions, for D >= 4. We identify special
members of these families for which the spatial slices display a trumpet
geometry. Using a generalization of the 1+log slicing condition that is
parametrized by a constant n we recover the results of Nakao, Abe, Yoshino and
Shibata in the limit of maximal slicing. We also construct a numerical code
that evolves the BSSN equations for D=5 in spherical symmetry using
moving-puncture coordinates, and demonstrate that these simulations settle down
to the trumpet solutions.Comment: 11 pages, 6 figures, submitted to PR
Analytical Tendex and Vortex Fields for Perturbative Black Hole Initial Data
Tendex and vortex fields, defined by the eigenvectors and eigenvalues of the
electric and magnetic parts of the Weyl curvature tensor, form the basis of a
recently developed approach to visualizing spacetime curvature. In particular,
this method has been proposed as a tool for interpreting results from numerical
binary black hole simulations, providing a deeper insight into the physical
processes governing the merger of black holes and the emission of gravitational
radiation. Here we apply this approach to approximate but analytical initial
data for both single boosted and binary black holes. These perturbative data
become exact in the limit of small boost or large binary separation. We hope
that these calculations will provide additional insight into the properties of
tendex and vortex fields, and will form a useful test for future numerical
calculations.Comment: 18 pages, 8 figures, submitted to PR
Maximally Rotating Supermassive Stars at the Onset of Collapse: Effects of Gas Pressure
The "direct collapse" scenario has emerged as a promising evolutionary track
for the formation of supermassive black holes early in the Universe. In an
idealized version of such a scenario, a uniformly rotating supermassive star
spinning at the mass-shedding (Keplerian) limit collapses gravitationally after
it reaches a critical configuration. Under the assumption that the gas is
dominated by radiation pressure, this critical configuration is characterized
by unique values of the dimensionless parameters and , where
is the angular momentum, the polar radius, and the mass. Motivated by
a previous perturbative treatment we adopt a fully nonlinear approach to
evaluate the effects of gas pressure on these dimensionless parameters for a
large range of masses. We find that gas pressure has a significant effect on
the critical configuration even for stellar masses as large as . We also calibrate two approximate treatments of the gas pressure
perturbation in a comparison with the exact treatment, and find that one
commonly used approximation in particular results in increasing deviations from
the exact treatment as the mass decreases, and the effects of gas pressure
increase. The other approximation, however, proves to be quite robust for all
masses .Comment: 13 pages, 7 figures, version accepted for publication in MNRA
A Simple Family of Analytical Trumpet Slices of the Schwarzschild Spacetime
We describe a simple family of analytical coordinate systems for the
Schwarzschild spacetime. The coordinates penetrate the horizon smoothly and are
spatially isotropic. Spatial slices of constant coordinate time feature a
trumpet geometry with an asymptotically cylindrical end inside the horizon at a
prescribed areal radius (with ) that serves as the free
parameter for the family. The slices also have an asymptotically flat end at
spatial infinity. In the limit the spatial slices lose their trumpet
geometry and become flat -- in this limit, our coordinates reduce to
Painlev\'e-Gullstrand coordinates.Comment: 7 pages, 3 figure
Dynamical perturbations of black-hole punctures: effects of slicing conditions
While numerous numerical relativity simulations adopt a 1+log slicing
condition, shock-avoiding slicing conditions form a viable and sometimes
advantageous alternative. Despite both conditions satisfying similar equations,
recent numerical experiments point to a qualitative difference in the behavior
of the lapse in the vicinity of the black-hole puncture: for 1+log slicing, the
lapse appears to decay approximately exponentially, while for shock-avoiding
slices it performs approximately harmonic oscillation. Motivated by this
observation, we consider dynamical coordinate transformations of the
Schwarzschild spacetime to describe small perturbations of static trumpet
geometries analytically. We find that the character of the resulting equations
depends on the (unperturbed) mean curvature at the black-hole puncture: for
1+log slicing it is positive, predicting exponential decay in the lapse, while
for shock-avoiding slices it vanishes, leading to harmonic oscillation. In
addition to identifying the value of the mean curvature as the origin of these
qualitative differences, our analysis provides insight into the dynamical
behavior of black-hole punctures for different slicing conditions.Comment: 8 pages, 2 figure
Phenotypically distinct neutrophils patrol uninfected human and mouse lymph nodes.
Neutrophils play a key role in innate immunity. As the dominant circulating phagocyte, they are rapidly recruited from the bloodstream to sites of infection or injury to internalize and destroy microbes. More recently, neutrophils have been identified in uninfected organs, challenging the classical view of their function. Here we show that neutrophils were present in lymph nodes (LNs) in homeostasis. Using flow cytometry and confocal imaging, we identified neutrophils within LNs in naive, unchallenged mice, including LNs draining the skin, lungs, and gastrointestinal tract. Neutrophils were enriched within specific anatomical regions, in the interfollicular zone, a site of T cell activation. Intravital two-photon microscopy demonstrated that LN neutrophils were motile, trafficked into LNs from both blood and tissues via high endothelial venules and afferent lymphatics, respectively, and formed interactions with dendritic cells in LNs. Murine and human LN neutrophils had a distinct phenotype compared with circulating neutrophils, with higher major histocompatibility complex II (MHCII) expression, suggesting a potential role in CD4 T cell activation. Upon ex vivo stimulation with IgG immune complex (IC), neutrophils up-regulated expression of MHCII and costimulatory molecules and increased T cell activation. In vivo, neutrophils were capable of delivering circulating IC to LNs, suggesting a broader functional remit. Overall, our data challenge the perception that neutrophil patrol is limited to the circulation in homeostasis, adding LNs to their routine surveillance territory.L.S.C.L. was funded by Wellcome Trust (104384/Z/14/Z). M.R.C. is supported by National Institute of Health Research (NIHR) Cambridge Biomedical Research Centre, Chan-Zuckerburg Initiative Human Cell Atlas Technology Development Grant, Medical Research Council New Investigator Research Grant (MR/N024907/1), Arthritis Research UK Cure Challenge Research Grant (21777), and NIHR Research Professorship (RP-2017-08- ST2-002)
Characterising the impact of sex on severe asthma (SA) in the UK Severe Asthma Registry (UKSAR)
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