58 research outputs found
On the smoothness of the multi-BMPV black hole spacetime
We demonstrate that, in a multi-BMPV black hole spacetime, the event horizon
is not smooth. We explicitly show that for a simpler configuration comprising a
line of static extremal black holes and a single BMPV black hole, the metric at
the horizon of the BMPV black hole is once, but not twice, continuously
differentiable. We argue that this result is also valid when all the black
holes are rotating. The Maxwell field strength is shown to be continuous, but
not differentiable at the horizon. We also briefly demonstrate that previous
work done to show lack of smoothness of static multi-centre solutions in five
dimensions is not significantly modified by the inclusion of a higher
derivative term in the action for five dimensional supergravity.Comment: 17 pages; reference adde
On the smoothness of multi-M2 brane horizons
We calculate the degree of horizon smoothness of multi- -brane solution
with branes along a common axis. We find that the metric is generically only
thrice continuously differentiable at any of the horizons. The four-form field
strength is found to be only twice continuously differentiable. We work with
Gaussian null-like co-ordinates which are obtained by solving geodesic
equations for multi- brane geometry. We also find different, exact
co-ordinate transformations which take the metric from isotropic co-ordinates
to co-ordinates in which metric is thrice differentiable at the horizon. Both
methods give the same result that the multi- brane metric is only thrice
continuously differentiable at the horizon.Comment: 24 pages, reference added, modified equation for non-singularity of
metri
On the smoothness of static multi-black hole solutions of higher-dimensional Einstein-Maxwell theory
Previous work has shown that static multi-black hole solutions of
higher-dimensional Einstein-Maxwell theory do not possess smooth horizons. We
show that the lack of smoothness is worse than previously demonstrated. We
consider solutions describing multiple black holes on a common axis. In five
dimensions, the metric is generically twice, but not three times, continuously
differentiable at the horizon. The Maxwell field is generically continuous, but
not differentiable, at the horizon. In more than five dimensions, the metric is
once, but not twice, continuously differentiable, and there is a
parallely-propagated curvature singularity at the horizon. The Maxwell field
strength is again continuous, but not differentiable, at the horizon.Comment: 19 pages; minor correction
Weighing the galactic disc using the Jeans equation: lessons from simulations
Using three-dimensional stellar kinematic data from simulated galaxies, we examine the efficacy of a Jeans equation analysis in reconstructing the total disk surface density, including the dark matter, at the ‘Solar’ radius. Our simulation data set includes galaxies formed in a cosmological context using state-of-the-art high-resolution cosmological zoom simulations, and other idealized models. The cosmologically formed galaxies have been demonstrated to lie on many of the observed scaling relations for late-type spirals, and thus offer an interesting surrogate for real galaxies with the obvious advantage that all the kinematical data are known perfectly. We show that the vertical velocity dispersion is typically the dominant kinematic quantity in the analysis, and that the traditional method of using only the vertical force is reasonably effective at low heights above the disk plane. At higher heights the inclusion of the radial force becomes increasingly important. We also show that the method is sensitive to uncertainties in the measured disk parameters, particularly the scalelengths of the assumed double exponential density distribution, and the scalelength of the radial velocity dispersion. In addition, we show that disk structure and low number statistics can lead to significant errors in the calculated surface densities. Finally, we examine the implications of our results for previous studies of this sort, suggesting that more accurate measurements of the scalelengths may help reconcile conflicting estimates of the local dark matter density in the literature
Simple and accurate modelling of the gravitational potential produced by thick and thin exponential discs
We present accurate models of the gravitational potential produced by a radially exponential disc mass distribution. The models are produced by combining three separate Miyamoto–Nagai discs. Such models have been used previously to model the disc of the Milky Way, but here we extend this framework to allow its application to discs of any mass, scalelength, and a wide range of thickness from infinitely thin to near spherical (ellipticities from 0 to 0.9). The models have the advantage of simplicity of implementation, and we expect faster run speeds over a double exponential disc treatment. The potentials are fully analytical, and differentiable at all points. The mass distribution of our models deviates from the radial mass distribution of a pure exponential disc by <0.4 per cent out to 4 disc scalelengths, and <1.9 per cent out to 10 disc scalelengths. We tabulate fitting parameters which facilitate construction of exponential discs for any scalelength, and a wide range of disc thickness (a user-friendly, web-based interface is also available). Our recipe is well suited for numerical modelling of the tidal effects of a giant disc galaxy on star clusters or dwarf galaxies. We consider three worked examples; the Milky Way thin and thick disc, and a discy dwarf galaxy
Life and death of a hero - Lessons learned from modeling the dwarf spheroidal Hercules: an incorrect orbit?
Hercules is a dwarf spheroidal satellite of the Milky Way, found at a
distance of about 138 kpc, and showing evidence of tidal disruption. It is very
elongated and exhibits a velocity gradient of 16 +/- 3 km/s/kpc. Using this
data a possible orbit of Hercules has previously been deduced in the
literature. In this study we make use of a novel approach to find a best fit
model that follows the published orbit. Instead of using trial and error, we
use a systematic approach in order to find a model that fits multiple
observables simultaneously. As such, we investigate a much wider parameter
range of initial conditions and ensure we have found the best match possible.
Using a dark matter free progenitor that undergoes tidal disruption, our
best-fit model can simultaneously match the observed luminosity, central
surface brightness, effective radius, velocity dispersion, and velocity
gradient of Hercules. However, we find it is impossible to reproduce the
observed elongation and the position angle of Hercules at the same time in our
models. This failure persists even when we vary the duration of the simulation
significantly, and consider a more cuspy density distribution for the
progenitor. We discuss how this suggests that the published orbit of Hercules
is very likely to be incorrect.Comment: accepted by MNRAS; 19 pages, 19 figures, 2 table
Ursa Major II - Reproducing the observed properties through tidal disruption
Recent deep photometry of the dwarf spheroidal Ursa Major II's morphology,
and spectroscopy of individual stars, have provided a number of new constraints
on its properties. With a velocity dispersion 6 km s, and under
the assumption that the galaxy is virialised, the mass-to-light ratio is found
to be approaching 2000 - apparently heavily dark matter dominated. Using
N-Body simulations, we demonstrate that the observed luminosity, ellipticity,
irregular morphology, velocity gradient, and the velocity dispersion can be
well reproduced through processes associated with tidal mass loss, and in the
absence of dark matter. These results highlight the considerable uncertainty
that exists in measurements of the dark matter content of Ursa Major II. The
dynamics of the inner tidal tails, and tidal stream, causes the observed
velocity dispersion of stars to be boosted to values of 5 km s (20
km s at times). This effect is responsible for raising the velocity
dispersion of our model to the observed values in UMaII. We test an iterative
rejection technique for removing unbound stars from samples of UMaII stars
whose positions on the sky, and line-of-sight velocities, are provided. We find
this technique is very effective at providing an accurate bound mass from this
information, and only fails when the galaxy has a bound mass less than 10 of
its initial mass. However when mass remains bound, mass overestimation by
3 orders of magnitude are seen. Additionally we find that mass measurements
are sensitive to measurement uncertainty in line-of-sight velocities.
Measurement uncertainties of 1-4 km s result in mass overestimates by a
factor of 1.3-5.7.Comment: 17 pages, 12 figures, accepted to MNRAS: 23rd, May, 201
Time-Dependent Multi-Centre Solutions from New Metrics with Holonomy Sim(n-2)
The classifications of holonomy groups in Lorentzian and in Euclidean
signature are quite different. A group of interest in Lorentzian signature in n
dimensions is the maximal proper subgroup of the Lorentz group, SIM(n-2).
Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg,
and a single four-dimensional example with a non-zero cosmological constant was
exhibited by Ghanam and Thompson. Here we reduce the problem of finding the
general -dimensional Einstein metric of SIM(n-2) holonomy, with and without
a cosmological constant, to solving a set linear generalised Laplace and
Poisson equations on an (n-2)-dimensional Einstein base manifold. Explicit
examples may be constructed in terms of generalised harmonic functions. A
dimensional reduction of these multi-centre solutions gives new time-dependent
Kaluza-Klein black holes and monopoles, including time-dependent black holes in
a cosmological background whose spatial sections have non-vanishing curvature.Comment: Typos corrected; 29 page
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