47,879 research outputs found
The Black Hole Particle Accelerator as a Machine to make Baby Universes
General relativity predicts that the inner horizon of an astronomically
realistic rotating black hole is subject to the mass inflation instability. The
inflationary instability acts like a gravity-powered particle accelerator of
extraordinary power, accelerating accreted streams of particles along the
principal outgoing and ingoing null directions at the inner horizon to
collision energies that would, if nothing intervened, typically exceed
exponentially the Planck energy. The inflationary instability is fueled by
ongoing accretion, and is occurring inevitably in essentially every black hole
in our Universe. This extravagant machine, the Black Hole Particle Accelerator,
has the hallmarks of a device to make baby universes. Since collisions are most
numerous inside supermassive black holes, reproductive efficiency requires our
Universe to make supermassive black holes efficiently, as is observed.Comment: 7 pages, 2 figures. NO honorable mention in the 2013 Essay
Competition of the Gravity Research Foundatio
Ways to improve your correlation functions
This paper describes a number of ways to improve on the standard method for measuring the two-point correlation function of large scale structure in the Universe. Issues addressed are: (1) the problem of the mean density, and how to solve it; (2) how to estimate the uncertainty in a measured correlation function; (3) minimum variance pair weighting; (4) unbiased estimation of the selection function when magnitudes are discrete; and (5) analytic computation of angular integrals in background pair counts
Omega from the anisotropy of the redshift correlation function
Peculiar velocities distort the correlation function of galaxies observed in redshift space. In the large scale, linear regime, the distortion takes a characteristic quadrupole plus hexadecapole form, with the amplitude of the distortion depending on the cosmological density parameter omega. Preliminary measurements are reported here of the harmonics of the correlation function in the CfA, SSRS, and IRAS 2 Jansky redshift surveys. The observed behavior of the harmonics agrees qualitatively with the predictions of linear theory on large scales in every survey. However, real anisotropy in the galaxy distribution induces large fluctuations in samples which do not yet probe a sufficiently fair volume of the Universe. In the CfA 14.5 sample in particular, the Great Wall induces a large negative quadrupole, which taken at face value implies an unrealistically large omega 20. The IRAS 2 Jy survey, which covers a substantially larger volume than the optical surveys and is less affected by fingers-of-god, yields a more reliable and believable value, omega = 0.5 sup +.5 sub -.25
Nonlinear Cosmological Power Spectra in Real and Redshift--Space
We present an expression for the nonlinear evolution of the cosmological
power spectrum based on following Lagrangian trajectories. This is simplified
using the Zel'dovich approximation to trace particle displacements, assuming
Gaussian initial conditions. The model is found to exhibit the transfer of
power from large to small scales expected in self- gravitating fields. We have
extended this analysis into redshift-space and found a solution for the
nonlinear, anisotropic redshift-space power spectrum in the limit of
plane--parallel redshift distortions. The quadrupole-to- monopole ratio is
calculated for the case of power-law initial spectra. We find that the shape of
this ratio depends on the shape of the initial spectrum, but when scaled to
linear theory depends only weakly on the redshift-space distortion parameter,
. The point of zero-crossing of the quadrupole, , is found to obey
a scaling relation. This model is found to be in agreement with -body
simulations on scales down to the zero-crossing of the quadrupole, although the
wavenumber at zero-crossing is underestimated. These results are applied to the
quadrupole--monopole ratio found in the merged QDOT+1.2 Jy IRAS redshift
survey. We have estimated that the distortion parameter is constrained to be
at the level. The local primordial spectral slope is not
well constrained, but analysis suggests in the translinear
regime. The zero-crossing scale of the quadrupole is
and from this we infer the amplitude of clustering is .
We suggest that the success of this model is due to nonlinear redshift--space
effects arising from infall onto caustics and is not dominated by virialised
cluster cores.Comment: 13 pages, uufiles, Latex with 6 postscript figures, submitted to
MNRA
Lagrangian Evolution of the Weyl Tensor
We derive the evolution equations for the electric and magnetic parts of the
Weyl tensor for cold dust from both general relativity and Newtonian gravity.
In a locally inertial frame at rest in the fluid frame, the Newtonian equations
agree with those of general relativity. We give explicit expressions for the
electric and magnetic parts of the Weyl tensor in the Newtonian limit. In
general, the magnetic part does not vanish, implying that the Lagrangian
evolution of the fluid is not purely local.Comment: 17 pages, AAS LateX v3.0, submitted to ApJ, MIT-CSR-94-0
Spherical Redshift Distortions
Peculiar velocities induce apparent line of sight displacements of galaxies
in redshift space, distorting the pattern of clustering in the radial versus
transverse directions. On large scales, the amplitude of the distortion yields
a measure of the dimensionless linear growth rate , where is the cosmological density and the linear
bias factor. To make the maximum statistical use of the data in a wide angle
redshift survey, and for the greatest accuracy, the spherical character of the
distortion needs to be treated properly, rather than in the simpler plane
parallel approximation. In the linear regime, the redshift space correlation
function is described by a spherical distortion operator acting on the true
correlation function. It is pointed out here that there exists an operator,
which is essentially the logarithmic derivative with respect to pair
separation, which both commutes with the spherical distortion operator, and at
the same time defines a characteristic scale of separation. The correlation
function can be expanded in eigenfunctions of this operator, and these
eigenfunctions are eigenfunctions of the distortion operator. Ratios of the
observed amplitudes of the eigenfunctions yield measures of the linear growth
rate in a manner independent of the shape of the correlation function.
More generally, the logarithmic derivative with
respect to depth , along with the square and component of the
angular momentum operator, form a complete set of commuting operators for the
spherical distortion operator acting on the density. The eigenfunctions of this
complete set of operators are spherical waves about the observer, with radial
part lying in logarithmic real or Fourier space.Comment: 15 pages, with 1 embedded EPS figur
Local light-ray rotation
We present a sheet structure that rotates the local ray direction through an
arbitrary angle around the sheet normal. The sheet structure consists of two
parallel Dove-prism sheets, each of which flips one component of the local
direction of transmitted light rays. Together, the two sheets rotate
transmitted light rays around the sheet normal. We show that the direction
under which a point light source is seen is given by a Mobius transform. We
illustrate some of the properties with movies calculated by ray-tracing
software.Comment: 9 pages, 6 figure
A note on dual giant gravitons in
We study some of the properties of dual giant gravitons - D2-branes wrapped
on an - in type IIA string theory on . In particular we confirm that the spectrum of small
fluctuations about the giant is both real and independent of the size of the
graviton. We also extend previously developed techniques for attaching open
strings to giants to this D2-brane giant and focus on two particular limits of
the resulting string sigma model: In the pp-wave limit we quantize the string
and compute the spectrum of bosonic excitations while in the semiclassical
limit, we read off the fast string Polyakov action and comment on the
comparison to the Landau-Lifshitz action for the dual open spin chain.Comment: v3 significantly changed: added coupling to RR 1-form and turned on
worldvolume gauge field, computed gauge field fluctuation, added comments on
closure of the sl(2) sector and re-written to improve clarity. This version
published in JHE
Metamaterials for light rays: ray optics without wave-optical analog in the ray-optics limit
Volumes of sub-wavelength electromagnetic elements can act like homogeneous
materials: metamaterials. In analogy, sheets of optical elements such as prisms
can act ray-optically like homogeneous sheet materials. In this sense, such
sheets can be considered to be metamaterials for light rays (METATOYs).
METATOYs realize new and unusual transformations of the directions of
transmitted light rays. We study here, in the ray-optics and scalar-wave
limits, the wave-optical analog of such transformations, and we show that such
an analog does not always exist. Perhaps, this is the reason why many of the
ray-optical possibilities offered by METATOYs have never before been
considered.Comment: 10 pages, 3 figures, references update
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