356 research outputs found
The formation of black holes in spherically symmetric gravitational collapse
We consider the spherically symmetric, asymptotically flat Einstein-Vlasov
system. We find explicit conditions on the initial data, with ADM mass M, such
that the resulting spacetime has the following properties: there is a family of
radially outgoing null geodesics where the area radius r along each geodesic is
bounded by 2M, the timelike lines are incomplete, and for r>2M
the metric converges asymptotically to the Schwarzschild metric with mass M.
The initial data that we construct guarantee the formation of a black hole in
the evolution. We also give examples of such initial data with the additional
property that the solutions exist for all and all Schwarzschild time,
i.e., we obtain global existence in Schwarzschild coordinates in situations
where the initial data are not small. Some of our results are also established
for the Einstein equations coupled to a general matter model characterized by
conditions on the matter quantities.Comment: 36 pages. A corollary on global existence in Schwarzschild
coordinates for data which are not small is added together with minor
modification
A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system
The stability features of steady states of the spherically symmetric
Einstein-Vlasov system are investigated numerically. We find support for the
conjecture by Zeldovich and Novikov that the binding energy maximum along a
steady state sequence signals the onset of instability, a conjecture which we
extend to and confirm for non-isotropic states. The sign of the binding energy
of a solution turns out to be relevant for its time evolution in general. We
relate the stability properties to the question of universality in critical
collapse and find that for Vlasov matter universality does not seem to hold.Comment: 29 pages, 10 figure
Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant
The behaviour of expanding cosmological models with collisionless matter and
a positive cosmological constant is analysed. It is shown that under the
assumption of plane or hyperbolic symmetry the area radius goes to infinity,
the spacetimes are future geodesically complete, and the expansion becomes
isotropic and exponential at late times. This proves a form of the cosmic no
hair theorem in this class of spacetimes
On the area of the symmetry orbits in symmetric spacetimes
We obtain a global existence result for the Einstein equations. We show that
in the maximal Cauchy development of vacuum symmetric initial data with
nonvanishing twist constant, except for the special case of flat Kasner initial
data, the area of the group orbits takes on all positive values. This
result shows that the areal time coordinate which covers these spacetimes
runs from zero to infinity, with the singularity occurring at R=0.Comment: The appendix which appears in version 1 has a technical problem (the
inequality appearing as the first stage of (52) is not necessarily true), and
since the appendix is unnecessary for the proof of our results, we leave it
out. version 2 -- clarifications added, version 3 -- reference correcte
Bounds on the mass-to-radius ratio for non-compact field configurations
It is well known that a spherically symmetric compact star whose energy
density decreases monotonically possesses an upper bound on its mass-to-radius
ratio, . However, field configurations typically will not be
compact. Here we investigate non-compact static configurations whose matter
fields have a slow global spatial decay, bounded by a power law behavior. These
matter distributions have no sharp boundaries. We derive an upper bound on the
fundamental ratio max_r{2m(r)/r} which is valid throughout the bulk. In its
simplest form, the bound implies that in any region of spacetime in which the
radial pressure increases, or alternatively decreases not faster than some
power law , one has . [For
the bound degenerates to .] In its general version, the bound
is expressed in terms of two physical parameters: the spatial decaying rate of
the matter fields, and the highest occurring ratio of the trace of the pressure
tensor to the local energy density.Comment: 4 page
A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3
We investigate the initial value problem for the Einstein-Euler equations of
general relativity under the assumption of Gowdy symmetry on T3, and we
construct matter spacetimes with low regularity. These spacetimes admit, both,
impulsive gravitational waves in the metric (for instance, Dirac mass curvature
singularities propagating at light speed) and shock waves in the fluid (i.e.,
discontinuities propagating at about the sound speed). Given an initial data
set, we establish the existence of a future development and we provide a global
foliation in terms of a globally and geometrically defined time-function,
closely related to the area of the orbits of the symmetry group. The main
difficulty lies in the low regularity assumed on the initial data set which
requires a distributional formulation of the Einstein-Euler equations.Comment: 24 page
An All-Photonic Molecule-Based D Flip-Flop
The photochromic fluorescence switching of a fulgimide derivative was used to implement the first molecule-based D (delay) flip-flop device, which works based on the principles of sequential logic. The device operates exclusively with photonic signals and can be conveniently switched in repeated cycles. \ua9 2011 American Chemical Society
A molecule-based 1 : 2 digital demultiplexer
A trichromophoric molecule consisting of a porphyrin linked to both a dihydropyrene and a dihydroindolizine-type photochrome, in combination with a third harmonic generating crystal, functions as a 1:2 digital demultiplexer with photonic inputs and outputs. Each of the two photochromes may be cycled independently between two metastable forms, leading to four photoisomers, three of which are used in the demultiplexer. These isomers interact photochemically with the porphyrin in order to yield the demultiplexer function. With the address input (1064-nm light) turned off, one Output of the device (porphyrin fluorescence) tracks the state of the data input (532-nm light). When the address input is turned on, the second output (absorbance at 572 nm) tracks the state of the data input, while the first output remains off. The demultiplexer does not require chemical or electrical inputs, and can cycle through its operational sequences multiple times
8-Triazolylpurines: Towards Fluorescent Inhibitors of the MDM2/p53 Interaction
Small molecule nonpeptidic mimics of alpha-helices are widely recognised as protein-protein interaction (PPIs) inhibitors. Protein-protein interactions mediate virtually all important regulatory pathways in a cell, and the ability to control and modulate PPIs is therefore of great significance to basic biology, where controlled disruption of protein networks is key to understanding network connectivity and function. We have designed and synthesised two series of 2,6,9-substituted 8-triazolylpurines as alpha-helix mimetics. The first series was designed based on low energy conformations but did not display any biological activity in a biochemical fluorescence polarisation assay targeting MDM2/p53. Although solution NMR conformation studies demonstrated that such molecules could mimic the topography of an alpha-helix, docking studies indicated that the same compounds were not optimal as inhibitors for the MDM2/p53 interaction. A new series of 8-triazolylpurines was designed based on a combination of docking studies and analysis of recently published inhibitors. The best compound displayed low micromolar inhibitory activity towards MDM2/p53 in a biochemical fluorescence polarisation assay. In order to evaluate the applicability of these compounds as biologically active and intrinsically fluorescent probes, their absorption/emission properties were measured. The compounds display fluorescent properties with quantum yields up to 50%
The Einstein-Vlasov System/Kinetic Theory
The main purpose of this article is to provide a guide to theorems on global
properties of solutions to the Einstein--Vlasov system. This system couples
Einstein's equations to a kinetic matter model. Kinetic theory has been an
important field of research during several decades in which the main focus has
been on non-relativistic and special relativistic physics, i.e., to model the
dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In
1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov
system. Since then many theorems on global properties of solutions to this
system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-
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