394 research outputs found
Formation of trapped surfaces for the spherically symmetric Einstein-Vlasov system
We consider the spherically symmetric, asymptotically flat, non-vacuum
Einstein equations, using as matter model a collisionless gas as described by
the Vlasov equation. We find explicit conditions on the initial data which
guarantee the formation of a trapped surface in the evolution which in
particular implies that weak cosmic censorship holds for these data. We also
analyze the evolution of solutions after a trapped surface has formed and we
show that the event horizon is future complete. Furthermore we find that the
apparent horizon and the event horizon do not coincide. This behavior is
analogous to what is found in certain Vaidya spacetimes. The analysis is
carried out in Eddington-Finkelstein coordinates.Comment: 2
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
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
Newtonian and General Relativistic Models of Spherical Shells - II
A family of potential-density pairs that represent spherical shells with
finite thickness is obtained from the superposition of spheres with finite
radii. Other families of shells with infinite thickness with a central hole are
obtained by inversion transformations of spheres and of the finite shells. We
also present a family of double shells with finite thickness. All
potential-density pairs are analytical and can be stated in terms of elementary
functions. For the above-mentioned structures, we study the circular orbits of
test particles and their stability with respect to radial perturbations. All
examples presented are found to be stable. A particular isotropic form of a
metric in spherical coordinates is used to construct a General Relativistic
version of the Newtonian families of spheres and shells. The matter of these
structures is anisotropic, and the degree of anisotropy is a function of the
radius.Comment: 22 pages, 7 figures, accepted for publication in MNRA
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
Multipole radiation in a collisonless gas coupled to electromagnetism or scalar gravitation
We consider the relativistic Vlasov-Maxwell and Vlasov-Nordstr\"om systems
which describe large particle ensembles interacting by either electromagnetic
fields or a relativistic scalar gravity model. For both systems we derive a
radiation formula analogous to the Einstein quadrupole formula in general
relativity.Comment: 21 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
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-
Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials
In this paper it is shown that unique solutions to the relativistic Boltzmann
equation exist for all time and decay with any polynomial rate towards their
steady state relativistic Maxwellian provided that the initial data starts out
sufficiently close in . If the initial data are continuous then
so is the corresponding solution. We work in the case of a spatially periodic
box. Conditions on the collision kernel are generic in the sense of
(Dudy{\'n}ski and Ekiel-Je{\.z}ewska, Comm. Math. Phys., 1988); this resolves
the open question of global existence for the soft potentials.Comment: 64 page
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