276 research outputs found
A new algorithm for anisotropic solutions
We establish a new algorithm that generates a new solution to the Einstein
field equations, with an anisotropic matter distribution, from a seed isotropic
solution. The new solution is expressed in terms of integrals of an isotropic
gravitational potential; and the integration can be completed exactly for
particular isotropic seed metrics. A good feature of our approach is that the
anisotropic solutions necessarily have an isotropic limit. We find two examples
of anisotropic solutions which generalise the isothermal sphere and the
Schwarzschild interior sphere. Both examples are expressed in closed form
involving elementary functions only.Comment: 16 pages, to appear in Pramana - J. Phy
A power-law distribution for tenure lengths of sports managers
We show that the tenure lengths for managers of sport teams follow a power law distribution with an exponent between 2 and 3. We develop a simple theoretical model which replicates this result. The model demonstrates that the empirical phenomenon can be understood as the macroscopic outcome of pairwise interactions among managers in a league, threshold effects in managerial performance evaluation, competitive market forces, and luck at the microscopic level
Inhomogeneous imperfect fluid spherical models without Big-Bang singularity
So far all known singularity-free cosmological models are cylindrically
symmetric. Here we present a new family of spherically symmetric non-singular
models filled with imperfect fluid and radial heat flow, and satisfying the
weak and strong energy conditions. For large anisotropy in pressure and
heat flux tend to vanish leading to a perfect fluid. There is a free function
of time in the model, which can be suitably chosen for non-singular behaviour
and there exist multiplicity of such choices.Comment: 8 pages, LaTeX versio
Clustering in gravitating N-body systems
We study gravitational clustering of mass points in three dimensions with
random initial positions and periodic boundary conditions (no expansion) by
numerical simulations. Correlation properties are well defined in the system
and a sort of thermodynamic limit can be defined for the transient regime of
cluste ring. Structure formation proceeds along two paths: (i) fluid-like
evolution of density perturbations at large scales and (ii) shift of the
granular (non fluid) properties from small to large scales. The latter
mechanism finally dominates at all scales and it is responsible for the
self-similar characteristics of the clustering.Comment: 7 pages, 3 figures. Accepted for publication in Europhys. Let
Renormalization Group Flow and Fragmentation in the Self-Gravitating Thermal Gas
The self-gravitating thermal gas (non-relativistic particles of mass m at
temperature T) is exactly equivalent to a field theory with a single scalar
field phi(x) and exponential self-interaction. We build up perturbation theory
around a space dependent stationary point phi_0(r) in a finite size domain
delta \leq r \leq R ,(delta << R), which is relevant for astrophysical applica-
tions (interstellar medium,galaxy distributions).We compute the correlations of
the gravitational potential (phi) and of the density and find that they scale;
the latter scales as 1/r^2. A rich structure emerges in the two-point correl-
tors from the phi fluctuations around phi_0(r). The n-point correlators are
explicitly computed to the one-loop level.The relevant effective coupling turns
out to be lambda=4 pi G m^2 / (T R). The renormalization group equations (RGE)
for the n-point correlator are derived and the RG flow for the effective
coupling lambda(tau) [tau = ln(R/delta), explicitly obtained.A novel dependence
on tau emerges here.lambda(tau) vanishes each time tau approaches discrete
values tau=tau_n = 2 pi n/sqrt7-0, n=0,1,2, ...Such RG infrared stable behavior
[lambda(tau) decreasing with increasing tau] is here connected with low density
self-similar fractal structures fitting one into another.For scales smaller
than the points tau_n, ultraviolet unstable behaviour appears which we connect
to Jeans' unstable behaviour, growing density and fragmentation. Remarkably, we
get a hierarchy of scales and Jeans lengths following the geometric progression
R_n=R_0 e^{2 pi n /sqrt7} = R_0 [10.749087...]^n . A hierarchy of this type is
expected for non-spherical geometries,with a rate different from e^{2 n/sqrt7}.Comment: LaTex, 31 pages, 11 .ps figure
Free streaming in mixed dark matter
Free streaming in a \emph{mixture} of collisionless non-relativistic dark
matter (DM) particles is studied by implementing methods from the theory of
multicomponent plasmas. The mixture includes Fermionic, condensed and non
condensed Bosonic particles decoupling in equilibrium while relativistic, heavy
non-relativistic thermal relics (WIMPs), and sterile neutrinos that decouple
\emph{out of equilibrium} when they are relativistic. The free-streaming length
is obtained from the marginal zero of the gravitational
polarization function, which separates short wavelength Landau-damped from long
wavelength Jeans-unstable \emph{collective} modes. At redshift we find ,where are the \emph{fractions} of the respective DM components of mass
that decouple when the effective number of ultrarelativistic degrees of
freedom is , and only depend on the distribution functions at
decoupling, given explicitly in all cases. If sterile neutrinos produced either
resonantly or non-resonantly that decouple near the QCD scale are the
\emph{only} DM component,we find (non-resonant), (resonant).If WIMPs with
decoupling at are present in the mixture with
, is \emph{dominated} by CDM. If a Bose Einstein condensate is a DM
component its free streaming length is consistent with CDM because of the
infrared enhancement of the distribution function.Comment: 19 pages, 2 figures. More discussions same conclusions and results.
Version to appear in Phys. Rev.
Mapping the three-body system - decay time and reversibility
In this paper we carry out a quantitative analysis of the three-body systems
and map them as a function of decaying time and intial conguration, look at
this problem as an example of a simple deterministic system, and ask to what
extent the orbits are really predictable. We have investigated the behavior of
about 200 000 general Newtonian three body systems using the simplest initial
conditions. Within our resolution these cover all the possible states where the
objects are initially at rest and have no angular momentum. We have determined
the decay time-scales of the triple systems and show that the distribution of
this parameter is fractal in appearance. Some areas that appear stable on large
scales exhibit very narrow strips of instability and the overall pattern,
dominated by resonances, reminds us of a traditional Maasai warrior shield.
Also an attempt is made to recover the original starting conguration of the
three bodies by backward integration. We find there are instances where the
evolution to the future and to the past lead to different orbits, in spite of
time symmetric initial conditions. This implies that even in simple
deterministic systems there exists an Arrow of Time.Comment: 8 pages, 9 figures. Accepted for publication in MNRAS. Includes
low-resolution figures. High-resolution figures are available as PNG
Binary Collisions and the Slingshot Effect
We derive the equations for the gravity assist manoeuvre in the general 2D
case without the constraints of circular planetary orbits or widely different
masses as assumed by Broucke, and obtain the slingshot conditions and maximum
energy gain for arbitrary mass ratios of two colliding rigid bodies. Using the
geometric view developed in an earlier paper by the authors the possible
trajectories are computed for both attractive or repulsive interactions
yielding a further insight on the slingshot mechanics and its parametrization.
The general slingshot manoeuvre for arbitrary masses is explained as a
particular case of the possible outcomes of attractive or repulsive binary
collisions, and the correlation between asymptotic information and orbital
parameters is obtained in general.Comment: 12 pages, 7 figures, accepted for publication Dec'07, Celestial
Mechanics and Dynamical Astronom
Anisotropic static solutions in modelling highly compact bodies
Einstein field equations for anisotropic spheres are solved and exact
interior solutions obtained. This paper extends earlier treatments to include
anisotropic models which accommodate a wider variety of physically viable
energy densities. Two classes of solutions are possible. The first class
contains the limiting case for the energy density which
arises in many astrophysical applications. In the second class the singularity
at the center of the star is not present in the energy density. The models
presented in this paper allow for increasing and decreasing profiles in the
behavior of the energy density.Comment: 9 pages, to appear in Pramana - J. Phy
Clustering of Primordial Black Holes. II. Evolution of Bound Systems
Primordial Black Holes (PBHs) that form from the collapse of density
perturbations are more clustered than the underlying density field. In a
previous paper, we showed the constraints that this has on the prospects of PBH
dark matter. In this paper we examine another consequence of this clustering:
the formation of bound systems of PBHs in the early universe. These would
hypothetically be the earliest gravitationally collapsed structures, forming
when the universe is still radiation dominated. Depending upon the size and
occupation of the clusters, PBH merging occurs before they would have otherwise
evaporated due to Hawking evaporation.Comment: 23 pages, 1 figure. Submitted to PR
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