13,896 research outputs found
Self-Gravitating Phase Transitions: Point Particles, Black Holes and Strings
We compute the quantum string entropy S_s(m,j) of the microscopic string
states of mass m and spin j in two physically relevant backgrounds: Kerr
(rotating) black holes and de Sitter (dS) space-time. We find a new formula for
the quantum gravitational entropy S_{sem} (M, J), as a function of the usual
Bekenstein-Hawking entropy S_{sem}^(0)(M, J). We compute the quantum string
emission by a black hole in de Sitter space-time (bhdS). In all these cases:
(i) strings with the highest spin, and (ii) in dS space-time, (iii) quantum
rotating black holes, (iv) quantum dS regime, (v) late bhdS evaporation, we
find a new gravitational phase transition with a common distinctive universal
feature: A square root branch point singularity in any space-time dimensions.
This is the same behavior as for the thermal self-gravitating gas of point
particles (de Vega-Sanchez transition), thus describing a new universality
class.Comment: Invited lecture at `Statistical Mechanics of Non-Extensive Systems',
Observatoire de Paris, 24-25 October 2005, to be published in a Special issue
of `Les Comptes rendus de l'Academie des sciences', Elsevie
Effects of regulation on a self-organized market
Adapting a simple biological model, we study the effects of control on the
market. Companies are depicted as sites on a lattice and labelled by a fitness
parameter (some `company-size' indicator). The chance of survival of a company
on the market at any given time is related to its fitness, its position on the
lattice and on some particular external influence, which may be considered to
represent regulation from governments or central banks. The latter is rendered
as a penalty for companies which show a very fast betterment in fitness space.
As a result, we find that the introduction of regulation on the market
contributes to lower the average fitness of companies.Comment: 7 pages, 2 figure
Galaxy phase-space density data exclude Bose-Einstein condensate Axion Dark Matter
Light scalars (as the axion) with mass m ~ 10^{-22} eV forming a
Bose-Einstein condensate (BEC) exhibit a Jeans length in the kpc scale and were
therefore proposed as dark matter (DM) candidates. Our treatment here is
generic, independent of the particle physics model and applies to all DM BEC,
in or out of equilibrium. Two observed quantities crucially constrain DM in an
inescapable way: the average DM density rho_{DM} and the phase-space density Q.
The observed values of rho_{DM} and Q in galaxies today constrain both the
possibility to form a BEC and the DM mass m. These two constraints robustly
exclude axion DM that decouples just after the QCD phase transition. Moreover,
the value m ~ 10^{-22} eV can only be obtained with a number of
ultrarelativistic degrees of freedom at decoupling in the trillions which is
impossible for decoupling in the radiation dominated era. In addition, we find
for the axion vacuum misalignment scenario that axions are produced strongly
out of thermal equilibrium and that the axion mass in such scenario turns to be
17 orders of magnitude too large to reproduce the observed galactic structures.
Moreover, we also consider inhomogenous gravitationally bounded BEC's supported
by the bosonic quantum pressure independently of any particular particle
physics scenario. For a typical size R ~ kpc and compact object masses M ~ 10^7
Msun they remarkably lead to the same particle mass m ~ 10^{-22} eV as the BEC
free-streaming length. However, the phase-space density for the gravitationally
bounded BEC's turns to be more than sixty orders of magnitude smaller than the
galaxy observed values. We conclude that the BEC's and the axion cannot be the
DM particle. However, an axion in the mili-eV scale may be a relevant source of
dark energy through the zero point cosmological quantum fluctuations.Comment: 8 pages, no figures. Expanded versio
Warm Dark Matter Galaxies with Central Supermassive Black-Holes
We generalize the Thomas-Fermi approach to galaxy structure to include
self-consistently and non-linearly central supermassive black holes. This
approach naturally incorporates the quantum pressure of the warm dark matter
(WDM) particles and shows its full powerful and clearness in the presence of
supermassive black holes (SPMHs). We find the main galaxy and central black
hole magnitudes: halo radius r_h , halo mass M_h, black hole mass M_BH,
velocity dispersion, phase space density, with their realistic astrophysical
values, masses and sizes over a wide galaxy range. The SMBH masses arise
naturally in this framework. Our extensive numerical calculations and detailed
analytic resolution show that with SMBH's, both WDM regimes: classical
(Boltzmann dilute) and quantum (compact) do necessarily co-exist in any galaxy:
from the smaller and compact galaxies to the largest ones. The transition from
the quantum to the classical region occurs precisely at the same point r_A
where the chemical potential vanishes. A novel halo structure with three
regions shows up: A small quantum compact core of radius r_A around the SMBH,
followed by a less compact region till the BH influence radius r_i, and then
for r> r_i the known halo galaxy shows up with its astrophysical size. Three
representative families of galaxy plus central SMBH solutions are found and
analyzed:small, medium and large galaxies having SMBH masses of 10^5, 10^7 and
10^9 M_sun respectively. A minimum galaxy size and mass ~ 10^7 M_sun larger
than the one without SMBH is found. Small galaxies in the range 10^4 M_sun <
M_h < 10^7 M_sun cannot harbor central SMBHs. We find novel scaling M_BH - r_h
- M_h relations. The galaxy equation of state is derived: The pressure P(r)
takes huge values in the SMBH vecinity and then sharply decreases entering the
classical region following a local perfect gas behaviour.(Abridged)Comment: 31 pages, 14 figures, new materia
Equation of state, universal profiles, scaling and macroscopic quantum effects in Warm Dark Matter galaxies
The Thomas-Fermi approach to galaxy structure determines selfconsistently and
nonlinearly the gravitational potential of the fermionic WDM particles given
their quantum distribution function f(E). Galaxy magnitudes as the halo radius
r_h, mass M_h, velocity dispersion and phase space density are obtained. We
derive the general equation of state for galaxies (relation between the
pressure and the density), and provide an analytic expression. This clearly
exhibits two regimes: (i) Large diluted galaxies for M_h > 2.3 10^6 Msun
corresponding to temperatures T_0 > 0.017 K, described by the classical self
gravitating WDM Boltzman regime and (ii) Compact dwarf galaxies for 1.6 10^6
Msun > M_h>M_{h,min}=30000 (2keV/m)^{16/5} Msun, T_0<0.011 K described by the
quantum fermionic WDM regime. The T_0=0 degenerate quantum limit predicts the
most compact and smallest galaxy (minimal radius and mass M_{h,min}). All
magnitudes in the diluted regime exhibit square root of M_h scaling laws and
are universal functions of r/r_h when normalized to their values at the origin
or at r_h. We find that universality in galaxies (for M_h > 10^6 Msun) reflects
the WDM perfect gas behaviour. These theoretical results contrasted to robust
and independent sets of galaxy data remarkably reproduce the observations. For
the small galaxies, 10^6>M_h>M_{h,min} corresponding to effective temperatures
T_0 < 0.017 K, the equation of state is galaxy dependent and the profiles are
no more universal. These non-universal properties in small galaxies account to
the quantum physics of the WDM fermions in the compact regime. Our results are
independent of any WDM particle physics model, they only follow from the
gravitational interaction of the WDM particles and their fermionic quantum
nature.Comment: 21 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:1309.229
Statistical Mechanics of the Self-Gravitating Gas: Thermodynamic Limit, Unstabilities and Phase Diagrams
We show that the self-gravitating gas at thermal equilibrium has an infinite
volume limit in the three ensembles (GCE, CE, MCE) when (N, V) -> infty,
keeping N/V^{1/3} fixed, that is, with eta = G m^2 N/[ V^{1/3} T] fixed. We
develop MonteCarlo simulations, analytic mean field methods (MF) and low
density expansions. We compute the equation of state and find it to be locally
p(r) = T rho_V(r), that is a local ideal gas equation of state. The system is
in a gaseous phase for eta < eta_T = 1.51024...and collapses into a very dense
object for eta > eta_T in the CE with the pressure becoming large and negative.
The isothermal compressibility diverges at eta = eta_T. We compute the
fluctuations around mean field for the three ensembles. We show that the
particle distribution can be described by a Haussdorf dimension 1 < D < 3.Comment: 12 pages, Invited lecture at `Statistical Mechanics of Non-Extensive
Systems', Observatoire de Paris, October 2005, to be published in a Special
issue of `Les Comptes rendus de l'Acade'mie des sciences', Elsevie
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