7,298 research outputs found
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
Planetoid String Solutions in 3 + 1 Axisymmetric Spacetimes
The string propagation equations in axisymmetric spacetimes are exactly
solved by quadratures for a planetoid Ansatz. This is a straight
non-oscillating string, radially disposed, which rotates uniformly around the
symmetry axis of the spacetime. In Schwarzschild black holes, the string stays
outside the horizon pointing towards the origin. In de Sitter spacetime the
planetoid rotates around its center. We quantize semiclassically these
solutions and analyze the spin/(mass) (Regge) relation for the planetoids,
which turns out to be non-linear.Comment: Latex file, 14 pages, two figures in .ps files available from the
author
Strings in Cosmological and Black Hole Backgrounds: Ring Solutions
The string equations of motion and constraints are solved for a ring shaped
Ansatz in cosmological and black hole spacetimes. In FRW universes with
arbitrary power behavior [R(X^0) = a\;|X^0|^{\a}\, ], the asymptotic form of
the solution is found for both and and we plot the
numerical solution for all times. Right after the big bang (), the
string energy decreasess as and the string size grows as for . Very
soon [ ] , the ring reaches its oscillatory regime with frequency
equal to the winding and constant size and energy. This picture holds for all
values of \a including string vacua (for which, asymptotically, \a = 1).
In addition, an exact non-oscillatory ring solution is found. For black hole
spacetimes (Schwarzschild, Reissner-Nordstr\oo m and stringy), we solve for
ring strings moving towards the center. Depending on their initial conditions
(essentially the oscillation phase), they are are absorbed or not by
Schwarzschild black holes. The phenomenon of particle transmutation is
explicitly observed (for rings not swallowed by the hole). An effective horizon
is noticed for the rings. Exact and explicit ring solutions inside the
horizon(s) are found. They may be interpreted as strings propagating between
the different universes described by the full black hole manifold.Comment: Paris preprint PAR-LPTHE-93/43. Uses phyzzx. Includes figures. Text
and figures compressed using uufile
Planetoid strings : solutions and perturbations
A novel ansatz for solving the string equations of motion and constraints in
generic curved backgrounds, namely the planetoid ansatz, was proposed recently
by some authors. We construct several specific examples of planetoid strings in
curved backgrounds which include Lorentzian wormholes, spherical Rindler
spacetime and the 2+1 dimensional black hole. A semiclassical quantisation is
performed and the Regge relations for the planetoids are obtained. The general
equations for the study of small perturbations about these solutions are
written down using the standard, manifestly covariant formalism. Applications
to special cases such as those of planetoid strings in Minkowski and spherical
Rindler spacetimes are also presented.Comment: 24 pages (including two figures), RevTex, expanded and figures adde
String dynamics in cosmological and black hole backgrounds: The null string expansion
We study the classical dynamics of a bosonic string in the --dimensional
flat Friedmann--Robertson--Walker and Schwarzschild backgrounds. We make a
perturbative development in the string coordinates around a {\it null} string
configuration; the background geometry is taken into account exactly. In the
cosmological case we uncouple and solve the first order fluctuations; the
string time evolution with the conformal gauge world-sheet --coordinate
is given by , where
are given by Eqs.\ (3.15), and is the exponent of the conformal factor
in the Friedmann--Robertson--Walker metric, i.e. . The string
proper size, at first order in the fluctuations, grows like the conformal
factor and the string energy--momentum tensor corresponds to that of
a null fluid. For a string in the black hole background, we study the planar
case, but keep the dimensionality of the spacetime generic. In the null
string expansion, the radial, azimuthal, and time coordinates are
and The first terms of the series represent a
{\it generic} approach to the Schwarzschild singularity at . First and
higher order string perturbations contribute with higher powers of . The
integrated string energy-momentum tensor corresponds to that of a null fluid in
dimensions. As the string approaches the singularity its proper
size grows indefinitely like . We end the paper
giving three particular exact string solutions inside the black hole.Comment: 17 pages, REVTEX, no figure
QFT, String Temperature and the String Phase of De Sitter Space-time
The density of mass levels \rho(m) and the critical temperature for strings
in de Sitter space-time are found. QFT and string theory in de Sitter space are
compared. A `Dual'-transform is introduced which relates classical to quantum
string lengths, and more generally, QFT and string domains. Interestingly, the
string temperature in De Sitter space turns out to be the Dual transform of the
QFT-Hawking-Gibbons temperature. The back reaction problem for strings in de
Sitter space is addressed selfconsistently in the framework of the `string
analogue' model (or thermodynamical approach), which is well suited to combine
QFT and string study.We find de Sitter space-time is a self-consistent solution
of the semiclassical Einstein equations in this framework. Two branches for the
scalar curvature R(\pm) show up: a classical, low curvature solution (-), and a
quantum high curvature solution (+), enterely sustained by the strings. There
is a maximal value for the curvature R_{\max} due to the string back reaction.
Interestingly, our Dual relation manifests itself in the back reaction
solutions: the (-) branch is a classical phase for the geometry with intrinsic
temperature given by the QFT-Hawking-Gibbons temperature.The (+) is a stringy
phase for the geometry with temperature given by the intrinsic string de Sitter
temperature. 2 + 1 dimensions are considered, but conclusions hold generically
in D dimensions.Comment: LaTex, 24 pages, no figure
Exact String Solutions in Nontrivial Backgrounds
We show how the classical string dynamics in -dimensional gravity
background can be reduced to the dynamics of a massless particle constrained on
a certain surface whenever there exists at least one Killing vector for the
background metric. We obtain a number of sufficient conditions, which ensure
the existence of exact solutions to the equations of motion and constraints.
These results are extended to include the Kalb-Ramond background. The
-brane dynamics is also analyzed and exact solutions are found. Finally, we
illustrate our considerations with several examples in different dimensions.
All this also applies to the tensionless strings.Comment: 22 pages, LaTeX, no figures; V2:Comments and references added;
V3:Discussion on the properties of the obtained solutions extended, a
reference and acknowledgment added; V4:The references renumbered, to appear
in Phys Rev.
Multi-String Solutions by Soliton Methods in De Sitter Spacetime
{\bf Exact} solutions of the string equations of motion and constraints are
{\bf systematically} constructed in de Sitter spacetime using the dressing
method of soliton theory. The string dynamics in de Sitter spacetime is
integrable due to the associated linear system. We start from an exact string
solution and the associated solution of the linear system , and we construct a new solution differing from
by a rational matrix in with at least four
poles . The periodi-
city condition for closed strings restrict to discrete values
expressed in terms of Pythagorean numbers. Here we explicitly construct solu-
tions depending on -spacetime coordinates, two arbitrary complex numbers
(the 'polarization vector') and two integers which determine the string
windings in the space. The solutions are depicted in the hyperboloid coor-
dinates and in comoving coordinates with the cosmic time . Despite of
the fact that we have a single world sheet, our solutions describe {\bf multi-
ple}(here five) different and independent strings; the world sheet time
turns to be a multivalued function of .(This has no analogue in flat space-
time).One string is stable (its proper size tends to a constant for , and its comoving size contracts); the other strings are unstable (their
proper sizes blow up for , while their comoving sizes tend to cons-
tants). These solutions (even the stable strings) do not oscillate in time. The
interpretation of these solutions and their dynamics in terms of the sinh-
Gordon model is particularly enlighting.Comment: 25 pages, latex. LPTHE 93-44. Figures available from the auhors under
reques
A method for solve integrable spin chains combining different representations
A non homogeneous spin chain in the representations and
of is analyzed. We find that the naive nested Bethe ansatz is not
applicable to this case. A method inspired in the nested Bethe ansatz, that can
be applied to more general cases, is developed for that chain. The solution for
the eigenvalues of the trace of the monodromy matrix is given as two coupled
Bethe equations different from that for a homogeneous chain. A conjecture about
the form of the solutions for more general chains is presented.
PACS: 75.10.Jm, 05.50+q 02.20 SvComment: PlainTeX, harvmac, 13 pages, 3 figures, to appear in Phys. Rev.
Cosmological evolution of warm dark matter fluctuations II: Solution from small to large scales and keV sterile neutrinos
We solve the cosmological evolution of warm dark matter (WDM) density
fluctuations with the Volterra integral equations of paper I. In the absence of
neutrinos, the anisotropic stress vanishes and the Volterra equations reduce to
a single integral equation. We solve numerically this equation both for DM
fermions decoupling at equilibrium and DM sterile neutrinos decoupling out of
equilibrium. We give the exact analytic solution for the density fluctuations
and gravitational potential at zero wavenumber. We compute the density contrast
as a function of the scale factor a for a wide range of wavenumbers k. At fixed
a, the density contrast grows with k for k
k_c, (k_c ~ 1.6/Mpc). The density contrast depends on k and a mainly through
the product k a exhibiting a self-similar behavior. Our numerical density
contrast for small k gently approaches our analytic solution for k = 0. For
fixed k < 1/(60 kpc), the density contrast generically grows with a while for k
> 1/(60 kpc) it exhibits oscillations since the RD era which become stronger as
k grows. We compute the transfer function of the density contrast for thermal
fermions and for sterile neutrinos in: a) the Dodelson-Widrow (DW) model and b)
in a model with sterile neutrinos produced by a scalar particle decay. The
transfer function grows with k for small k and then decreases after reaching a
maximum at k = k_c reflecting the time evolution of the density contrast. The
integral kernels in the Volterra equations are nonlocal in time and their
falloff determine the memory of the past evolution since decoupling. This
falloff is faster when DM decouples at equilibrium than when it decouples out
of equilibrium. Although neutrinos and photons can be neglected in the MD era,
they contribute in the MD era through their memory from the RD era.Comment: 27 pages, 6 figures. To appear in Phys Rev
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