430 research outputs found
Critical Exponents and Stability at the Black Hole Threshold for a Complex Scalar Field
This paper continues a study on Choptuik scaling in gravitational collapse of
a complex scalar field at the threshold for black hole formation. We perform a
linear perturbation analysis of the previously derived complex critical
solution, and calculate the critical exponent for black hole mass, . We also show that this critical solution is unstable via a
growing oscillatory mode.Comment: 15 pages of latex/revtex; added details of numerics, in press in Phys
Rev D; 1 figure included, or available by anonymous ftp to
ftp://ftp.itp.ucsb.edu/figures/nsf-itp-95-58.ep
Criticality and Bifurcation in the Gravitational Collapse of a Self-Coupled Scalar Field
We examine the gravitational collapse of a non-linear sigma model in
spherical symmetry. There exists a family of continuously self-similar
solutions parameterized by the coupling constant of the theory. These solutions
are calculated together with the critical exponents for black hole formation of
these collapse models. We also find that the sequence of solutions exhibits a
Hopf-type bifurcation as the continuously self-similar solutions become
unstable to perturbations away from self-similarity.Comment: 18 pages; one figure, uuencoded postscript; figure is also available
at http://www.physics.ucsb.edu/people/eric_hirschman
New bounds for Tsallis parameter in a noncommutative phase-space entropic gravity and nonextensive Friedmann equations
In this paper, we have analyzed the nonextensive Tsallis statistical
mechanics in the light of Verlinde's formalism. We have obtained, with the aid
of a noncommutative phase-space entropic gravity, a new bound for Tsallis
nonextensive (NE) parameter (TNP) that is clearly different from the ones
present in the current literature. We derived the Friedmann equations in a NE
scenario. We also obtained here a relation between the gravitational constant
and the TNP.Comment: 15 pages. Final version to appear in Physica
Deconfinement Transition for Quarks on a Line
We examine the statistical mechanics of a 1-dimensional gas of both adjoint
and fundamental representation quarks which interact with each other through
1+1-dimensional U(N) gauge fields. Using large-N expansion we show that, when
the density of fundamental quarks is small, there is a first order phase
transition at a critical temperature and adjoint quark density which can be
interpreted as deconfinement. When the fundamental quark density is comparable
to the adjoint quark density, the phase transition becomes a third order one.
We formulate a way to distinguish the phases by considering the expectation
values of high winding number Polyakov loop operators.Comment: Reported problems with figures fixed; 38 pages, LaTeX, 5 figures,
epsfi
Thermodynamics of doubly charged CGHS model and D1-D5-KK black holes of IIB supergravity
We study the doubly charged Callan-Giddings-Harvey-Strominger (CGHS) model,
which has black hole solutions that were found to be U-dual to the D1-D5-KK
black holes of the IIB supergravity. We derive the action of the model via a
spontaneous compactification on S^3 of the IIB supergravity on S^1*T^4 and
obtain the general static solutions including black holes corresponding to
certain non-asymptotically flat black holes in the IIB supergravity.
Thermodynamics of them is established by computing the entropy, temperature,
chemical potentials, and mass in the two-dimensional setup, and the first law
of thermodynamics is explicitly verified. The entropy is in precise agreement
with that of the D1-D5-KK black holes, and the mass turns out to be consistent
with the infinite Lorentz boost along the M theory circle that is a part of the
aforementioned U-dual chain.Comment: 21 pages, Revte
Observational Consequences of a Landscape
In this paper we consider the implications of the "landscape" paradigm for
the large scale properties of the universe. The most direct implication of a
rich landscape is that our local universe was born in a tunnelling event from a
neighboring vacuum. This would imply that we live in an open FRW universe with
negative spatial curvature. We argue that the "overshoot" problem, which in
other settings would make it difficult to achieve slow roll inflation, actually
favors such a cosmology.
We consider anthropic bounds on the value of the curvature and on the
parameters of inflation. When supplemented by statistical arguments these
bounds suggest that the number of inflationary efolds is not very much larger
than the observed lower bound. Although not statistically favored, the
likelihood that the number of efolds is close to the bound set by observations
is not negligible. The possible signatures of such a low number of efolds are
briefly described.Comment: 21 pages, 4 figures v2: references adde
Granular discharge and clogging for tilted hoppers
We measure the flux of spherical glass beads through a hole as a systematic
function of both tilt angle and hole diameter, for two different size beads.
The discharge increases with hole diameter in accord with the Beverloo relation
for both horizontal and vertical holes, but in the latter case with a larger
small-hole cutoff. For large holes the flux decreases linearly in cosine of the
tilt angle, vanishing smoothly somewhat below the angle of repose. For small
holes it vanishes abruptly at a smaller angle. The conditions for zero flux are
discussed in the context of a {\it clogging phase diagram} of flow state vs
tilt angle and ratio of hole to grain size
Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory
We study quartic matrix models with partition function Z[E,J]=\int dM
\exp(trace(JM-EM^2-(\lambda/4)M^4)). The integral is over the space of
Hermitean NxN-matrices, the external matrix E encodes the dynamics, \lambda>0
is a scalar coupling constant and the matrix J is used to generate correlation
functions. For E not a multiple of the identity matrix, we prove a universal
algebraic recursion formula which gives all higher correlation functions in
terms of the 2-point function and the distinct eigenvalues of E. The 2-point
function itself satisfies a closed non-linear equation which must be solved
case by case for given E. These results imply that if the 2-point function of a
quartic matrix model is renormalisable by mass and wavefunction
renormalisation, then the entire model is renormalisable and has vanishing
\beta-function.
As main application we prove that Euclidean \phi^4-quantum field theory on
four-dimensional Moyal space with harmonic propagation, taken at its
self-duality point and in the infinite volume limit, is exactly solvable and
non-trivial. This model is a quartic matrix model, where E has for N->\infty
the same spectrum as the Laplace operator in 4 dimensions. Using the theory of
singular integral equations of Carleman type we compute (for N->\infty and
after renormalisation of E,\lambda) the free energy density
(1/volume)\log(Z[E,J]/Z[E,0]) exactly in terms of the solution of a non-linear
integral equation. Existence of a solution is proved via the Schauder fixed
point theorem.
The derivation of the non-linear integral equation relies on an assumption
which we verified numerically for coupling constants 0<\lambda\leq (1/\pi).Comment: LaTeX, 64 pages, xypic figures. v4: We prove that recursion formulae
and vanishing of \beta-function hold for general quartic matrix models. v3:
We add the existence proof for a solution of the non-linear integral
equation. A rescaling of matrix indices was necessary. v2: We provide
Schwinger-Dyson equations for all correlation functions and prove an
algebraic recursion formula for their solutio
An action for the exact string black hole
A local action is constructed describing the exact string black hole
discovered by Dijkgraaf, Verlinde and Verlinde in 1992. It turns out to be a
special 2D Maxwell-dilaton gravity theory, linear in curvature and field
strength. Two constants of motion exist: mass M>1, determined by the level k,
and U(1)-charge Q>0, determined by the value of the dilaton at the origin. ADM
mass, Hawking temperature T_H \propto \sqrt{1-1/M} and Bekenstein-Hawking
entropy are derived and studied in detail. Winding/momentum mode duality
implies the existence of a similar action, arising from a branch ambiguity,
which describes the exact string naked singularity. In the strong coupling
limit the solution dual to AdS_2 is found to be the 5D Schwarzschild black
hole. Some applications to black hole thermodynamics and 2D string theory are
discussed and generalizations - supersymmetric extension, coupling to matter
and critical collapse, quantization - are pointed out.Comment: 41 pages, 2 eps figures, dedicated to Wolfgang Kummer on occasion of
his Emeritierung; v2: added ref; v3: extended discussion in sections 3.2, 3.3
and at the end of 5.3 by adding 2 pages of clarifying text; updated refs;
corrected typo
Cosmological parameters from SDSS and WMAP
We measure cosmological parameters using the three-dimensional power spectrum
P(k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in
combination with WMAP and other data. Our results are consistent with a
``vanilla'' flat adiabatic Lambda-CDM model without tilt (n=1), running tilt,
tensor modes or massive neutrinos. Adding SDSS information more than halves the
WMAP-only error bars on some parameters, tightening 1 sigma constraints on the
Hubble parameter from h~0.74+0.18-0.07 to h~0.70+0.04-0.03, on the matter
density from Omega_m~0.25+/-0.10 to Omega_m~0.30+/-0.04 (1 sigma) and on
neutrino masses from <11 eV to <0.6 eV (95%). SDSS helps even more when
dropping prior assumptions about curvature, neutrinos, tensor modes and the
equation of state. Our results are in substantial agreement with the joint
analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive
consistency check with independent redshift survey data and analysis
techniques. In this paper, we place particular emphasis on clarifying the
physical origin of the constraints, i.e., what we do and do not know when using
different data sets and prior assumptions. For instance, dropping the
assumption that space is perfectly flat, the WMAP-only constraint on the
measured age of the Universe tightens from t0~16.3+2.3-1.8 Gyr to
t0~14.1+1.0-0.9 Gyr by adding SDSS and SN Ia data. Including tensors, running
tilt, neutrino mass and equation of state in the list of free parameters, many
constraints are still quite weak, but future cosmological measurements from
SDSS and other sources should allow these to be substantially tightened.Comment: Minor revisions to match accepted PRD version. SDSS data and ppt
figures available at http://www.hep.upenn.edu/~max/sdsspars.htm
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