11,704 research outputs found
Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity
A stability criterion is derived in general relativity for self-similar
solutions with a scalar field and those with a stiff fluid, which is a perfect
fluid with the equation of state . A wide class of self-similar
solutions turn out to be unstable against kink mode perturbation. According to
the criterion, the Evans-Coleman stiff-fluid solution is unstable and cannot be
a critical solution for the spherical collapse of a stiff fluid if we allow
sufficiently small discontinuity in the density gradient field in the initial
data sets. The self-similar scalar-field solution, which was recently found
numerically by Brady {\it et al.} (2002 {\it Class. Quantum. Grav.} {\bf 19}
6359), is also unstable. Both the flat Friedmann universe with a scalar field
and that with a stiff fluid suffer from kink instability at the particle
horizon scale.Comment: 15 pages, accepted for publication in Classical and Quantum Gravity,
typos correcte
Primordial black hole evolution in tensor-scalar cosmology
A perturbative analysis shows that black holes do not remember the value of
the scalar field at the time they formed if changes in
tensor-scalar cosmology. Moreover, even when the black hole mass in the
Einstein frame is approximately unaffected by the changing of , in the
Jordan-Fierz frame the mass increases. This mass increase requires a reanalysis
of the evaporation of primordial black holes in tensor-scalar cosmology. It
also implies that there could have been a significant magnification of the
(Jordan-Fierz frame) mass of primordial black holes.Comment: 4 pages, revte
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Self-similar cosmological solutions with dark energy. II: black holes, naked singularities and wormholes
We use a combination of numerical and analytical methods, exploiting the
equations derived in a preceding paper, to classify all spherically symmetric
self-similar solutions which are asymptotically Friedmann at large distances
and contain a perfect fluid with equation of state with
. The expansion of the Friedmann universe is accelerated in this
case. We find a one-parameter family of self-similar solutions representing a
black hole embedded in a Friedmann background. This suggests that, in contrast
to the positive pressure case, black holes in a universe with dark energy can
grow as fast as the Hubble horizon if they are not too large. There are also
self-similar solutions which contain a central naked singularity with negative
mass and solutions which represent a Friedmann universe connected to either
another Friedmann universe or some other cosmological model. The latter are
interpreted as self-similar cosmological white hole or wormhole solutions. The
throats of these wormholes are defined as two-dimensional spheres with minimal
area on a spacelike hypersurface and they are all non-traversable because of
the absence of a past null infinity.Comment: 12 pages, 19 figures, 1 table, final version to appear in Physical
Review
Macroscopic quantum tunnelling of Bose-Einstein condensates in a finite potential well
Bose-Einstein condensates are studied in a potential of finite depth which
supports both bound and quasi-bound states. This potential, which is harmonic
for small radii and decays as a Gaussian for large radii, models experimentally
relevant optical traps. The nonlinearity, which is proportional to both the
number of atoms and the interaction strength, can transform bound states into
quasi-bound ones. The latter have a finite lifetime due to tunnelling through
the barriers at the borders of the well. We predict the lifetime and stability
properties for repulsive and attractive condensates in one, two, and three
dimensions, for both the ground state and excited soliton and vortex states. We
show, via a combination of the variational and WKB approximations, that
macroscopic quantum tunnelling in such systems can be observed on time scales
of 10 milliseconds to 10 seconds.Comment: J. Phys. B: At. Mol. Opt. Phys. in pres
Convergence to a self-similar solution in general relativistic gravitational collapse
We study the spherical collapse of a perfect fluid with an equation of state
by full general relativistic numerical simulations. For 0, it has been known that there exists a general relativistic counterpart
of the Larson-Penston self-similar Newtonian solution. The numerical
simulations strongly suggest that, in the neighborhood of the center, generic
collapse converges to this solution in an approach to a singularity and that
self-similar solutions other than this solution, including a ``critical
solution'' in the black hole critical behavior, are relevant only when the
parameters which parametrize initial data are fine-tuned. This result is
supported by a mode analysis on the pertinent self-similar solutions. Since a
naked singularity forms in the general relativistic Larson-Penston solution for
0, this will be the most serious known counterexample against
cosmic censorship. It also provides strong evidence for the self-similarity
hypothesis in general relativistic gravitational collapse. The direct
consequence is that critical phenomena will be observed in the collapse of
isothermal gas in Newton gravity, and the critical exponent will be
given by , though the order parameter cannot be the black
hole mass.Comment: 22 pages, 15 figures, accepted for publication in Physical Review D,
reference added, typos correcte
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