4,418 research outputs found
A general variational principle for spherically symmetric perturbations in diffeomorphism covariant theories
We present a general method for the analysis of the stability of static,
spherically symmetric solutions to spherically symmetric perturbations in an
arbitrary diffeomorphism covariant Lagrangian field theory. Our method involves
fixing the gauge and solving the linearized gravitational field equations to
eliminate the metric perturbation variable in terms of the matter variables. In
a wide class of cases--which include f(R) gravity, the Einstein-aether theory
of Jacobson and Mattingly, and Bekenstein's TeVeS theory--the remaining
perturbation equations for the matter fields are second order in time. We show
how the symplectic current arising from the original Lagrangian gives rise to a
symmetric bilinear form on the variables of the reduced theory. If this
bilinear form is positive definite, it provides an inner product that puts the
equations of motion of the reduced theory into a self-adjoint form. A
variational principle can then be written down immediately, from which
stability can be tested readily. We illustrate our method in the case of
Einstein's equation with perfect fluid matter, thereby re-deriving, in a
systematic manner, Chandrasekhar's variational principle for radial
oscillations of spherically symmetric stars. In a subsequent paper, we will
apply our analysis to f(R) gravity, the Einstein-aether theory, and
Bekenstein's TeVeS theory.Comment: 13 pages; submitted to Phys. Rev. D. v2: changed formatting, added
conclusion, corrected sign convention
Stability of spherically symmetric solutions in modified theories of gravity
In recent years, a number of alternative theories of gravity have been
proposed as possible resolutions of certain cosmological problems or as toy
models for possible but heretofore unobserved effects. However, the
implications of such theories for the stability of structures such as stars
have not been fully investigated. We use our "generalized variational
principle", described in a previous work, to analyze the stability of static
spherically symmetric solutions to spherically symmetric perturbations in three
such alternative theories: Carroll et al.'s f(R) gravity, Jacobson &
Mattingly's "Einstein-aether theory", and Bekenstein's TeVeS. We find that in
the presence of matter, f(R) gravity is highly unstable; that the stability
conditions for spherically symmetric curved vacuum Einstein-aether backgrounds
are the same as those for linearized stability about flat spacetime, with one
exceptional case; and that the "kinetic terms" of vacuum TeVeS are indefinite
in a curved background, leading to an instability.Comment: ReVTex; 20 pages, 3 figures. v2: references added, submitted to PRD;
v3: expanded discussion of TeVeS; v4: minor typos corrected (version to
appear in PRD
Creation of macroscopic superposition states from arrays of Bose-Einstein condensates
We consider how macroscopic quantum superpositions may be created from arrays
of Bose-Einstein condensates. We study a system of three condensates in Fock
states, all with the same number of atoms and show that this has the form of a
highly entangled superposition of different quasi-momenta. We then show how, by
partially releasing these condensates and detecting an interference pattern
where they overlap, it is possible to create a macroscopic superposition of
different relative phases for the remaining portions of the condensates. We
discuss methods for confirming these superpositions.Comment: 7 pages, 5 figure
Just how long can you live in a black hole and what can be done about it?
We study the problem of how long a journey within a black hole can last.
Based on our observations, we make two conjectures. First, for observers that
have entered a black hole from an asymptotic region, we conjecture that the
length of their journey within is bounded by a multiple of the future
asymptotic ``size'' of the black hole, provided the spacetime is globally
hyperbolic and satisfies the dominant-energy and non-negative-pressures
conditions. Second, for spacetimes with Cauchy surfaces (or an
appropriate generalization thereof) and satisfying the dominant energy and
non-negative-pressures conditions, we conjecture that the length of a journey
anywhere within a black hole is again bounded, although here the bound requires
a knowledge of the initial data for the gravitational field on a Cauchy
surface. We prove these conjectures in the spherically symmetric case. We also
prove that there is an upper bound on the lifetimes of observers lying ``deep
within'' a black hole, provided the spacetime satisfies the
timelike-convergence condition and possesses a maximal Cauchy surface. Further,
we investigate whether one can increase the lifetime of an observer that has
entered a black hole, e.g., by throwing additional matter into the hole.
Lastly, in an appendix, we prove that the surface area of the event horizon
of a black hole in a spherically symmetric spacetime with ADM mass
is always bounded by , provided
that future null infinity is complete and the spacetime is globally hyperbolic
and satisfies the dominant-energy condition.Comment: 20 pages, REVTeX 3.0, 6 figures included, self-unpackin
Classical field techniques for condensates in one-dimensional rings at finite temperatures
For a condensate in a one-dimensional ring geometry, we compare the
thermodynamic properties of three conceptually different classical field
techniques: stochastic dynamics, microcanonical molecular dynamics, and the
classical field method. Starting from non-equilibrium initial conditions, all
three methods approach steady states whose distribution and correlation
functions are in excellent agreement with an exact evaluation of the partition
function in the high-temperature limit. Our study helps to establish these
various classical field techniques as powerful non-perturbative tools for
systems at finite temperatures.Comment: 7 pages, 7 figures; minor changes, one reference adde
The Cosmic Censor Forbids Naked Topology
For any asymptotically flat spacetime with a suitable causal structure
obeying (a weak form of) Penrose's cosmic censorship conjecture and satisfying
conditions guaranteeing focusing of complete null geodesics, we prove that
active topological censorship holds. We do not assume global hyperbolicity, and
therefore make no use of Cauchy surfaces and their topology. Instead, we
replace this with two underlying assumptions concerning the causal structure:
that no compact set can signal to arbitrarily small neighbourhoods of spatial
infinity (``-avoidance''), and that no future incomplete null geodesic is
visible from future null infinity. We show that these and the focusing
condition together imply that the domain of outer communications is simply
connected. Furthermore, we prove lemmas which have as a consequence that if a
future incomplete null geodesic were visible from infinity, then given our
-avoidance assumption, it would also be visible from points of spacetime
that can communicate with infinity, and so would signify a true naked
singularity.Comment: To appear in CQG, this improved version contains minor revisions to
incorporate referee's suggestions. Two revised references. Plain TeX, 12
page
Ultracold Bosonic Atoms in Disordered Optical Superlattices
The influence of disorder on ultracold atomic Bose gases in quasiperiodic
optical lattices is discussed in the framework of the one-dimensional
Bose-Hubbard model. It is shown that simple periodic modulations of the well
depths generate a rich phase diagram consisting of superfluid, Mott insulator,
Bose-glass and Anderson localized phases. The detailed evolution of mean
occupation numbers and number fluctuations as function of modulation amplitude
and interaction strength is discussed. Finally, the signatures of the different
phases, especially of the Bose-glass phase, in matter-wave interference
experiments are investigated.Comment: 4 pages, 4 figures, using REVTEX
Greenhouse gas balance over thaw-freeze cycles in discontinuous zone permafrost
Peat in the discontinuous permafrost zone contains a globally significant reservoir of carbon that has undergone multiple permafrost-thaw cycles since the end of the mid-Holocene (~3700 years before present). Periods of thaw increase C decomposition rates which leads to the release of CO2 and CH4 to the atmosphere creating potential climate feedback. To determine the magnitude and direction of such feedback, we measured CO2 and CH4 emissions and modeled C accumulation rates and radiative fluxes from measurements of two radioactive tracers with differing lifetimes to describe the C balance of the peatland over multiple permafrost-thaw cycles since the initiation of permafrost at the site. At thaw features, the balance between increased primary production and higher CH4 emission stimulated by warmer temperatures and wetter conditions favors C sequestration and enhanced peat accumulation. Flux measurements suggest that frozen plateaus may intermittently (order of years to decades) act as CO2 sources depending on temperature and net ecosystem respiration rates, but modeling results suggest that—despite brief periods of net C loss to the atmosphere at the initiation of thaw—integrated over millennia, these sites have acted as net C sinks via peat accumulation. In greenhouse gas terms, the transition from frozen permafrost to thawed wetland is accompanied by increasing CO2 uptake that is partially offset by increasing CH4 emissions. In the short-term (decadal time scale) the net effect of this transition is likely enhanced warming via increased radiative C emissions, while in the long-term (centuries) net C deposition provides a negative feedback to climate warming
Lifetimes of spherically symmetric closed universes
It is proven that any spherically symmetric spacetime that possesses a
compact Cauchy surface and that satisfies the dominant-energy and
non-negative-pressures conditions must have a finite lifetime in the sense that
all timelike curves in such a spacetime must have a length no greater than , where is the mass associated with the spheres of
symmetry. This result gives a complete resolution, in the spherically symmetric
case, of one version of the closed-universe recollapse conjecture (though it is
likely that a slightly better bound can be established). This bound has the
desirable properties of being computable from the (spherically symmetric)
initial data for the spacetime and having a very simple form. In fact, its form
is the same as was established, using a different method, for the spherically
symmetric massless scalar field spacetimes, thereby proving a conjecture
offered in that work. Prospects for generalizing these results beyond the
spherically symmetric case are discussed.Comment: 12 pages (uuencoded postscript; self-unpacking), NCSU-MP-940
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