836 research outputs found
Chaos in Robertson-Walker Cosmology
Chaos in Robertson-Walker cosmological models where gravity is coupled to one
or more scalar fields has been studied by a few authors, mostly using numerical
simulations. In this paper we begin a systematic study of the analytical
aspect. We consider one conformally coupled scalar field and, using the fact
that the model is integrable when the field is massless, we show in detail how
homoclinic chaos arises for nonzero masses using a perturbative method.Comment: 16 pages, Tex, no figures. Minor changes have been added. To appear
in Journal of Mathematical Physic
Thermodynamics and area in Minkowski space: Heat capacity of entanglement
Tracing over the degrees of freedom inside (or outside) a sub-volume V of
Minkowski space in a given quantum state |psi>, results in a statistical
ensemble described by a density matrix rho. This enables one to relate quantum
fluctuations in V when in the state |psi>, to statistical fluctuations in the
ensemble described by rho. These fluctuations scale linearly with the surface
area of V. If V is half of space, then rho is the density matrix of a canonical
ensemble in Rindler space. This enables us to `derive' area scaling of
thermodynamic quantities in Rindler space from area scaling of quantum
fluctuations in half of Minkowski space. When considering shapes other than
half of Minkowski space, even though area scaling persists, rho does not have
an interpretation as a density matrix of a canonical ensemble in a curved, or
geometrically non-trivial, background.Comment: 17 page
Where are the degrees of freedom responsible for black hole entropy?
Considering the entanglement between quantum field degrees of freedom inside
and outside the horizon as a plausible source of black hole entropy, we address
the question: {\it where are the degrees of freedom that give rise to this
entropy located?} When the field is in ground state, the black hole area law is
obeyed and the degrees of freedom near the horizon contribute most to the
entropy. However, for excited state, or a superposition of ground state and
excited state, power-law corrections to the area law are obtained, and more
significant contributions from the degrees of freedom far from the horizon are
shown.Comment: 6 pages, 4 figures, Invited talk at Theory Canada III, Edmonton,
Alberta, Canada, June 16, 200
The Semiclassical Limit of Loop Quantum Cosmology
The continuum and semiclassical limits of isotropic, spatially flat loop
quantum cosmology are discussed, with an emphasis on the role played by the
Barbero-Immirzi parameter \gamma in controlling space-time discreteness. In
this way, standard quantum cosmology is shown to be the simultaneous limit
\gamma \to 0, j \to \infty of loop quantum cosmology. Here, j is a label of the
volume eigenvalues, and the simultaneous limit is technically the same as the
classical limit \hbar \to 0, l \to \infty of angular momentum in quantum
mechanics. Possible lessons for semiclassical states at the dynamical level in
the full theory of quantum geometry are mentioned.Comment: 10 page
On the "renormalization" transformations induced by cycles of expansion and contraction in causal set cosmology
We study the ``renormalization group action'' induced by cycles of cosmic
expansion and contraction, within the context of a family of stochastic
dynamical laws for causal sets derived earlier. We find a line of fixed points
corresponding to the dynamics of transitive percolation, and we prove that
there exist no other fixed points and no cycles of length two or more. We also
identify an extensive ``basin of attraction'' of the fixed points but find that
it does not exhaust the full parameter space. Nevertheless, we conjecture that
every trajectory is drawn toward the fixed point set in a suitably weakened
sense.Comment: 22 pages, 1 firgure, submitted to Phys. Rev.
On alternative approaches to Lorentz violation in loop quantum gravity inspired models
Recent claims point out that possible violations of Lorentz symmetry
appearing in some semiclassical models of extended matter dynamics motivated by
loop quantum gravity can be removed by a different choice of canonically
conjugated variables. In this note we show that such alternative is
inconsistent with the choice of variables in the underlying quantum theory
together with the semiclassical approximation, as long as the correspondence
principle is maintained. A consistent choice will violate standard Lorentz
invariance. Thus, to preserve a relativity principle in this framework, the
linear realization of Lorentz symmetry should be extended or superseded.Comment: 4 pages, revtex4, no figures, references adde
Gravitational collapse in loop quantum gravity
In this paper we study the gravitational collapse in loop quantum gravity. We
consider the space-time region inside the Schwarzschild black hole event
horizon and we divide this region in two parts, the first one where the matter
(dust matter) is localized and the other (outside) where the metric is
Kantowski-Sachs type. We calculate the state solving Hamiltonian constraint and
we obtain a set of three difference equations that give a regular and natural
evolution beyond the classical singularity point in "r=0" localized.Comment: 16 pages, 2 figure
Expansion-induced contribution to the precession of binary orbits
We point out the existence of new effects of global spacetime expansion on
local binary systems. In addition to a possible change of orbital size, there
is a contribution to the precession of elliptic orbits, to be added to the
well-known general relativistic effect in static spacetimes, and the
eccentricity can change. Our model calculations are done using geodesics in a
McVittie metric, representing a localized system in an asymptotically
Robertson-Walker spacetime; we give a few numerical estimates for that case,
and indicate ways in which the model should be improved.Comment: revtex, 7 pages, no figures; revised for publication in Classical and
Quantum Gravity, with minor changes in response to referees' comment
Evidence for a continuum limit in causal set dynamics
We find evidence for a continuum limit of a particular causal set dynamics
which depends on only a single ``coupling constant'' and is easy to
simulate on a computer. The model in question is a stochastic process that can
also be interpreted as 1-dimensional directed percolation, or in terms of
random graphs.Comment: 24 pages, 19 figures, LaTeX, adjusted terminolog
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