4,045 research outputs found
Thermodynamics of the Stephani Universes
We examine the consistency of the thermodynamics of the most general class of
conformally flat solution with an irrotational perfect fluid source (the
Stephani Universes). For the case when the isometry group has dimension
, the Gibbs-Duhem relation is always integrable, but if it is only
integrable for the particular subclass (containing FRW cosmologies)
characterized by and by admitting a conformal motion parallel to the
4-velocity. We provide explicit forms of the state variables and equations of
state linking them. These formal thermodynamic relations are determined up to
an arbitrary function of time which reduces to the FRW scale factor in the FRW
limit of the solutions. We show that a formal identification of this free
parameter with a FRW scale factor determined by FRW dynamics leads to an
unphysical temperature evolution law. If this parameter is not identified with
a FRW scale factor, it is possible to find examples of solutions and formal
equations of state complying with suitable energy conditions and reasonable
asymptotic behavior and temperature laws.Comment: 25 pages, Plain.TeX, four figure
Interactive mixture of inhomogeneous dark fluids driven by dark energy: a dynamical systems analysis
We examine the evolution of an inhomogeneous mixture of non-relativistic
pressureless cold dark matter (CDM), coupled to dark energy (DE) characterised
by the equation of state parameter , with the interaction term
proportional to the DE density. This coupled mixture is the source of a
spherically symmetric Lema\^\ itre-Tolman-Bondi (LTB) metric admitting an
asymptotic Friedman-Lema\^\ itre-Robertson-Walker (FLRW) background. Einstein's
equations reduce to a 5-dimensional autonomous dynamical system involving
quasi--local variables related to suitable averages of covariant scalars and
their fluctuations. The phase space evolution around the critical points
(past/future attractors and five saddles) is examined in detail. For all
parameter values and both directions of energy flow (CDM to DE and DE to CDM)
the phase space trajectories are compatible with a physically plausible early
cosmic times behaviour near the past attractor. This result compares favourably
with mixtures with the interaction driven by the CDM density in which
conditions for a physically plausible past evolution are more restrictive.
Numerical examples are provided describing the evolution of an initial profile
that can be associated with idealised structure formation scenariosComment: 23 pages, IOP format, 8 figure
Towards a physical interpretation for the Stephani Universes
A physicaly reasonable interpretation is provided for the perfect fluid,
sphericaly symmetric, conformally flat ``Stephani Universes''. The free
parameters of this class of exact solutions are determined so that the ideal
gas relation is identicaly fulfiled, while the full equation of state
of a classical monatomic ideal gas and a matter-radiation mixture holds up to a
good approximation in a near dust, matter dominated regime. Only the models
having spacelike slices with positive curvature admit a regular evolution
domain that avoids an unphysical singularity. In the matter dominated regime
these models are dynamicaly and observationaly indistinguishable from
``standard'' FLRW cosmology with a dust source.Comment: 17 pages, 2 figures, LaTeX with revtex style, submitted to General
Relativity and Gravitatio
Evolution of radial profiles in regular Lemaitre-Tolman-Bondi dust models
We undertake a comprehensive and rigorous analytic study of the evolution of
radial profiles of covariant scalars in regular Lemaitre-Tolman-Bondi dust
models. We consider specifically the phenomenon of "profile inversions" in
which an initial clump profile of density, spatial curvature or the expansion
scalar, might evolve into a void profile (and vice versa). Previous work in the
literature on models with density void profiles and/or allowing for density
profile inversions is given full generalization, with some erroneous results
corrected. We prove rigorously that if an evolution without shell crossings is
assumed, then only the 'clump to void' inversion can occur in density profiles,
and only in hyperbolic models or regions with negative spatial curvature. The
profiles of spatial curvature follow similar patterns as those of the density,
with 'clump to void' inversions only possible for hyperbolic models or regions.
However, profiles of the expansion scalar are less restrictive, with profile
inversions necessarily taking place in elliptic models. We also examine radial
profiles in special LTB configurations: closed elliptic models, models with a
simultaneous big bang singularity, as well as a locally collapsing elliptic
region surrounded by an expanding hyperbolic background. The general analytic
statements that we obtain allow for setting up the right initial conditions to
construct fully regular LTB models with any specific qualitative requirements
for the profiles of all scalars and their time evolution. The results presented
can be very useful in guiding future numerical work on these models and in
revising previous analytic work on all their applications.Comment: Final version to appear in Classical and Quantum Gravity. Readers
eager to know the results and implications without having to go through the
technical detail are recommended to go directly to the summary and discussion
in the final section (section 11). Typos have been corrected and an important
reference has been adde
The Disciplined Use of Simplifying Assumptions
Submitted to the ACM SIGSOFT Second Software Engineering Symposium: Workshop on Rapid Prototyping. Columbia, Maryland, April 19-21, 1982.Simplifying assumptions — everyone uses them but no one's programming tool explicitly supports them. In programming, as in other kinds of engineering design, simplifying assumptions are an important method for dealing with complexity. Given a complex programming problem, expert programmers typically choose simplifying assumptions which, though false, allow them to arrive rapidly at a program which addresses the important features of the problem without being distracted by all of its details. The simplifying assumptions are then incrementally retracted with corresponding modifications to the initial program. This methodology is particularly applicable to rapid prototyping because the main questions of interest can often be answered using only the initial program.
Simplifying assumptions can easily be misused. In order to use them effectively two key issues must be addressed. First, simplifying assumptions should be chosen which simplify the design problems significantly without changing the essential character of the program which needs to be implemented. Second, the designer must keep track of all the assumptions he is making so that he can later retract them in an orderly manner. By explicitly dealing with these issues, a programming assistant system could directly support the use of simplifying assumptions as a disciplined part of the software development process.MIT Artificial Intelligence Laborator
On the Thermodynamics of Simple Non-Isentropic Perfect Fluids in General Relativity
We examine the consistency of the thermodynamics of irrotational and
non-isentropic perfect fluids complying with matter conservation by looking at
the integrability conditions of the Gibbs-Duhem relation. We show that the
latter is always integrable for fluids of the following types: (a) static, (b)
isentropic (admits a barotropic equation of state), (c) the source of a
spacetime for which , where is the dimension of the orbit of the
isometry group. This consistency scheme is tested also in two large classes of
known exact solutions for which , in general: perfect fluid Szekeres
solutions (classes I and II). In none of these cases, the Gibbs-Duhem relation
is integrable, in general, though specific particular cases of Szekeres class
II (all complying with ) are identified for which the integrability of
this relation can be achieved. We show that Szekeres class I solutions satisfy
the integrability conditions only in two trivial cases, namely the spherically
symmetric limiting case and the Friedman-Roberson-Walker (FRW) cosmology.
Explicit forms of the state variables and equations of state linking them are
given explicitly and discussed in relation to the FRW limits of the solutions.
We show that fixing free parameters in these solutions by a formal
identification with FRW parameters leads, in all cases examined, to unphysical
temperature evolution laws, quite unrelated to those of their FRW limiting
cosmologies.Comment: 29 pages, Plain.Te
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