109 research outputs found
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
Cylindrically symmetric dust spacetime
We present an explicit exact solution of Einstein's equations for an
inhomogeneous dust universe with cylindrical symmetry. The spacetime is
extremely simple but nonetheless it has new surprising features. The universe
is ``closed'' in the sense that the dust expands from a big-bang singularity
but recollapses to a big-crunch singularity. In fact, both singularities are
connected so that the whole spacetime is ``enclosed'' within a single
singularity of general character. The big-bang is not simultaneous for the
dust, and in fact the age of the universe as measured by the dust particles
depends on the spatial position, an effect due to the inhomogeneity, and their
total lifetime has no non-zero lower limit. Part of the big-crunch singularity
is naked. The metric depends on a parameter and contains flat spacetime as a
non-singular particular case. For appropriate values of the parameter the
spacetime is a small perturbation of Minkowski spacetime. This seems to
indicate that flat spacetime may be unstable against some global {\it
non-vacuum} perturbations.Comment: LaTeX, 6 pages, 1 figure. Uses epsfig package. Submitted to Classical
and Quantum Gravit
Silent universes with a cosmological constant
We study non-degenerate (Petrov type I) silent universes in the presence of a
non-vanishing cosmological constant L. In contrast to the L=0 case, for which
the orthogonally spatially homogeneous Bianchi type I metrics most likely are
the only admissible metrics, solutions are shown to exist when L is positive.
The general solution is presented for the case where one of the eigenvalues of
the expansion tensor is 0.Comment: 11 pages; several typos corrected which were still present in CGQ
version; minor change
Cosmological models with flat spatial geometry
The imposition of symmetries or special geometric properties on submanifolds
is less restrictive than to impose them in the full space-time. Starting from
this idea, in this paper we study irrotational dust cosmological models in
which the geometry of the hypersurfaces generated by the fluid velocity is
flat, which supposes a relaxation of the restrictions imposed by the
Cosmological Principle. The method of study combines covariant and tetrad
methods that exploits the geometrical and physical properties of these models.
This procedure will allow us to determine all the space-times within this class
as well as to study their properties. Some important consequences and
applications of this study are also discussed.Comment: 12 pages, LaTeX2e, IOP style. To appear in Classical and Quantum
Gravit
Knotting probabilities after a local strand passage in unknotted self-avoiding polygons
We investigate the knotting probability after a local strand passage is
performed in an unknotted self-avoiding polygon on the simple cubic lattice. We
assume that two polygon segments have already been brought close together for
the purpose of performing a strand passage, and model this using Theta-SAPs,
polygons that contain the pattern Theta at a fixed location. It is proved that
the number of n-edge Theta-SAPs grows exponentially (with n) at the same rate
as the total number of n-edge unknotted self-avoiding polygons, and that the
same holds for subsets of n-edge Theta-SAPs that yield a specific
after-strand-passage knot-type. Thus the probability of a given
after-strand-passage knot-type does not grow (or decay) exponentially with n,
and we conjecture that instead it approaches a knot-type dependent amplitude
ratio lying strictly between 0 and 1. This is supported by critical exponent
estimates obtained from a new maximum likelihood method for Theta-SAPs that are
generated by a composite (aka multiple) Markov Chain Monte Carlo BFACF
algorithm. We also give strong numerical evidence that the after-strand-passage
knotting probability depends on the local structure around the strand passage
site. Considering both the local structure and the crossing-sign at the strand
passage site, we observe that the more "compact" the local structure, the less
likely the after-strand-passage polygon is to be knotted. This trend is
consistent with results from other strand-passage models, however, we are the
first to note the influence of the crossing-sign information. Two measures of
"compactness" are used: the size of a smallest polygon that contains the
structure and the structure's "opening" angle. The opening angle definition is
consistent with one that is measurable from single molecule DNA experiments.Comment: 31 pages, 12 figures, submitted to Journal of Physics
Kinematic self-similar locally rotationally symmetric models
A brief summary of results on kinematic self-similarities in general
relativity is given. Attention is focussed on locally rotationally symmetric
models admitting kinematic self-similar vectors. Coordinate expressions for the
metric and the kinematic self-similar vector are provided.
Einstein's field equations for perfect fluid models are investigated and all
the homothetic perfect fluid solutions admitting a maximal four-parameter group
of isometries are given.Comment: 12 pages, LaTeX, final version, to appear in Class. Quantum Gra
Observable Effects of Scalar Fields and Varying Constants
We show by using the method of matched asymptotic expansions that a
sufficient condition can be derived which determines when a local experiment
will detect the cosmological variation of a scalar field which is driving the
spacetime variation of a supposed constant of Nature. We extend our earlier
analyses of this problem by including the possibility that the local region is
undergoing collapse inside a virialised structure, like a galaxy or galaxy
cluster. We show by direct calculation that the sufficient condition is met to
high precision in our own local region and we can therefore legitimately use
local observations to place constraints upon the variation of "constants" of
Nature on cosmological scales.Comment: Invited Festscrift Articl
Evolution of the density contrast in inhomogeneous dust models
With the help of families of density contrast indicators, we study the
tendency of gravitational systems to become increasingly lumpy with time.
Depending upon their domain of definition, these indicators could be local or
global. We make a comparative study of these indicators in the context of
inhomogeneous cosmological models of Lemaitre--Tolman and Szekeres. In
particular, we look at the temporal asymptotic behaviour of these indicators
and ask under what conditions, and for which class of models, they evolve
monotonically in time. We find that for the case of ever-expanding models,
there is a larger class of indicators that grow monotonically with time,
whereas the corresponding class for the recollapsing models is more restricted.
Nevertheless, in the absence of decaying modes, indicators exist which grow
monotonically with time for both ever-expanding and recollapsing models
simultaneously. On the other hand, no such indicators may found which grow
monotonically if the decaying modes are allowed to exist. We also find the
conditions for these indicators to be non-divergent at the initial singularity
in both models. Our results can be of potential relevance for understanding
structure formation in inhomogeneous settings and in debates regarding
gravitational entropy and arrow of time. In particular, the spatial dependence
of turning points in inhomogeneous cosmologies may result in multiple density
contrast arrows in recollapsing models over certain epochs. We also find that
different notions of asymptotic homogenisation may be deduced, depending upon
the density contrast indicators used.Comment: 22 pages, 1 figure. To be published in Classical and Quantum Gravit
Physics at a 100 TeV pp collider: Higgs and EW symmetry breaking studies
This report summarises the physics opportunities for the study of Higgs
bosons and the dynamics of electroweak symmetry breaking at the 100 TeV pp
collider.Comment: 187 pages, 94 figures. Chapter 2 of the "Physics at the FCC-hh"
Repor
Left-right symmetry at LHC and precise 1-loop low energy data
Despite many tests, even the Minimal Manifest Left-Right Symmetric Model
(MLRSM) has never been ultimately confirmed or falsified. LHC gives a new
possibility to test directly the most conservative version of left-right
symmetric models at so far not reachable energy scales. If we take into account
precise limits on the model which come from low energy processes, like the muon
decay, possible LHC signals are strongly limited through the correlations of
parameters among heavy neutrinos, heavy gauge bosons and heavy Higgs particles.
To illustrate the situation in the context of LHC, we consider the "golden"
process . For instance, in a case of degenerate heavy neutrinos
and heavy Higgs masses at 15 TeV (in agreement with FCNC bounds) we get
fb at TeV which is consistent with muon
decay data for a very limited masses in the range (3008 GeV, 3040 GeV).
Without restrictions coming from the muon data, masses would be in the
range (1.0 TeV, 3.5 TeV). Influence of heavy Higgs particles themselves on the
considered LHC process is negligible (the same is true for the light, SM
neutral Higgs scalar analog). In the paper decay modes of the right-handed
heavy gauge bosons and heavy neutrinos are also discussed. Both scenarios with
typical see-saw light-heavy neutrino mixings and the mixings which are
independent of heavy neutrino masses are considered. In the second case heavy
neutrino decays to the heavy charged gauge bosons not necessarily dominate over
decay modes which include only light, SM-like particles.Comment: 16 pages, 10 figs, KL-KS and new ATLAS limits taken into accoun
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