7,645 research outputs found
Hydrostatic Equilibrium of a Perfect Fluid Sphere with Exterior Higher-Dimensional Schwarzschild Spacetime
We discuss the question of how the number of dimensions of space and time can
influence the equilibrium configurations of stars. We find that dimensionality
does increase the effect of mass but not the contribution of the pressure,
which is the same in any dimension. In the presence of a (positive)
cosmological constant the condition of hydrostatic equilibrium imposes a lower
limit on mass and matter density. We show how this limit depends on the number
of dimensions and suggest that is more effective in 4D than in
higher dimensions. We obtain a general limit for the degree of compactification
(gravitational potential on the boundary) of perfect fluid stars in
-dimensions. We argue that the effects of gravity are stronger in 4D than in
any other number of dimensions. The generality of the results is also
discussed
Brane classical and quantum cosmology from an effective action
Motivated by the Randall-Sundrum brane-world scenario, we discuss the
classical and quantum dynamics of a (d+1)-dimensional boundary wall between a
pair of (d+2)-dimensional topological Schwarzschild-AdS black holes. We assume
there are quite general -- but not completely arbitrary -- matter fields living
on the boundary ``brane universe'' and its geometry is that of an
Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The effective action
governing the model in the mini-superspace approximation is derived. We find
that the presence of black hole horizons in the bulk gives rise to a complex
action for certain classically allowed brane configurations, but that the
imaginary contribution plays no role in the equations of motion. Classical and
instanton brane trajectories are examined in general and for special cases, and
we find a subset of configuration space that is not allowed at the classical or
semi-classical level; these correspond to spacelike branes carrying tachyonic
matter. The Hamiltonization and Dirac quantization of the model is then
performed for the general case; the latter involves the manipulation of the
Hamiltonian constraint before it is transformed into an operator that
annihilates physical state vectors. The ensuing covariant Wheeler-DeWitt
equation is examined at the semi-classical level, and we consider the possible
localization of the brane universe's wavefunction away from the cosmological
singularity. This is easier to achieve for branes with low density and/or
spherical spatial sections.Comment: Shortened to match version accepted by Phys. Rev. D (unabridged text
found in version 2), 42 pages, 9 figures, Rextex
Self-similar cosmologies in 5D: spatially flat anisotropic models
In the context of theories of Kaluza-Klein type, with a large extra
dimension, we study self-similar cosmological models in 5D that are
homogeneous, anisotropic and spatially flat. The "ladder" to go between the
physics in 5D and 4D is provided by Campbell-Maagard's embedding theorems. We
show that the 5-dimensional field equations determine the form of
the similarity variable. There are three different possibilities: homothetic,
conformal and "wave-like" solutions in 5D. We derive the most general
homothetic and conformal solutions to the 5D field equations. They require the
extra dimension to be spacelike, and are given in terms of one arbitrary
function of the similarity variable and three parameters. The Riemann tensor in
5D is not zero, except in the isotropic limit, which corresponds to the case
where the parameters are equal to each other. The solutions can be used as 5D
embeddings for a great variety of 4D homogeneous cosmological models, with and
without matter, including the Kasner universe. Since the extra dimension is
spacelike, the 5D solutions are invariant under the exchange of spatial
coordinates. Therefore they also embed a family of spatially {\it
inhomogeneous} models in 4D. We show that these models can be interpreted as
vacuum solutions in braneworld theory. Our work (I) generalizes the 5D
embeddings used for the FLRW models; (II) shows that anisotropic cosmologies
are, in general, curved in 5D, in contrast with FLRW models which can always be
embedded in a 5D Riemann-flat (Minkowski) manifold; (III) reveals that
anisotropic cosmologies can be curved and devoid of matter, both in 5D and 4D,
even when the metric in 5D explicitly depends on the extra coordinate, which is
quite different from the isotropic case.Comment: Typos corrected. Minor editorial changes and additions in the
Introduction and Summary section
Exterior spacetime for stellar models in 5-dimensional Kaluza-Klein gravity
It is well-known that Birkhoff's theorem is no longer valid in theories with
more than four dimensions. Thus, in these theories the effective 4-dimensional
picture allows the existence of different possible, non-Schwarzschild,
scenarios for the description of the spacetime outside of a spherical star,
contrary to general relativity in 4D. We investigate the exterior spacetime of
a spherically symmetric star in the context of Kaluza-Klein gravity. We take a
well-known family of static spherically symmetric solutions of the Einstein
equations in an empty five-dimensional universe, and analyze possible stellar
exteriors that are conformal to the metric induced on four-dimensional
hypersurfaces orthogonal to the extra dimension. All these exteriors are
continuously matched with the interior of the star. Then, without making any
assumptions about the interior solution, we prove the following statement: the
condition that in the weak-field limit we recover the usual Newtonian physics
singles out an unique exterior. This exterior is "similar" to Scharzschild
vacuum in the sense that it has no effect on gravitational interactions.
However, it is more realistic because instead of being absolutely empty, it is
consistent with the existence of quantum zero-point fields. We also examine the
question of how would the deviation from the Schwarzschild vacuum exterior
affect the parameters of a neutron star. In the context of a model star of
uniform density, we show that the general relativity upper limit M/R < 4/9 is
significantly increased as we go away from the Schwarzschild vacuum exterior.
We find that, in principle, the compactness limit of a star can be larger than
1/2, without being a black hole. The generality of our approach is also
discussed.Comment: Typos corrected. Accepted for publication in Classical and Quantum
Gravit
Mass and Charge in Brane-World and Non-Compact Kaluza-Klein Theories in 5 Dim
In classical Kaluza-Klein theory, with compactified extra dimensions and
without scalar field, the rest mass as well as the electric charge of test
particles are constants of motion. We show that in the case of a large extra
dimension this is no longer so. We propose the Hamilton-Jacobi formalism,
instead of the geodesic equation, for the study of test particles moving in a
five-dimensional background metric. This formalism has a number of advantages:
(i) it provides a clear and invariant definition of rest mass, without the
ambiguities associated with the choice of the parameters used along the motion
in 5D and 4D, (ii) the electromagnetic field can be easily incorporated in the
discussion, and (iii) we avoid the difficulties associated with the "splitting"
of the geodesic equation. For particles moving in a general 5D metric, we show
how the effective rest mass, as measured by an observer in 4D, varies as a
consequence of the large extra dimension. Also, the fifth component of the
momentum changes along the motion. This component can be identified with the
electric charge of test particles. With this interpretation, both the rest mass
and the charge vary along the trajectory. The constant of motion is now a
combination of these quantities. We study the cosmological variations of charge
and rest mass in a five-dimensional bulk metric which is used to embed the
standard k = 0 FRW universes. The time variations in the fine structure
"constant" and the Thomson cross section are also discussed.Comment: V2: References added, discussion extended. V3 is identical to V2,
references updated. To appear in General Relativity and Gravitatio
Additional spectra of asteroid 1996 FG3, backup target of the ESA MarcoPolo-R mission
Near-Earth binary asteroid (175706) 1996 FG3 is the current backup target of
the ESA MarcoPolo-R mission, selected for the study phase of ESA M3 missions.
It is a primitive (C-type) asteroid that shows significant variation in its
visible and near-infrared spectra. Here we present new spectra of 1996 FG3 and
we compare our new data with other published spectra, analysing the variation
in the spectral slope. The asteroid will not be observable again over the next
three years at least. We obtained the spectra using DOLORES and NICS
instruments at the Telescopio Nazionale Galileo (TNG), a 3.6m telescope located
at El Roque de los Muchachos Observatory in La Palma, Spain. To compare with
other published spectra of the asteroid, we computed the spectral slope S', and
studied any plausible correlation of this quantity with the phase angle
(alpha). In the case of visible spectra, we find a variation in spectral slope
of Delta S' = 0.15 +- 0.10 %/10^3 A/degree for 3 < alpha < 18 degrees, in good
agreement with the values found in the literature for the phase reddening
effect. In the case of the near-infrared, we find a variation in the slope of
Delta S' = 0.04 +- 0.08 %/10^3 A/degree for 6 < alpha < 51 degrees. Our
computed variation in S' agrees with the only two values found in the
literature for the phase reddening in the near-infrared. The variation in the
spectral slope of asteroid 1996 FG3 shows a trend with the phase angle at the
time of the observations, both in the visible and the near-infrared. It is
worth noting that, to fully explain this spectral variability we should take
into account other factors, like the position of the secondary component of the
binary asteroid 1999 FG3 with respect to the primary, or the spin axis
orientation at the time of the observations. More data are necessary for an
analysis of this kind.Comment: 4 pages, 3 figures, Accepted in A&A 25 June 201
Cosmological Implications of a Non-Separable 5D Solution of the Vacuum Einstein Field Equations
An exact class of solutions of the 5D vacuum Einstein field equations (EFEs)
is obtained. The metric coefficients are found to be non-separable functions of
time and the extra coordinate and the induced metric on = constant
hypersurfaces has the form of a Friedmann-Robertson-Walker cosmology. The 5D
manifold and 3D and 4D submanifolds are in general curved, which distinguishes
this solution from previous ones in the literature. The singularity structure
of the manifold is explored: some models in the class do not exhibit a big
bang, while other exhibit a big bang and a big crunch. For the models with an
initial singularity, the equation of state of the induced matter evolves from
radiation like at early epochs to Milne-like at late times and the big bang
manifests itself as a singular hypersurface in 5D. The projection of comoving
5D null geodesics onto the 4D submanifold is shown to be compatible with
standard 4D comoving trajectories, while the expansion of 5D null congruences
is shown to be in line with conventional notions of the Hubble expansion.Comment: 8 pages, in press in J. Math. Phy
Experimentally based sea urchin gene regulatory network and the causal explanation of developmental phenomenology
Gene regulatory networks (GRNs) for development underlie cell fate specification
and differentiation. Network topology, logic, and dynamics can be obtained
by thorough experimental analysis. Our understanding of the GRN controlling
endomesoderm specification in the sea urchin embryo has attained an advanced
level such that it explains developmental phenomenology.Here we review how the
network explains the mechanisms utilized in development to control the formation
of dynamic expression patterns of transcription factors and signaling molecules.
The network represents the genomic program controlling timely activation of
specification and differentiation genes in the correct embryonic lineages. It can
also be used to study evolution of body plans. We demonstrate how comparing
the sea urchin GRN to that of the sea star and to that of later developmental
stages in the sea urchin, reveals mechanisms underlying the origin of evolutionary
novelty. The experimentally based GRN for endomesoderm specification in the
sea urchin embryo provides unique insights into the system level properties of
cell fate specification and its evolution
Modeling the dynamics of transcriptional gene regulatory networks for animal development
The dynamic process of cell fate specification is regulated by networks of regulatory genes. The architecture of the network defines the temporal order of specification events. To understand the dynamic control of the developmental process, the kinetics of mRNA and protein synthesis and the response of the cis-regulatory modules to transcription factor concentration must be considered. Here we review mathematical models for mRNA and protein synthesis kinetics which are based on experimental measurements of the rates of the relevant processes. The model comprises the response functions of cis-regulatory modules to their transcription factor inputs, by incorporating binding site occupancy and its dependence on biologically measurable quantities. We use this model to simulate gene expression, to distinguish between cis-regulatory execution of “AND” and “OR” logic functions, rationalize the oscillatory behavior of certain transcriptional auto-repressors and to show how linked subcircuits can be dealt with. Model simulations display the effects of mutation of binding sites, or perturbation of upstream gene expression. The model is a generally useful tool for understanding gene regulation and the dynamics of cell fate specification
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