869 research outputs found
Isotropic cosmological singularities 1: Polytropic perfect fluid spacetimes
We consider the conformal Einstein equations for polytropic perfect fluid
cosmologies which admit an isotropic singularity. For the polytropic index
gamma strictly greater than 1 and less than or equal to 2 it is shown that the
Cauchy problem for these equations is well-posed, that is to say that solutions
exist, are unique and depend smoothly on the data, with data consisting of
simply the 3-metric of the singularity. The analogous result for gamma=1 (dust)
is obtained when Bianchi type symmetry is assumed.Comment: LaTeX, 43 pages, no figures, submitted to Ann. Phy
Collapsing Shells and the Isoperimetric Inequality for Black Holes
Recent results of Trudinger on Isoperimetric Inequalities for non-convex
bodies are applied to the gravitational collapse of a lightlike shell of matter
to form a black hole. Using some integral identities for co-dimension two
surfaces in Minkowski spacetime, the area of the apparent horizon is shown
to be bounded above in terms of the mass by the , which is
consistent with the Cosmic Censorship Hypothesis. The results hold in four
spacetime dimensions and above.Comment: 16 pages plain TE
Isotropic cosmological singularities: other matter models
Isotropic cosmological singularities are singularities which can be removed
by rescaling the metric. In some cases already studied (gr-qc/9903008,
gr-qc/9903009, gr-qc/9903018) existence and uniqueness of cosmological models
with data at the singularity has been established. These were cosmologies with,
as source, either perfect fluids with linear equations of state or massless,
collisionless particles. In this article we consider how to extend these
results to a variety of other matter models. These are scalar fields, massive
collisionless matter, the Yang-Mills plasma of Choquet-Bruhat, or matter
satisfying the Einstein-Boltzmann equation.Comment: LaTeX, 19 pages, no figure
A comment on Liu and Yau's positive quasi-local mass
Liu and Yau (Phys.Rev.Lett. 90, 231102, 2003) propose a definition of quasi-local mass for any space-like, topological 2-sphere with positive Gauss curvature (and subject to a second, convexity, condition). They are able to show it is positive using a result of Shi and Tam (J.Diff.Geom. 62, 79, 2002). However, as we show here, their definition can give a strictly positive mass for a sphere in flat space
Scalar--flat K\"ahler metrics with conformal Bianchi V symmetry
We provide an affirmative answer to a question posed by Tod \cite{Tod:1995b},
and construct all four-dimensional Kahler metrics with vanishing scalar
curvature which are invariant under the conformal action of Bianchi V group.
The construction is based on the combination of twistor theory and the
isomonodromic problem with two double poles. The resulting metrics are
non-diagonal in the left-invariant basis and are explicitly given in terms of
Bessel functions and their integrals. We also make a connection with the LeBrun
ansatz, and characterise the associated solutions of the SU(\infty) Toda
equation by the existence a non-abelian two-dimensional group of point
symmetries.Comment: Dedicated to Maciej Przanowski on the occasion of his 65th birthday.
Minor corrections. To appear in CQ
Einstein--Maxwell--Dilaton metrics from three--dimensional Einstein--Weyl structures
A class of time dependent solutions to Einstein--Maxwell-dilaton
theory with attractive electric force is found from Einstein--Weyl structures
in (2+1) dimensions corresponding to dispersionless Kadomtsev--Petviashvili and
Toda equations. These solutions are obtained from time--like
Kaluza--Klein reductions of solitons.Comment: 12 pages, to be published in Class.Quantum Gra
Energy distribution of charged dilaton black holes
Chamorro and Virbhadra studied, using the energy-momentum complex of
Einstein, the energy distribution associated with static spherically symmetric
charged dilaton black holes for an arbitrary value of the coupling parameter
which controls the strength of the dilaton to the Maxwell field. We
study the same in Tolman's prescription and get the same result as obtained by
Chamorro and Virbhadra. The energy distribution of charged dilaton black holes
depends on the value of and the total energy is independent of this
parameter.Comment: 8 pages, RevTex, no figure
Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric
Understanding DNA based Nanostructures
We use molecular dynamics (MD) simulations to understand the structure, and stability of various Paranemic crossover (PX) DNA molecules and their topoisomer JX molecules, synthesized recently by Seeman and coworkers at New York University (NYU). Our studies include all atoms (4432 to 6215) of the PX structures with an explicit description of solvent and ions (for a total of up to 42,000 atoms) with periodic boundary conditions. We report the effect of divalent counterions Mg(+2) on the structural and thermodynamic properties of these molecules and compare them to our previously reported results in presence of monovalent Na+ ions. The dynamic structures averaged over the 3-nanosecond simulations preserves the Watson-Crick hydrogen bonding as well as the helical structure. We find that PX65 is the most stable structure both in Na+ and Mg(+2) in accordance with the experimental results. PX65 has helical twist and other helical structural parameters close to the values for normal B-DNA of similar length and sequence. Our strain energy calculations demonstrate that stability of the crossover structure increases with the increase in crossover points
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