763 research outputs found
High and Low Dimensions in The Black Hole Negative Mode
The negative mode of the Schwarzschild black hole is central to Euclidean
quantum gravity around hot flat space and for the Gregory-Laflamme black string
instability. We analyze the eigenvalue as a function of space-time dimension by
constructing two perturbative expansions: one for large d and the other for
small d-3, and determining as many coefficients as we are able to compute
analytically. Joining the two expansions we obtain an interpolating rational
function accurate to better than 2% through the whole range of dimensions
including d=4.Comment: 17 pages, 4 figures. v2: added reference. v3: published versio
A Dialogue of Multipoles: Matched Asymptotic Expansion for Caged Black Holes
No analytic solution is known to date for a black hole in a compact
dimension. We develop an analytic perturbation theory where the small parameter
is the size of the black hole relative to the size of the compact dimension. We
set up a general procedure for an arbitrary order in the perturbation series
based on an asymptotic matched expansion between two coordinate patches: the
near horizon zone and the asymptotic zone. The procedure is ordinary
perturbation expansion in each zone, where additionally some boundary data
comes from the other zone, and so the procedure alternates between the zones.
It can be viewed as a dialogue of multipoles where the black hole changes its
shape (mass multipoles) in response to the field (multipoles) created by its
periodic "mirrors", and that in turn changes its field and so on. We present
the leading correction to the full metric including the first correction to the
area-temperature relation, the leading term for black hole eccentricity and the
"Archimedes effect". The next order corrections will appear in a sequel. On the
way we determine independently the static perturbations of the Schwarzschild
black hole in dimension d>=5, where the system of equations can be reduced to
"a master equation" - a single ordinary differential equation. The solutions
are hypergeometric functions which in some cases reduce to polynomials.Comment: 47 pages, 12 figures, minor corrections described at the end of the
introductio
On Black-Brane Instability In an Arbitrary Dimension
The black-hole black-string system is known to exhibit critical dimensions
and therefore it is interesting to vary the spacetime dimension , treating
it as a parameter of the system. We derive the large asymptotics of the
critical, i.e. marginally stable, string following an earlier numerical
analysis. For a background with an arbitrary compactification manifold we give
an expression for the critical mass of a corresponding black brane. This
expression is completely explicit for , the dimensional torus of
an arbitrary shape. An indication is given that by employing a higher
dimensional torus, rather than a single compact dimension, the total critical
dimension above which the nature of the black-brane black-hole phase transition
changes from sudden to smooth could be as low as .Comment: 1+14 pages, 2 eps figures. Replaced with the published versio
Caged Black Holes: Black Holes in Compactified Spacetimes II - 5d Numerical Implementation
We describe the first convergent numerical method to determine static black
hole solutions (with S^3 horizon) in 5d compactified spacetime. We obtain a
family of solutions parametrized by the ratio of the black hole size and the
size of the compact extra dimension. The solutions satisfy the demanding
integrated first law. For small black holes our solutions approach the 5d
Schwarzschild solution and agree very well with new theoretical predictions for
the small corrections to thermodynamics and geometry. The existence of such
black holes is thus established. We report on thermodynamical (temperature,
entropy, mass and tension along the compact dimension) and geometrical
measurements. Most interestingly, for large masses (close to the
Gregory-Laflamme critical mass) the scheme destabilizes. We interpret this as
evidence for an approach to a physical tachyonic instability. Using
extrapolation we speculate that the system undergoes a first order phase
transition.Comment: 42 pages, 19 eps figures; v2: 3 references added, version to appear
in Phys.Rev.
The Final State of Black Strings and p-Branes, and the Gregory-Laflamme Instability
It is shown that the usual entropy argument for the Gregory-Laflamme (GL)
instability for appropriate black strings and -branes gives
surprising agreement up to a few percent. This may provide a strong support to
the GL's horizon fragmentation, which would produce the array of
higher-dimensional Schwarzschild-type's black holes finally. On the other hand,
another estimator for the size of the black hole end-state relative to the
compact dimension indicates a second order (i.e., smooth) phase transition for
some appropriate compactifications and total dimension of spacetime
wherein the entropy argument is not appropriate. In this case,
Horowitz-Maeda-type's non-uniform black strings or -branes can be the final
state of the GL instability.Comment: More emphasis on a second order phase transition. The computation
result is unchange
From Black Strings to Black Holes
Using recently developed numerical methods, we examine neutral compactified
non-uniform black strings which connect to the Gregory-Laflamme critical point.
By studying the geometry of the horizon we give evidence that this branch of
solutions may connect to the black hole solutions, as conjectured by Kol. We
find the geometry of the topology changing solution is likely to be nakedly
singular at the point where the horizon radius is zero. We show that these
solutions can all be expressed in the coordinate system discussed by Harmark
and Obers.Comment: 6 pages, 5 figures, RevTe
On non-uniform smeared black branes
We investigate charged dilatonic black -branes smeared on a transverse
circle. The system can be reduced to neutral vacuum black branes, and we
perform static perturbations for the reduced system to construct non-uniform
solutions. At each order a single master equation is derived, and the
Gregory-Laflamme critical wavelength is determined. Based on the non-uniform
solutions, we discuss thermodynamic properties of this system and argue that in
a microcanonical ensemble the non-uniform smeared branes are entropically
disfavored even near the extremality, if the spacetime dimension is , which is the critical dimension for the vacuum case. However, the critical
dimension is not universal. In a canonical ensemble the vacuum non-uniform
black branes are thermodynamically favorable at , whereas the
non-uniform smeared branes are favorable at near the extremality.Comment: 24 pages, 2 figures; v2: typos corrected, submitted to
Class.Quant.Gra
Synthesis, in vitro antioxidant and antimicrobial activities of some novel 3-substitued-4-(3-methoxy-4-isobutyryloxybenzylideneamino)-4,5-dihydro- 1H-1,2,4-triazol-5-one derivatives
271-282In this study, 3-alkyl(aryl)-4-amino-4,5-dihydro-1H-1,2,4-triazol-5-ones have been reacted with 3-methoxy-4-isobutyryloxybenzaldehyde 2 to afford the corresponding nine new 3-alkyl(aryl)-4-(3-methoxy-4-isobutyryloxybenzylideneamino)-4,5-dihydro-1H-1,2,4-triazol-5-ones 3. Then, the acetylation reactions of compounds 3 have been investigated and 4 type compounds have been obtained. The compounds 3 have also been treated with morpholine/1-methylpiperazine in the presence of formaldehyde according to the Mannich reaction to synthesize 1-(morpholine-4-yl-methyl)-3-alkyl(aryl)-4-(3-methoxy-4-isobutyryloxy-benzylideneamino)-4,5-dihydro-1H-1,2,4-triazol-5-ones 5, and 1-(1-methylpiperazin-4-yl-methyl)-3-alkyl(aryl)-4-(3-methoxy-4-isobutyryloxybenzylideneamino)-4,5-dihydro-1H-1,2,4-triazol-5-ones 6, respectively. The structures of twenty four new compounds have been characterized by IR, 1H and 13C NMR and MS spectroscopic methods. In addition, the newly synthesized compounds have been screened for their antimicrobial activities. Furthermore, these twenty four new compounds have been analyzed for their in vitro potential antioxidant activities by three different methods
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