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 $D$, treating it as a parameter of the system. We derive the large $D$ 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 ${\bf T}^n$, the $n$ 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 $D\leq 11$.Comment: 1+14 pages, 2 eps figures. Replaced with the published versio

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Arvioitu julkaisuaik

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 coming peace and social democracy

Arivoitu julkaisuaik

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 $some$ appropriate black strings and $p$-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 $other$ 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 $p$-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 $p$-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 $D \le 13 +p$, 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 $D > 12+p$, whereas the non-uniform smeared branes are favorable at $D > 14+p$ 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