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.

Discovery of a nonyrast Kπ=8+ isomer in Dy162, and the influence of competing K-mixing mechanisms on its highly forbidden decay

The Gd160(Be9,α3n)Dy162 reaction has been used to study high-spin states in Dy162. Pulsed beam conditions were utilized for enhanced isomer sensitivity. An isomer at 2188.1(3) keV with a half-life of 8.3(3) μs has been discovered and assigned Kπ= 8+ with a two-quasineutron configuration. Among 11 γ-ray decay branches, an E2, ΔK=8 transition to the ground-state band was observed with a reduced hindrance of fν=35, agreeing well with systematics correlating fν with the product of the valence neutron and proton numbers (NpNn) over an extended N,Z range. Small deviations from NpNn dependence are analyzed for a range of two-quasiparticle isomer decays and interpreted as arising from a weak dependence on the isomer excitation energy relative to the yrast line

Small Black Holes on Cylinders

We find the metric of small black holes on cylinders, i.e. neutral and static black holes with a small mass in d-dimensional Minkowski-space times a circle. The metric is found using an ansatz for black holes on cylinders proposed in hep-th/0204047. We use the new metric to compute corrections to the thermodynamics which is seen to deviate from that of the (d+1)-dimensional Schwarzschild black hole. Moreover, we compute the leading correction to the relative binding energy which is found to be non-zero. We discuss the consequences of these results for the general understanding of black holes and we connect the results to the phase structure of black holes and strings on cylinders.Comment: 23 pages, 1 figure. v2: typos corrected, introduction expanded, v3: presentation of sections 2 and 3 reordered and improved, explanatory remarks added, refs adde

The Collapse of Large Extra Dimensions

In models of spacetime that are the product of a four-dimensional spacetime with an ``extra'' dimension, there is the possibility that the extra dimension will collapse to zero size, forming a singularity. We ask whether this collapse is likely to destroy the spacetime. We argue, by an appeal to the four-dimensional cosmic censorship conjecture, that--at least in the case when the extra dimension is homogeneous--such a collapse will lead to a singularity hidden within a black string. We also construct explicit initial data for a spacetime in which such a collapse is guaranteed to occur and show how the formation of a naked singularity is likely avoided.Comment: Uses revtex

Caged Black Holes: Black Holes in Compactified Spacetimes I -- Theory

In backgrounds with compact dimensions there may exist several phases of black objects including the black-hole and the black-string. The phase transition between them raises puzzles and touches fundamental issues such as topology change, uniqueness and Cosmic Censorship. No analytic solution is known for the black hole, and moreover, one can expect approximate solutions only for very small black holes, while the phase transition physics happens when the black hole is large. Hence we turn to numerical solutions. Here some theoretical background to the numerical analysis is given, while the results will appear in a forthcoming paper. Goals for a numerical analysis are set. The scalar charge and tension along the compact dimension are defined and used as improved order parameters which put both the black hole and the black string at finite values on the phase diagram. Predictions for small black holes are presented. The differential and the integrated forms of the first law are derived, and the latter (Smarr's formula) can be used to estimate the ``overall numerical error''. Field asymptotics and expressions for physical quantities in terms of the numerical ones are supplied. Techniques include ``method of equivalent charges'', free energy, dimensional reduction, and analytic perturbation for small black holes.Comment: 23 pages. v3: version to be published in PRD, 3 references adde

Geodesic motions in extraordinary string geometry

The geodesic properties of the extraordinary vacuum string solution in (4+1) dimensions are analyzed by using Hamilton-Jacobi method. The geodesic motions show distinct properties from those of the static one. Especially, any freely falling particle can not arrive at the horizon or singularity. There exist stable null circular orbits and bouncing timelike and null geodesics. To get into the horizon {or singularity}, a particle need to follow a non-geodesic trajectory. We also analyze the orbit precession to show that the precession angle has distinct features for each geometry such as naked singularity, black string, and wormhole.Comment: 15 pages, 11 figure

New Phases of Near-Extremal Branes on a Circle

We study the phases of near-extremal branes on a circle, by which we mean near-extremal branes of string theory and M-theory with a circle in their transverse space. We find a map that takes any static and neutral Kaluza-Klein black hole, i.e. any static and neutral black hole on Minkowski-space times a circle M^d x S^1, and map it to a corresponding solution for a near-extremal brane on a circle. The map is derived using first a combined boost and U-duality transformation on the Kaluza-Klein black hole, transforming it to a solution for a non-extremal brane on a circle. The resulting solution for a near-extremal brane on a circle is then obtained by taking a certain near-extremal limit. As a consequence of the map, we can transform the neutral non-uniform black string branch into a new non-uniform phase of near-extremal branes on a circle. Furthermore, we use recently obtained analytical results on small black holes in Minkowski-space times a circle to get new information about the localized phase of near-extremal branes on a circle. This gives in turn predictions for the thermal behavior of the non-gravitational theories dual to these near-extremal branes. In particular, we give predictions for the thermodynamics of supersymmetric Yang-Mills theories on a circle, and we find a new stable phase of (2,0) Little String Theory in the canonical ensemble for temperatures above its Hagedorn temperature.Comment: 72 pages, 5 figures. v2: Typos fixed, refs. added. v3: Sec. 3.2 fixe

Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes

We construct and analyze a large class of exact five- and six-dimensional regular and static solutions of the vacuum Einstein equations. These solutions describe sequences of Kaluza-Klein bubbles and black holes, placed alternately so that the black holes are held apart by the bubbles. Asymptotically the solutions are Minkowski-space times a circle, i.e. Kaluza-Klein space, so they are part of the (\mu,n) phase diagram introduced in hep-th/0309116. In particular, they occupy a hitherto unexplored region of the phase diagram, since their relative tension exceeds that of the uniform black string. The solutions contain bubbles and black holes of various topologies, including six-dimensional black holes with ring topology S^3 x S^1 and tuboid topology S^2 x S^1 x S^1. The bubbles support the S^1's of the horizons against gravitational collapse. We find two maps between solutions, one that relates five- and six-dimensional solutions, and another that relates solutions in the same dimension by interchanging bubbles and black holes. To illustrate the richness of the phase structure and the non-uniqueness in the (\mu,n) phase diagram, we consider in detail particular examples of the general class of solutions.Comment: 71 pages, 22 figures, v2: Typos fixed, comment added in sec. 5.

Small localized black holes in a braneworld: Formulation and numerical method

No realistic black holes localized on a 3-brane in the Randall-Sundrum infinite braneworld have been found so far. The problem of finding a static black hole solution is reduced to a boundary value problem. We solve it by means of a numerical method, and show numerical examples of a localized black hole whose horizon radius is small compared to the bulk curvature scale. The sequence of small localized black holes exhibits a smooth transition from a five-dimensional Schwarzschild black hole, which is a solution in the limit of small horizon radius. The localized black hole tends to flatten as its horizon radius increases. However, it becomes difficult to find black hole solutions as its horizon radius increases.Comment: RevTeX, 13 pages, 6 figures, references corrected, typos corrected; to appear in Phys.Rev.

Multilayered feed forward Artificial Neural Network model to predict the average summer-monsoon rainfall in India

In the present research, possibility of predicting average summer-monsoon rainfall over India has been analyzed through Artificial Neural Network models. In formulating the Artificial Neural Network based predictive model, three layered networks have been constructed with sigmoid non-linearity. The models under study are different in the number of hidden neurons. After a thorough training and test procedure, neural net with three nodes in the hidden layer is found to be the best predictive model.Comment: 19 pages, 1 table, 3 figure