Topology, Entropy and Witten Index of Dilaton Black Holes

We have found that for extreme dilaton black holes an inner boundary must be introduced in addition to the outer boundary to give an integer value to the Euler number. The resulting manifolds have (if one identifies imaginary time) topology $S^1 \times R \times S^2$ and Euler number $\chi = 0$ in contrast to the non-extreme case with $\chi=2$. The entropy of extreme $U(1)$ dilaton black holes is already known to be zero. We include a review of some recent ideas due to Hawking on the Reissner-Nordstr\"om case. By regarding all extreme black holes as having an inner boundary, we conclude that the entropy of {\sl all} extreme black holes, including $[U(1)]^2$ black holes, vanishes. We discuss the relevance of this to the vanishing of quantum corrections and the idea that the functional integral for extreme holes gives a Witten Index. We have studied also the topology of ``moduli space'' of multi black holes. The quantum mechanics on black hole moduli spaces is expected to be supersymmetric despite the fact that they are not HyperK\"ahler since the corresponding geometry has torsion unlike the BPS monopole case. Finally, we describe the possibility of extreme black hole fission for states with an energy gap. The energy released, as a proportion of the initial rest mass, during the decay of an electro-magnetic black hole is 300 times greater than that released by the fission of an ${}^{235} U$ nucleus.Comment: 51 pages, 4 figures, LaTeX. Considerably extended version. New sections include discussion of the Witten index, topology of the moduli space, black hole sigma model, and black hole fission with huge energy releas

Birth of Closed Strings and Death of Open Strings during Tachyon Condensation

The tremendous progress achieved through the study of black holes and branes suggests that their time dependent generalizations called Spacelike branes (S-branes) may prove similarly useful. An example of an established approach to S-branes is to include a string boundary interaction and we first summarize evidence for the death of open string degrees of freedom for the homogeneous rolling tachyon on a decaying brane. Then, we review how to extract the flat S-brane worldvolumes describing the homogeneous rolling tachyon and how large deformations correspond to creation of lower dimensional strings and branes. These S-brane worldvolumes are governed by S-brane actions which are on equal footing to D-brane actions, since they are derived by imposing conformality on the string worldsheet, as well as by analyzing fluctuations of time dependent tachyon configurations. As further examples we generalize previous solutions of the S-brane actions so as to describe multiple decaying and nucleating closed fundamental strings. Conceptually S-brane actions are therefore different from D-brane actions and can provide a description of time dependent strings/branes and possibly their interactions.Comment: 15 pages, 7 eps figures; invited review for Modern Physics Letters A, including new solutions for S-brane actions. v2 published version, minor typos correcte

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 $A$ of the apparent horizon is shown to be bounded above in terms of the mass $M$ by the $16 \pi G^2 M^2$, which is consistent with the Cosmic Censorship Hypothesis. The results hold in four spacetime dimensions and above.Comment: 16 pages plain TE

HLA-B27 Positivity: associated health implications

HLA-B27 positivity makes the onset of autoimmune diseases such as uveitis, ankylosing spondylitis and Crohn's disease more likely to occur. Ankylosing spondylitis and Crohn's disease are two types of HLA-B27 positive diseases that demonstrate a direct association with uveitis. Although the possession of HLA-B27 positivity is not mandatory for autoimmune diseases such as uveitis to occur, HLA-B27 positivity not only makes it more likely but may modify the clinical picture in which a patient presents. In relation to assessment and diagnosis it is imperative that the medical history of patients is thoroughly examined to ensure pathological sequelae are appropriately treated. Nurses play an important role in assessing patients that have uveitis and should suspect ankylosing spondylitis or Crohn's disease may be present

Generation of Multiple Circular Walls on a Thin Film of Nematic Liquid Crystal by Laser Scanning

We found that multiple circular walls (MCW) can be generated on a thin film of a nematic liquid crystal through a spiral scanning of a focused IR laser. The ratios between radii of adjacent rings of MCW were almost constant. These constant ratios can be explained theoretically by minimization of the Frank elastic free energy of nematic medium. The director field on a MCW exhibits chiral symmetry-breaking although the elastic free energies of both chiral MCWs are degenerated, i.e., the director on a MCW can rotate clockwise or counterclockwise along the radial direction.Comment: 10 pages, 5 figures. Submitted to Chemical Physics Letters 2nd Editio

lordif: An R Package for Detecting Differential Item Functioning Using Iterative Hybrid Ordinal Logistic Regression/Item Response Theory and Monte Carlo Simulations

Logistic regression provides a flexible framework for detecting various types of differential item functioning (DIF). Previous efforts extended the framework by using item response theory (IRT) based trait scores, and by employing an iterative process using group--specific item parameters to account for DIF in the trait scores, analogous to purification approaches used in other DIF detection frameworks. The current investigation advances the technique by developing a computational platform integrating both statistical and IRT procedures into a single program. Furthermore, a Monte Carlo simulation approach was incorporated to derive empirical criteria for various DIF statistics and effect size measures. For purposes of illustration, the procedure was applied to data from a questionnaire of anxiety symptoms for detecting DIF associated with age from the Patient--Reported Outcomes Measurement Information System.

BPS states of D=4 N=1 supersymmetry

We find the combinations of momentum and domain-wall charges corresponding to BPS states preserving 1/4, 1/2 or 3/4 of D=4 N=1 supersymmetry, and we show how the supersymmetry algebra implies their stability. These states form the boundary of the convex cone associated with the Jordan algebra of $4\times 4$ real symmetric matrices, and we explore some implications of the associated geometry. For the Wess-Zumino model we derive the conditions for preservation of 1/4 supersymmetry when one of two parallel domain-walls is rotated and in addition show that this model does not admit any classical configurations with 3/4 supersymmetry. Our analysis also provides information about BPS states of N=1 D=4 anti-de Sitter supersymmetry.Comment: Latex, 27 pages. Various corrections and improvements including an expanded discussion on BPS states in ad

Universal properties of the near-horizon optical geometry

We make use of the fact that the optical geometry near a static non-degenerate Killing horizon is asymptotically hyperbolic to investigate universal features of black hole physics. We show how the Gauss-Bonnet theorem allows certain lensing scenarios to be ruled in or out. We find rates for the loss of scalar, vector and fermionic `hair' as objects fall quasi- statically towards the horizon. In the process we find the Lienard-Wiechert potential for hyperbolic space and calculate the force between electrons mediated by neutrinos, extending the flat space result of Feinberg and Sucher. We use the enhanced conformal symmetry of the Schwarzschild and Reissner-Nordstrom backgrounds to re-derive the electrostatic field due to a point charge in a simple fashion