Compactifications of Deformed Conifolds, Branes and the Geometry of Qubits

We present three families of exact, cohomogeneity-one Einstein metrics in $(2n+2)$ dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of solutions are Fubini-Study metrics on the complex projective spaces $CP^{n+1}$, written in a Stenzel form, whose principal orbits are the Stiefel manifolds $V_2(R ^{n+2})=SO(n+2)/SO(n)$ divided by $Z_2$. The second family are also Einstein-K\"ahler metrics, now on the Grassmannian manifolds $G_2(R^{n+3})=SO(n+3)/((SO(n+1)\times SO(2))$, whose principal orbits are the Stiefel manifolds $V_2(R^{n+2})$ (with no $Z_2$ factoring in this case). The third family are Einstein metrics on the product manifolds $S^{n+1}\times S^{n+1}$, and are K\"ahler only for $n=1$. Some of these metrics are believed to play a role in studies of consistent string theory compactifications and in the context of the AdS/CFT correspondence. We also elaborate on the geometric approach to quantum mechanics based on the K\"ahler geometry of Fubini-Study metrics on $CP^{n+1}$, and we apply the formalism to study the quantum entanglement of qubits.Comment: 31 page

Thermodynamics of Magnetised Kerr-Newman Black Holes

The thermodynamics of a magnetised Kerr-Newman black hole is studied to all orders in the appended magnetic field $B$. The asymptotic properties of the metric and other fields are dominated by the magnetic flux that extends to infinity along the axis, leading to subtleties in the calculation of conserved quantities such as the angular momentum and the mass. We present a detailed discussion of the implementation of a Wald-type procedure to calculate the angular momentum, showing how ambiguities that are absent in the usual asymptotically-flat case may be resolved by the requirement of gauge invariance. We also present a formalism from which we are able to obtain an expression for the mass of the magnetised black holes. The expressions for the mass and the angular momentum are shown to be compatible with the first law of thermodynamics and a Smarr type relation. Allowing the appended magnetic field $B$ to vary results in an extra term in the first law of the form $-\mu dB$ where $\mu$ is interpreted as an induced magnetic moment. Minimising the total energy with respect to the total charge $Q$ at fixed values of the angular momentum and energy of the seed metric allows an investigation of Wald's process. The Meissner effect is shown to hold for electrically neutral extreme black holes. We also present a derivation of the angular momentum for black holes in the four-dimensional STU model, which is ${\cal N}=2$ supergravity coupled to three vector multiplets.Comment: 27 page

Bulk/Boundary Thermodynamic Equivalence, and the Bekenstein and Cosmic-Censorship Bounds for Rotating Charged AdS Black Holes

We show that one may pass from bulk to boundary thermodynamic quantities for rotating AdS black holes in arbitrary dimensions so that if the bulk quantities satisfy the first law of thermodynamics then so do the boundary CFT quantities. This corrects recent claims that boundary CFT quantities satisfying the first law may only be obtained using bulk quantities measured with respect to a certain frame rotating at infinity, and which therefore do not satisfy the first law. We show that the bulk black hole thermodynamic variables, or equivalently therefore the boundary CFT variables, do not always satisfy a Cardy-Verlinde type formula, but they do always satisfy an AdS-Bekenstein bound. The universal validity of the Bekenstein bound is a consequence of the more fundamental cosmic censorship bound, which we find to hold in all cases examined. We also find that at fixed entropy, the temperature of a rotating black hole is bounded above by that of a non-rotating black hole, in four and five dimensions, but not in six or more dimensions. We find evidence for universal upper bounds for the area of cosmological event horizons and black-hole horizons in rotating black-hole spacetimes with a positive cosmological constant.Comment: Latex, 42 page

Interacting Intersections

Intersecting p-branes can be viewed as higher-dimensional interpretations of multi-charge extremal p-branes, where some of the individual p-branes undergo diagonal dimensional oxidation, while the others oxidise vertically. Although the naive vertical oxidation of a single p-brane gives a continuum of p-branes, a more natural description arises if one considers a periodic array of p-branes in the higher dimension, implying a dependence on the compactification coordinates. This still reduces to the single lower-dimensional p-brane when viewed at distances large compared with the period. Applying the same logic to the multi-charge solutions, we are led to consider more general classes of intersecting p-brane solutions, again depending on the compactification coordinates, which turn out to be described by interacting functions rather than independent harmonic functions. These new solutions also provide a more satisfactory interpretation for the lower-dimensional multi-charge p-branes, which otherwise appear to be nothing more than the improbable coincidence of charge-centres of individual constituents with zero binding energy.Comment: 20 pages, Latex, references adde

Understanding College Application Decisions Why College Sports Success Matters

Using a unique, national data set that indicates where students choose to send their SAT scores, the authors find that college sports success has a large impact on student application decisions. For example, a school that has a stellar year in basketball or football on average receives up to 10% more SAT scores. Certain demographic groups (males, Blacks, out-of-state students, and students who played sports in high school) are more likely to be influenced by sports success than their counterparts. The authors explore the reasons why students might be influenced by these sporting events and present evidence that attention/accessibility helps explain these findings

Crime and property values: Evidence from the 1990s crime drop

Does a dramatic drop in crime lead to an increase in property values? To date, the literature on how crime influences property values has focused solely within a single metropolitan area and has been limited primarily to cross-sectional analysis. In this study we exploit the dramatic, nationwide decrease in crime that occurred in the 1990s to examine the relationship between changes in crime rates and property values. To do this, we compile information on changes in property values and crime during the 1990s in nearly 3000 urban zip codes throughout the U.S. Using a fixed-effects framework as well as an instrumental variables strategy, our analysis implies a large and statistically significant association between crime and property values. The estimated elasticities of property values with respect to crime range from − 0.15 to − 0.35. Furthermore, zip codes in the top decile in terms of crime reduction saw property value increases of 7–19% during the 1990s. Both the empirical analysis and a graphical analysis are suggestive that decreasing crime leads to increasing property values. Highlights ► We exploit the sharp decrease in crime in the 1990s to examine the relationship between crime and property values. ► Information on changes in property values and crime in nearly 3000 U.S. zip codes are used to conduct the analysis. ► Our analysis implies a large and statistically significant association between crime and property values. ► The top decile of zip codes (in terms of crime reduction) saw property value increases between 7 and 19% during the 1990s