Extremal Black Holes in Dynamical Chern-Simons Gravity

Rapidly rotating black hole solutions in theories beyond general relativity play a key role in experimental gravity, as they allow us to compute observables in extreme spacetimes that deviate from the predictions of general relativity. Such solutions are often difficult to find in beyond-general-relativity theories due to the inclusion of additional fields that couple to the metric non-linearly and non-minimally. In this paper, we consider rotating black hole solutions in one such theory, dynamical Chern-Simons gravity, where the Einstein-Hilbert action is modified by the introduction of a dynamical scalar field that couples to the metric through the Pontryagin density. We treat dynamical Chern-Simons gravity as an effective field theory and work in the decoupling limit, where corrections are treated as small perturbations from general relativity. We perturb about the maximally-rotating Kerr solution, the so-called extremal limit, and develop mathematical insight into the analysis techniques needed to construct solutions for generic spin. First we find closed-form, analytic expressions for the extremal scalar field, and then determine the trace of the metric perturbation, giving both in terms of Legendre decompositions. Retaining only the first three and four modes in the Legendre representation of the scalar field and the trace, respectively, suffices to ensure a fidelity of over 99% relative to full numerical solutions. The leading-order mode in the Legendre expansion of the trace of the metric perturbation contains a logarithmic divergence at the extremal Kerr horizon, which is likely to be unimportant as it occurs inside the perturbed dynamical Chern-Simons horizon. The techniques employed here should enable the construction of analytic, closed-form expressions for the scalar field and metric perturbations on a background with arbitrary rotation.Comment: 25+9 pages (single column), 10 figures, 1 table; matches published versio

Internal versus External Capital Markets

This paper presents a framework for analyzing the costs and benefits of internal vs. external capital allocation. We focus primarily on comparing an internal capital market to bank lending. While both represent centralized forms of financing, in the former case the financing is owner-provided, while in the latter case it is not. We argue that the ownership aspect of internal capital allocation has three important consequences: 1) it leads to more monitoring than bank lending; 2) it reduces managers' entrepreneurial incentives; and 3) it makes it easier to efficiently redeploy the assets of projects that are performing poorly under existing management.

Asymptotic Exit Location Distributions in the Stochastic Exit Problem

Consider a two-dimensional continuous-time dynamical system, with an attracting fixed point $S$. If the deterministic dynamics are perturbed by white noise (random perturbations) of strength $\epsilon$, the system state will eventually leave the domain of attraction $\Omega$ of $S$. We analyse the case when, as $\epsilon\to0$, the exit location on the boundary $\partial\Omega$ is increasingly concentrated near a saddle point $H$ of the deterministic dynamics. We show that the asymptotic form of the exit location distribution on $\partial\Omega$ is generically non-Gaussian and asymmetric, and classify the possible limiting distributions. A key role is played by a parameter $\mu$, equal to the ratio $|\lambda_s(H)|/\lambda_u(H)$ of the stable and unstable eigenvalues of the linearized deterministic flow at $H$. If $\mu<1$ then the exit location distribution is generically asymptotic as $\epsilon\to0$ to a Weibull distribution with shape parameter $2/\mu$, on the $O(\epsilon^{\mu/2})$ length scale near $H$. If $\mu>1$ it is generically asymptotic to a distribution on the $O(\epsilon^{1/2})$ length scale, whose moments we compute. The asymmetry of the asymptotic exit location distribution is attributable to the generic presence of a `classically forbidden' region: a wedge-shaped subset of $\Omega$ with $H$ as vertex, which is reached from $S$, in the $\epsilon\to0$ limit, only via `bent' (non-smooth) fluctuational paths that first pass through the vicinity of $H$. We deduce from the presence of this forbidden region that the classical Eyring formula for the small-$\epsilon$ exponential asymptotics of the mean first exit time is generically inapplicable.Comment: This is a 72-page Postscript file, about 600K in length. Hardcopy requests to [email protected] or [email protected]

Escape tactics used by bluegills and fathead minnows to avoid predation by tiger muskellunge

To explain why esocids prefer cylindrical, soft-rayed prey over compressed, spiny-rayed prey, we quantified behavioral interaction between tiger muskellunge (F1 hybrid of male northern pike Esox lucius and female muskellunge E. masquinongy) and fathead minnows (Pimephales promelas) and bluegills (Lepomis macrochirus). Tiger muskellunge required four times as many strikes and longer pursuits to capture bluegills than fathead minnows. Tiger muskellunge attacked each prey species differently; fathead minnows were grasped at midbody and bluegills were attacked in the caudal area. Each prey species exhibited different escape tactics. Fathead minnows remained in open water and consistently schooled; bluegills dispersed throughout the tank and sought cover by moving to corners and edges. Due to their antipredatory behavior (dispersing, cover seeking, and remaining motionless) and morphology (deep body and spines), bluegills were less susceptible to capture by tiger muskellunge than were fathead minnows.Funding for this project was provided by the Federal Aid in Fish Restoration Act under Dingell-Johnson Project F-57-R

Robotic-Assisted Laparoscopic Management of Ureteral Endometriosis

This report describes 2 cases of ureteral obstruction secondary to endometriosis managed with robotic-assisted laparoscopic partial ureterectomy and ureteroneocystostomy

Magnetohydrodynamics of the Weakly Ionized Solar Photosphere

We investigate the importance of ambipolar diffusion and Hall currents for high-resolution comprehensive ('realistic') photospheric simulations. To do so we extended the radiative magnetohydrodynamics code \emph{MURaM} to use the generalized Ohm's law under the assumption of local thermodynamic equilibrium. We present test cases comparing analytical solutions with numerical simulations for validation of the code. Furthermore, we carried out a number of numerical experiments to investigate the impact of these neutral-ion effects in the photosphere. We find that, at the spatial resolutions currently used (5-20 km per grid point), the Hall currents and ambipolar diffusion begin to become significant -- with flows of 100 m/s in sunspot light bridges, and changes of a few percent in the thermodynamic structure of quiet-Sun magnetic features. The magnitude of the effects is expected to increase rapidly as smaller-scale variations are resolved by the simulations.Comment: accepted Ap

Extremal black holes in dynamical Chern–Simons gravity

Rapidly rotating black hole (BH) solutions in theories beyond general relativity (GR) play a key role in experimental gravity, as they allow us to compute observables in extreme spacetimes that deviate from the predictions of GR. Such solutions are often difficult to find in beyond-general-relativity theories due to the inclusion of additional fields that couple to the metric nonlinearly and non-minimally. In this paper, we consider rotating BH solutions in one such theory, dynamical Chern–Simons (dCS) gravity, where the Einstein–Hilbert action is modified by the introduction of a dynamical scalar field that couples to the metric through the Pontryagin density. We treat dCS gravity as an effective field theory and work in the decoupling limit, where corrections are treated as small perturbations from GR. We perturb about the maximally rotating Kerr solution, the so-called extremal limit, and develop mathematical insight into the analysis techniques needed to construct solutions for generic spin. First we find closed-form, analytic expressions for the extremal scalar field, and then determine the trace of the metric perturbation, giving both in terms of Legendre decompositions. Retaining only the first three and four modes in the Legendre representation of the scalar field and the trace, respectively, suffices to ensure a fidelity of over 99% relative to full numerical solutions. The leading-order mode in the Legendre expansion of the trace of the metric perturbation contains a logarithmic divergence at the extremal Kerr horizon, which is likely to be unimportant as it occurs inside the perturbed dCS horizon. The techniques employed here should enable the construction of analytic, closed-form expressions for the scalar field and metric perturbations on a background with arbitrary rotation

Exome sequencing identifies nonsegregating nonsense ATM and PALB2 variants in familial pancreatic cancer.

We sequenced 11 germline exomes from five families with familial pancreatic cancer (FPC). One proband had a germline nonsense variant in ATM with somatic loss of the variant allele. Another proband had a nonsense variant in PALB2 with somatic loss of the variant allele. Both variants were absent in a relative with FPC. These findings question the causal mechanisms of ATM and PALB2 in these families and highlight challenges in identifying the causes of familial cancer syndromes using exome sequencing

Structural equation model-based genome scan for the metabolic syndrome

BACKGROUND: The metabolic syndrome is characterized by the clustering of several traits, including obesity, hypertension, decreased levels of HDL cholesterol, and increased levels of glucose and triglycerides. Because these traits cluster, there are likely common genetic factors involved. RESULTS: We used a multivariate structural equation model (SEM) approach to scan the genome for loci involved in the metabolic syndrome. We found moderate evidence for linkage on chromosomes 2, 3, 11, 13, and 15, and these loci appear to have different relative effects on the component traits of the metabolic syndrome. CONCLUSION: Our results suggest that the metabolic syndrome components, diabetes, obesity, and hypertension, are under the pleiotropic control of several loci