The river model of black holes

This paper presents an under-appreciated way to conceptualize stationary black holes, which we call the river model. The river model is mathematically sound, yet simple enough that the basic picture can be understood by non-experts. %that can by understood by non-experts. In the river model, space itself flows like a river through a flat background, while objects move through the river according to the rules of special relativity. In a spherical black hole, the river of space falls into the black hole at the Newtonian escape velocity, hitting the speed of light at the horizon. Inside the horizon, the river flows inward faster than light, carrying everything with it. We show that the river model works also for rotating (Kerr-Newman) black holes, though with a surprising twist. As in the spherical case, the river of space can be regarded as moving through a flat background. However, the river does not spiral inward, as one might have anticipated, but rather falls inward with no azimuthal swirl at all. Instead, the river has at each point not only a velocity but also a rotation, or twist. That is, the river has a Lorentz structure, characterized by six numbers (velocity and rotation), not just three (velocity). As an object moves through the river, it changes its velocity and rotation in response to tidal changes in the velocity and twist of the river along its path. An explicit expression is given for the river field, a six-component bivector field that encodes the velocity and twist of the river at each point, and that encapsulates all the properties of a stationary rotating black hole.Comment: 16 pages, 4 figures. The introduction now refers to the paper of Unruh (1981) and the extensive work on analog black holes that it spawned. Thanks to many readers for feedback that called attention to our omissions. Submitted to the American Journal of Physic

All Together Now: Legal Responses to the Introduction of Aquatic Nuisance Species in Washington Through Ballast Water

Aquatic nuisance species (ANS) are a substantial threat to the global environment, causing harm to ecosystems and costing U.S. industry billions of dollars per year. To combat ANS, legal regimes are being established on the international, federal, and state levels. In some western states, advocates have proposed legislation that is more stringent than the international and federal legal regimes\u27 voluntary ballast-water-exchange regulations. This Comment argues that Washington and the United States should remain in conformity with the international legal regime and should not enact regulations calling for mandatory ballast water-exchange at this time. Instead, the U.S. Coast Guard should strengthen its regulations in accordance with the National Invasive Species Act (NISA), development of regional panels should continue, and the United States should enact a national decision-support system. Furthermore, states should bolster their legal regimes in conjunction with NISA by funding ANS coordinators, developing ANS management plans, participating in ANS regional panels, and furthering education regarding ANS

Determining Pilot Manning for Bomber Longevity

In support of US Air Force efforts to conserve resources without sacrificing capability, this research examines the question of whether the 509th Bomb Wing could continue to provide maximum combat capability with fewer assigned pilots. During peacetime, pilot proficiency training comprises the majority of annual flying hours for the small B-2 bomber fleet. Optimal pilot manning will decrease the accumulation of excess wear on the airframes; helping to extend the viable life of the B-2 fleet and preserve the deterrent and combat capabilities that it provides to the United States. The operations and maintenance activity flows for B-2 aircraft and pilots in a notional sustained combat scenario are constructed in an Arena discrete-event simulation model. The model provides the capability to determine optimum manning levels for combat-qualified B-2 pilots across a range of fleet mission capable rates. Determination of actual optimum manning levels is sensitive to duration and probability parameters which are unavailable for use in this work. Notional parameter estimates are used to assess combat mission capability and pilot manning

Oligopoly Intermediation, Relative Rivalry, and the Mode of Competition

Policy design in oligopolistic settings depends critically on the mode of competition between firms. We develop a model of oligopoly intermediation that reveals the mode of competition to be an equilibrium outcome that depends on the relative degree of rivalry between firms in the upstream and downstream markets. We examine two forms of sequential pricing games: Purchasing to stock (PTS), in which firms select input prices prior to setting consumer prices; and purchasing to order (PTO), in which firms sell forward contracts to consumers prior to selecting input prices. The equilibrium outcomes of the model range between Bertrand and Cournot depending on the relative degree of rivarly between firms in the upstream and downstream markets. Prices are strategic complements and the equilibrium prices coincide with the Bertrand outcome when the markets are equally rivalrous, while prices are strategic substitutes when the degree of rivalry is sufficiently high in one market relative to the other. Cournot outcomes emerge under circumstances in which prices are strategically independent in either the upstream or downstream market. We derive testable implications for the mode of competition that depend only on primitive conditions of supply and demand functions

Oligopoly Intermediation, Relative Rivalry, and the Mode of Competition

Policy design in oligopolistic settings depends critically on the mode of competition between firms. We develop a model of oligopoly intermediation that reveals the mode of competition to be an equilibrium outcome that depends on the relative degree of rivalry between firms in the upstream and downstream markets. We examine two forms of sequential pricing games: Purchasing to stock (PTS), in which firms select input prices prior to setting consumer prices; and purchasing to order (PTO), in which firms sell forward contracts to consumers prior to selecting input prices. The equilibrium outcomes of the model range between Bertrand and Cournot depending on the relative degree of rivarly between firms in the upstream and downstream markets. Prices are strategic complements and the equilibrium prices coincide with the Bertrand outcome when the markets are equally rivalrous, while prices are strategic substitutes when the degree of rivalry is sufficiently high in one market relative to the other. Cournot outcomes emerge under circumstances in which prices are strategically independent in either the upstream or downstream market. We derive testable implications for the mode of competition that depend only on primitive conditions of supply and demand functions

The Economics-Security Nexus in the US-China Trade Conflict decoupling dilemmas

For more than two decades, China was enmeshed in transnational trade and investment networks. The complex interdependence that characterised the relationship between the United States and China is now threatened by policies that incentivise decoupling, including the partial unwinding of multinational supply chains. Since 2018 the ‘trade war’ between the US and China has taken on elements of a ‘tech war’, in which national security concerns replace economic logic. The area for win–win gains is reduced, as both countries pursue policies of greater technological autonomy. The bilateral rift creates challenges for companies and third parties who have no wish to take sides and complicates APEC’s goal to promote growth and accelerate regional economic integration

Optimal Estimation of Several Linear Parameters in the Presence of Lorentzian Thermal Noise

In a previous article we developed an approach to the optimal (minimum variance, unbiased) statistical estimation technique for the equilibrium displacement of a damped, harmonic oscillator in the presence of thermal noise. Here, we expand that work to include the optimal estimation of several linear parameters from a continuous time series. We show that working in the basis of the thermal driving force both simplifies the calculations and provides additional insight to why various approximate (not optimal) estimation techniques perform as they do. To illustrate this point, we compare the variance in the optimal estimator that we derive for thermal noise with those of two approximate methods which, like the optimal estimator, suppress the contribution to the variance that would come from the irrelevant, resonant motion of the oscillator. We discuss how these methods fare when the dominant noise process is either white displacement noise or noise with power spectral density that is inversely proportional to the frequency ($1/f$ noise). We also construct, in the basis of the driving force, an estimator that performs well for a mixture of white noise and thermal noise. To find the optimal multi-parameter estimators for thermal noise, we derive and illustrate a generalization of traditional matrix methods for parameter estimation that can accommodate continuous data. We discuss how this approach may help refine the design of experiments as they allow an exact, quantitative comparison of the precision of estimated parameters under various data acquisition and data analysis strategies.Comment: 16 pages, 10 figures. Accepted for publication in Classical and Quantum Gravit

Optical investigation of thermoelectric topological crystalline insulator Pb0.77_{0.77}Sn0.23_{0.23}Se

Pb$_{0.77}$Sn$_{0.23}$Se is a novel alloy of two promising thermoelectric materials PbSe and SnSe that exhibits a temperature dependent band inversion below 300 K. Recent work has shown that this band inversion also coincides with a trivial to nontrivial topological phase transition. To understand how the properties critical to thermoelectric efficiency are affected by the band inversion, we measured the broadband optical response of Pb$_{0.77}$Sn$_{0.23}$Se as a function of temperature. We find clear optical evidence of the band inversion at $160\pm15$ K, and use the extended Drude model to accurately determine a $T^{3/2}$ dependence of the bulk carrier lifetime, associated with electron-acoustic phonon scattering. Due to the high bulk carrier doping level, no discriminating signatures of the topological surface states are found, although their presence cannot be excluded from our data.Comment: 11 pages, 6 figure