On Equivalence of Critical Collapse of Non-Abelian Fields

We continue our study of the gravitational collapse of spherically symmetric skyrmions. For certain families of initial data, we find the discretely self-similar Type II critical transition characterized by the mass scaling exponent $\gamma \approx 0.20$ and the echoing period $\Delta \approx 0.74$. We argue that the coincidence of these critical exponents with those found previously in the Einstein-Yang-Mills model is not accidental but, in fact, the two models belong to the same universality class.Comment: 7 pages, REVTex, 2 figures included, accepted for publication in Physical Review

Universality and properties of neutron star type I critical collapses

We study the neutron star axisymmetric critical solution previously found in the numerical studies of neutron star mergers. Using neutron star-like initial data and performing similar merger simulations, we demonstrate that the solution is indeed a semi-attractor on the threshold plane separating the basin of a neutron star and the basin of a black hole in the solution space of the Einstein equations. In order to explore the extent of the attraction basin of the neutron star semiattractor, we construct initial data phase spaces for these neutron star-like initial data. From these phase spaces, we also observe several interesting dynamical scenarios where the merged object is supported from prompt collapse. The properties of the critical index of the solution, in particular, its dependence on conserved quantities, are then studied. From the study, it is found that a family of neutron star semi-attractors exist that can be classified by both their rest masses and ADM masses.Comment: 13 pages, 12 figures, 1 new reference adde

Scale invariance and critical gravitational collapse

We examine ways to write the Choptuik critical solution as the evolution of scale invariant variables. It is shown that a system of scale invariant variables proposed by one of the authors does not evolve periodically in the Choptuik critical solution. We find a different system, based on maximal slicing. This system does evolve periodically, and may generalize to the case of axisymmetry or of no symmetry at all.Comment: 7 pages, 3 figures, Revtex, discussion modified to clarify presentatio

Late-time evolution of nonlinear gravitational collapse

We study numerically the fully nonlinear gravitational collapse of a self-gravitating, minimally-coupled, massless scalar field in spherical symmetry. Our numerical code is based on double-null coordinates and on free evolution of the metric functions: The evolution equations are integrated numerically, whereas the constraint equations are only monitored. The numerical code is stable (unlike recent claims) and second-order accurate. We use this code to study the late-time asymptotic behavior at fixed $r$ (outside the black hole), along the event horizon, and along future null infinity. In all three asymptotic regions we find that, after the decay of the quasi-normal modes, the perturbations are dominated by inverse power-law tails. The corresponding power indices agree with the integer values predicted by linearized theory. We also study the case of a charged black hole nonlinearly perturbed by a (neutral) self-gravitating scalar field, and find the same type of behavior---i.e., quasi-normal modes followed by inverse power-law tails, with the same indices as in the uncharged case.Comment: 14 pages, standard LaTeX, 18 Encapsulated PostScript figures. A new convergence test and a determination of QN ringing were added, in addition to correction of typos and update of reference

The naked singularity in the global structure of critical collapse spacetimes

We examine the global structure of scalar field critical collapse spacetimes using a characteristic double-null code. It can integrate past the horizon without any coordinate problems, due to the careful choice of constraint equations used in the evolution. The limiting sequence of sub- and supercritical spacetimes presents an apparent paradox in the expected Penrose diagrams, which we address in this paper. We argue that the limiting spacetime converges pointwise to a unique limit for all r>0, but not uniformly. The r=0 line is different in the two limits. We interpret that the two different Penrose diagrams differ by a discontinuous gauge transformation. We conclude that the limiting spacetime possesses a singular event, with a future removable naked singularity.Comment: RevTeX 4; 6 pages, 7 figure

Microgrids and Resilience to Climate-Driven Impacts on Public Health

“Resilience” has burst into the lexicons of several policy areas in recent years, owing in no small part to climate change’s amplification of extreme events that severely disrupt the operation of natural, social, and engineered systems. Fostering resilience means anticipating severe disruptions and planning, investing, and designing so that such disruptions, which are certain to occur, are made shallower in depth and shorter in duration. Thus a resilient system or community can continue functioning despite disruptive events, return more swiftly to routine function following disruption, and incorporate new information so as to improve operations in extremis and speed future restorations. As different policy communities apply the concept of resilience to their respective missions, they emphasize different objectives. This article examines how the definitions adopted by the public health and electricity communities can, but do not necessarily, converge in responses to electricity outages so severe that they affect the operation of critical infrastructure, such as wastewater treatment and drinking water facilities, hospitals, and cooling centers. Currently, such outages cause a form of handoff from utilities to their customers: grid power fails and a small constellation of backup generators maintained by atomized campuses, facilities, or individual structures switch on, or fail to switch on, or were never purchased and so leave the location dark and its equipment inoperative. This handoff is operational, but it reflects legal obligations—and their limits. Enter the microgrid, a specially designed segment of the electricity distribution grid’s mesh that can either operate seamlessly as part of the wider grid, or as an independent “island” that serves some or all of the electricity users within its boundary even when the wider grid fails. Microgrids can, but do not necessarily, mitigate the adverse public health implications of the handoff that accompanies widespread and severe grid failure. To encourage the convergence of public health and electricity policy priorities in decisions about microgrid siting, design, and operation, this article makes several recommendations. Some of these should ideally be taken up at the federal level, but the bulk of the work they recommend should take place at the state-level, and would necessarily be implemented at the state and local levels

To Negotiate a Carbon Tax: A Rough Map of Policy Interactions, Tradeoffs, and Risks

Sooner or later, the federal government will assign a price to carbon dioxide emissions via legislation. The contents of that legislation will reflect negotiated agreement—built on various political tradeoffs—over a host of policy issues, ranging from taxes to energy efficiency standards. These tradeoffs would implicate not only the scope and price assigned by the carbon pricing policy, but also the policies with which it would interact. This paper anticipates that price will take the form of a carbon tax and describes interactions between that tax and various existing and proposed policies relating to climate change, energy, and environmental protection. Specifically, it proposes a typology for those interactions and applies it to characterize particular policies. It also notes how trading off particular policies for a more robust carbon tax could undermine the climate change mitigation goal of such a tax

Scaling of curvature in sub-critical gravitational collapse

We perform numerical simulations of the gravitational collapse of a spherically symmetric scalar field. For those data that just barely do not form black holes we find the maximum curvature at the position of the central observer. We find a scaling relation between this maximum curvature and distance from the critical solution. The scaling relation is analogous to that found by Choptuik for black hole mass for those data that do collapse to form black holes. We also find a periodic wiggle in the scaling exponent.Comment: Revtex, 2 figures, Discussion modified, to appear in Phys. Rev.

How Much Does the Existing Regulatory Patchwork Reduce U.S. Greenhouse Gas Emissions?

This paper offers an answer to the question, “What levels of greenhouse gas (“GHG”) emissions reduction do the constituent programs in the U.S.’s existing regulatory patchwork achieve?” Its answer represents an attempt to measure the same effect from eight regulatory interventions: EPA’s Prevention of Significant Deterioration program, as it is expected to operate following the Supreme Court’s UARG v. EPA decision in 2014; EPA’s Clean Power Plan; EPA’s renewable fuel standard; the federal Corporate Average Fuel Economy standards for light, medium, and heavy duty vehicles; the renewable electricity generation Production Tax Credit and Investment Tax Credit; the Regional Greenhouse Gas Initiative, which encompasses 9 states in the mid-Atlantic and Northeast; California’s Global Warming Solutions Act of 2006, Assembly Bill 32; and state renewable portfolio standards. Notably, though it seeks to measure the same effect of diverse policies, this paper does not purport to measure the aggregated net effects of those policies on GHG emissions. Most important among its conclusions are the following. First, federal CAFE standards, the Clean Power Plan, and state renewable portfolio standards will be crucial for achieving emissions reduction goals. Second, the reductions available from the renewable fuel standard are uncertain and highly contentious. And third—an important subtext—the effectiveness (and costeffectiveness) of this patchwork of programs is unwieldy even to measure, much less to ensure