Thermodynamics of frozen stars

The frozen star is a recent proposal for a non-singular solution of Einstein's equations that describes an ultracompact object which closely resembles a black hole from an external perspective. The frozen star is also meant to be an alternative, classical description of an earlier proposal, the highly quantum polymer model. Here, we show that the thermodynamic properties of frozen stars closely resemble those of black holes: Frozen stars radiate thermally, with a temperature and an entropy that are perturbatively close to those of black holes of the same mass. Their entropy is calculated using the Euclidean-action method of Gibbons and Hawking. We then discuss their dynamical formation by estimating the probability for a collapsing shell of "normal" matter to transition, quantum mechanically, into a frozen star. This calculation followed from a reinterpretation of a transitional region between the Euclidean frozen star and its Schwarzschild exterior as a Euclidean instanton that mediates a phase transition from the Minkowski interior of an incipient Schwarzschild black hole to a microstate of the frozen star interior. It is shown that, up to negligible corrections, the probability of this transition is $e^{-A/4}$, with $A$ being the star's surface area. Taking into account that the dimension of the phase space is $e^{+A/4}$, we conclude that the total probability for the formation of the frozen star is of order unity. The duration of this transition is estimated, which we then use to argue, relying on an analogy to previous results, about the scaling of the magnitude of the off-diagonal corrections to the number operator for the Hawking-like particles. Such scaling was shown to imply that the corresponding Page curve indeed starts to go down at about the Page time, as required by unitarity

Collagen-Binding Peptidoglycans Inhibit MMP Mediated Collagen Degradation and Reduce Dermal Scarring

Scarring of the skin is a large unmet clinical problem that is of high patient concern and impact. Wound healing is complex and involves numerous pathways that are highly orchestrated, leaving the skin sealed, but with abnormal organization and composition of tissue components, namely collagen and proteoglycans, that are then remodeled over time. To improve healing and reduce or eliminate scarring, more rapid restoration of healthy tissue composition and organization offers a unique approach for development of new therapeutics. A synthetic collagen-binding peptidoglycan has been developed that inhibits matrix metalloproteinase-1 and 13 (MMP-1 and MMP-13) mediated collagen degradation. We investigated the synthetic peptidoglycan in a rat incisional model in which a single dose was delivered in a hyaluronic acid (HA) vehicle at the time of surgery prior to wound closure. The peptidoglycan treatment resulted in a significant reduction in scar tissue at 21 days as measured by histology and visual analysis. Improved collagen architecture of the treated wounds was demonstrated by increased tensile strength and transmission electron microscopy (TEM) analysis of collagen fibril diameters compared to untreated and HA controls. The peptidoglycan's mechanism of action includes masking existing collagen and inhibiting MMP-mediated collagen degradation while modulating collagen organization. The peptidoglycan can be synthesized at low cost with unique design control, and together with demonstrated preclinical efficacy in reducing scarring, warrants further investigation for dermal wound healing

Corruption and Openness

We report an intriguing empirical observation. The relationship between corruption and output depends on the economy's degree of openness: in open economies, corruption and GNP per capita are strongly negatively correlated, but closed economies display no relationship at all. This stylized fact is robust to a variety of different empirical specifications. In particular, the same basic pattern persists if we use alternative measures of openness, if we focus on different time periods, if we restrict the sample to include only highly corrupt countries, and if we restrict attention to specific geographic areas or to poor countries. We find that the degree of financial openness is primarily what determines whether corruption and output are correlated. Moreover, corruption is negatively related to capital accumulation in open economies, but not in closed economies. We present a model, consistent with these findings, in which the main channel through which corruption affects output is capital drain.