Horizon shells and BMS-like soldering transformations

We revisit the theory of null shells in general relativity, with a particular emphasis on null shells placed at horizons of black holes. We study in detail the considerable freedom that is available in the case that one solders two metrics together across null hypersurfaces (such as Killing horizons) for which the induced metric is invariant under translations along the null generators. In this case the group of soldering transformations turns out to be infinite dimensional, and these solderings create non-trivial horizon shells containing both massless matter and impulsive gravitational wave components. We also rephrase this result in the language of Carrollian symmetry groups. To illustrate this phenomenon we discuss in detail the example of shells on the horizon of the Schwarzschild black hole (with equal interior and exterior mass), uncovering a rich classical structure at the horizon and deriving an explicit expression for the general horizon shell energy-momentum tensor. In the special case of BMS-like soldering supertranslations we find a conserved shell-energy that is strikingly similar to the standard expression for asymptotic BMS supertranslation charges, suggesting a direct relation between the physical properties of these horizon shells and the recently proposed BMS supertranslation hair of a black hole.

The effect of 3 versus 6 years of zoledronic acid treatment of osteoporosis: a randomized extension to the HORIZON-Pivotal Fracture Trial (PFT)

Zoledronic acid 5 mg (ZOL) annually for 3 years reduces fracture risk in postmenopausal women with osteoporosis. To investigate long-term effects of ZOL on bone mineral density (BMD) and fracture risk, the Health Outcomes and Reduced Incidence with Zoledronic acid Once Yearly-Pivotal Fracture Trial (HORIZON-PFT) was extended to 6 years. In this international, multicenter, double-blind, placebo-controlled extension trial, 1233 postmenopausal women who received ZOL for 3 years in the core study were randomized to 3 additional years of ZOL (Z6, n = 616) or placebo (Z3P3, n = 617). The primary endpoint was femoral neck (FN) BMD percentage change from year 3 to 6 in the intent-to-treat (ITT) population. Secondary endpoints included other BMD sites, fractures, biochemical bone turnover markers, and safety. In years 3 to 6, FN-BMD remained constant in Z6 and dropped slightly in Z3P3 (between-treatment difference = 1.04%; 95% confidence interval 0.4 to 1.7; p = 0.0009) but remained above pretreatment levels. Other BMD sites showed similar differences. Biochemical markers remained constant in Z6 but rose slightly in Z3P3, remaining well below pretreatment levels in both. New morphometric vertebral fractures were lower in the Z6 (n = 14) versus Z3P3 (n = 30) group (odds ratio = 0.51; p = 0.035), whereas other fractures were not different. Significantly more Z6 patients had a transient increase in serum creatinine >0.5 mg/dL (0.65% versus 2.94% in Z3P3). Nonsignificant increases in Z6 of atrial fibrillation serious adverse events (2.0% versus 1.1% in Z3P3; p = 0.26) and stroke (3.1% versus 1.5% in Z3P3; p = 0.06) were seen. Postdose symptoms were similar in both groups. Reports of hypertension were significantly lower in Z6 versus Z3P3 (7.8% versus 15.1%, p < 0.001). Small differences in bone density and markers in those who continued versus those who stopped treatment suggest residual effects, and therefore, after 3 years of annual ZOL, many patients may discontinue therapy up to 3 years. However, vertebral fracture reductions suggest that those at high fracture risk, particularly vertebral fracture, may benefit by continued treatment.

Carbon sequestration in Himalaya's alpine meadows: Mitigating cropping encroachment on pastures in Northern Pakistan

Rangelands store about 30% of the world’s carbon and support over 120 million pastoralists globally. Adjusting the management of remote alpine pastures bears a substantial climate change mitigation potential that can provide livelihood support for marginalized pastoralists through carbon payment. Landless pastoralists in Northern Pakistan seek higher income by cropping potatoes and peas over alpine pastures. However, tilling steep slopes without terracing exposes soil to erosion. Moreover, yields decline rapidly requiring increasing fertilizer inputs. Under these conditions, carbon payment could be a feasible option to compensate pastoralists for renouncing hazardous cropping while favoring pastoral activities. The study quantifies and compares C on cropped and grazed land. The hypothesis was that cropping on alpine pastures reduces former carbon storage. The study area located in the Naran valley of the Pakistani Himalayas receives an annual average of 819 mm of rain and 764 mm of snow. Average temperatures remain below 0°C from November to March while frost may occur all year round. A total of 72 soil core samples were collected discriminating land use (cropping, pasture), aspect (North, South), elevation (low 3000, middle 3100, and high 3200 m a.s.l.), and soil depth (shallow 0-10, deep 10-30 cm). Thirty six biomass samples were collected over the same independent variables (except for soil depth) using a 10x10x20 cm steal box inserted in the ground for each sample. Aboveground biomass and coarse roots were separated from the soil aggregate and oven-dried. Soil organic carbon (SOC) and biomass carbon (BC) were estimated through a potassium dichromate oxidation treatment. The samples were collected during the second week of October 2010 at the end of the grazing and cropping season and before the first snowfall. The data was statistically analyzed by means of a one-way analysis of variance. Results show that all variables taken separately have a significant effect on mean SOC [%]: crop/pasture 1.33/1.6, North/South 1.61/1.32, low/middle/high 1.09/1.62/1.68, shallow/deep 1.4/1.53. However, for BC, only land use has a significant effect with more than twice the amount of carbon in pastures [g m-2]: crop/pasture 127/318. These preliminary findings suggest that preventing the conversion of pastures into cropping fields in the Naran valley avoids an average loss of 12.2 t C ha-1 or 44.8 t CO2eq ha-1 representing a foreseeable compensation of 672 € ha-1 for the Naran landless pastoralists who would renounce cropping. The ongoing study shall provide a complete picture for carbon payment integrating key aspects such as the rate of cropping encroachment over pastures per year, the methane leakage from the system due to livestock enteric fermentation, the expected cropping income vs. livestock income and the transaction costs of implementing the mitigation project, certifying it, and verifying carbon credits. A net present value over an infinite time horizon for the mitigation scenario shall be estimated on an iterative simulation to consider weather and price uncertainties. The study will also provide an estimate of the minimum price of carbon at which pastoralists would consider engaging in the mitigation activity.