A Strategic Evaluation of Public Interest Litigation in South Africa

Based on three case studies, discusses trends and challenges in public interest litigations in South Africa, the most effective combination of strategies in advancing social change, and the role of litigation in social mobilization

Proof of the Riemannian Penrose Inequality with Charge for Multiple Black Holes

We present a proof of the Riemannian Penrose inequality with charge in the context of asymptotically flat initial data sets for the Einstein-Maxwell equations, having possibly multiple black holes with no charged matter outside the horizon, and satisfying the relevant dominant energy condition. The proof is based on a generalization of Hubert Bray's conformal flow of metrics adapted to this setting.Comment: 37 pages; final version; to appear in J. Differential Geo

On the Riemannian Penrose inequality with charge and the cosmic censorship conjecture

We note an area-charge inequality orignially due to Gibbons: if the outermost horizon $S$ in an asymptotically flat electrovacuum initial data set is connected then $|q|\leq r$, where $q$ is the total charge and $r=\sqrt{A/4\pi}$ is the area radius of $S$. A consequence of this inequality is that for connected black holes the following lower bound on the area holds: $r\geq m-\sqrt{m^2-q^2}$. In conjunction with the upper bound $r\leq m + \sqrt{m^2-q^2}$ which is expected to hold always, this implies the natural generalization of the Riemannian Penrose inequality: $m\geq 1/2(r+q^2/r)$.Comment: 4 pages; 1st revision, added a generalization, added a reference; 2nd revision, minor correction

Lower Bounds for the Area of Black Holes in Terms of Mass, Charge, and Angular Momentum

The most general formulation of Penrose's inequality yields a lower bound for ADM mass in terms of the area, charge, and angular momentum of black holes. This inequality is in turn equivalent to an upper and lower bound for the area in terms of the remaining quantities. In this note, we establish the lower bound for a single black hole in the setting of axisymmetric maximal initial data sets for the Einstein-Maxwell equations, when the non-electromagnetic matter fields are not charged and satisfy the dominant energy condition. It is shown that the inequality is saturated if and only if the initial data arise from the extreme Kerr-Newman spacetime. Further refinements are given when either charge or angular momentum vanish. Lastly, we discuss the validity of the lower bound in the presence of multiple black holes.Comment: 12 pages; section 2 revised; to appear in Phys. Rev.

Investigation into the use of a tapered element oscillating microbalance for real-time particulate measurement

Characterizing particulate matter (PM) in diesel exhaust emissions during transient test cycles has been a challenge for researchers. Acquisition of real-time PM data was proposed by the use of a Rupprecht and Patashnick Co., Inc. Series 1105 Diesel Particulate Monitor Tapered Element Oscillating Microbalance (TEOM) mass measuring device. The objectives of testing with a TEOM diesel particulate analyzer were to validate its collection capability and evaluate its real-time characteristics on transient test cycles. Conventional PM filtration was used as the base line for evaluating the TEOM collection capability. To evaluate real-time TEOM characteristics, the real-time mass rate data were separated into positive and negative values, then integrated over the duration of the test. The integrated positive mass was divided by the integrated negative mass to create a positive-to-negative mass ratio. This ratio was indicative of real PM collected versus moisture released from the filter. TEOM sample tube temperatures at 35°C yielded the best TEOM to conventional PM filtration ratio. However, a compromise between conventional filter data and real-time data was made in selecting the temperature set point of 40°C as the most desirable sampling temperature. Sample flow rate was varied from one to four liters per minute (lpm). The 1 lpm set point provided the best TEOM to conventional filtration ratio. The flow rate of 3 lpm was chosen to be a compromise between TEOM to conventional filtration ratio and real-time results. The best TEOM to conventional filtration ratio measured was 0.97. The filter collection efficiency of a new filter was found to be a significant source of variability. When the initial test with a new filter was disregarded, the 99% confidence interval in TEOM results was +/-4.3%. In comparison, the 99% confidence interval in conventional PM results was +/-1.7%