Abstract: Spinning black holes store rotational energy that can be extracted. When a black hole is immersed in an externally supplied magnetic field, reconnection of magnetic field lines within the ergosphere can generate negative energy (relative to infinity) particles that fall into the black hole event horizon while the other accelerated particles escape stealing energy from the black hole. We show analytically that energy extraction via magnetic reconnection is possible when the black hole spin is high (dimensionless spin a similar to 1) and the plasma is strongly magnetized (plasma magnetization sigma(0) > 1/3). The parameter space region where energy extraction is allowed depends on the plasma magnetization and the orientation of the reconnecting magnetic field lines. For sigma(0) >> 1, the asymptotic negative energy at infinity per enthalpy of the decelerated plasma that is swallowed by a maximally rotating black hole is found to be epsilon(infinity)(-) similar or equal to – root sigma(0)/3. The accelerated plasma that escapes to infinity and takes away black hole energy asymptotes the energy at infinity per enthalpy epsilon(infinity)(+) similar or equal to root 3 sigma(0).. We show that the maximum power extracted from the black hole by the escaping plasma is P-extr(max) similar to 0.1M(2) root sigma(0)w(0) (here, M is the black hole mass and w(0) is the plasma enthalpy density) for the collisionless plasma regime and one order of magnitude lower for the collisional regime. Energy extraction causes a significant spindown of the black hole when a similar to 1. The maximum efficiency of the plasma energization process via magnetic reconnection in the ergosphere is found to be eta(max) similar or equal to 3/2. Since fast magnetic reconnection in the ergosphere should occur intermittently in the scenario proposed here, the associated emission within a few gravitational radii from the black hole is expected to display a bursty nature.

Abstract: Variance-based sensitivity indices play an important role in scientific computation and data mining, thus the significance of developing numerical methods for efficient and reliable estimation of these sensitivity indices based on (expensive) computer simulators and/or data cannot be emphasized too much. In this article, the estimation of these sensitivity indices is treated as a statistical inference problem. Two principle lemmas are first proposed as rules of thumb for making the inference. After that, the posterior features for all the (partial) variance terms involved in the main and total effect indices are analytically derived (not in closed form) based on Bayesian Probabilistic Integration (BPI). This forms a data-driven method for estimating the sensitivity indices as well as the involved discretization errors. Further, to improve the efficiency of the developed method for expensive simulators, an acquisition function, named Posterior Variance Contribution (PVC), is utilized for realizing optimal designs of experiments, based on which an adaptive BPI method is established. The application of this framework is illustrated for the calculation of the main and total effect indices, but the proposed two principle lemmas also apply to the calculation of interaction effect indices. The performance of the development is demonstrated by an illustrative numerical example and three engineering benchmarks with finite element models.