3 2009 Fermi Symposium, Washington, D.C., Nov. 2-5 sphere in a form that allows one to search for ana- lytic solutions. We derive an exact solution which does not give energy extraction, and an approximation solution which generalizes the Blandford-Znajek split monopole solution to arbitrary values of the black-hole spin parameter. This solution is considered in light of evidence for jetted outflows from black-hole sources. The blast-wave physics developed over the past two decades to explain the extraordinarily luminous radi- ation from GRBs is also presented, including spectral and temporal SEDs from external ahocks and colliding shells, photospheric emission, and neutron decoupling in the expanding fireball. If jetted black holes make the most energetic radi- ations in nature, with particle acceleration occurring via Fermi processes, a remaining question of funda- mental importance is the energy source for these ra- diations. Accretion onto supermassive black holes ob- viously powers the luminous quasi-thermal emissions in active galaxies, but less obvious are the reasons for the differences between radio-quiet and radio-loud AGNs, or for the different classes of GRBs, including X-ray flashes, low-luminosity GRBs, and long dura- tion GRBs. The science covered in our book and, in particu- lar, the hypotheses outlined in the first section, will be addressed by the ongoing observational activity in high-energy astronomy. The hypothesis that the highest energy and most luminous radiations in na- ture, including the bright γ -ray flares from blazars and GRBs, and the UHECRs from unknown extragalac- tic sources, are energized by the rotational energy of spinning black holes, can be tested with observatories now in operation. This assertion will be established or refuted as new data is collected and analyzed. We consider whether these differences may be due to the spin of the black hole, with the energy extracted through the Blandford-Znajek process. A treatment of general relativity and black-hole electrodynamics is given based on a “3+1” formalism that provides a more compact approach than found in the original treatment. On this basis, we have recast the con- straint equation for a force-free black-hole magneto- This work has been supported by the Office of Naval Research and NASA. Acknowledgments III. SUMMARY D. Energy Extraction through Blandford-Znajek Processes [1] Dermer, C. D., & Menon, G. 2009, “High Energy Ra- diation from Black Holes: Gamma Rays, Cosmic Rays, and Neutrinos,” (Princeton University Press: Prince- ton, NJ) eConf C091122