http://creativecommons.org/licenses/by-nc/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 2/28 created outside the horizon flows towards the horizon, resulting in the positive outward energy flux. This is an analogy with the mechanical Penrose process, in which the rotational energy of a BH is extracted by making it absorb negative-energy particles [28][29][30]. However, MHD simulations demonstrate that no regions of negative particle energy are seen in the steady state [12], although a transient inflow of negative particle energy is possible as a feedback from generation of an outward MHD wave [11]. The role of negative electromagnetic energy density in the steady state has been discussed recently [K09; 31, 32], although the concept of 'advection of the steady field' is ambiguous. Below we show that the sign of the electromagnetic energy density depends on the coordinates, and thus the negative field energy is not physically essential (see Section 4.4 below).We argue that the causal production mechanism of the electromagnetic AM and Poynting fluxes cannot be fully understood by investigating only the steady-state structure. We examine a time-dependent process evolving towards the steady state with an analytical toy model to clarify how the steady outward fluxes are created. In order to find the essential physics, our analysis is performed both in the Boyer-Lindquist (BL) and the Kerr-Schild (KS) coordinate systems. Most of the previous analytical studies used the BL coordinates [e.g. 10, 17, 33-36] [but see 37], most of the recent numerical simulations used the KS coordinates [e.g. K04; 2, 3, 12, 13] [but see e.g. 16, 38], and both of them focused on the steady-state structure. 1 Our new analytical studies of time-dependent process in the BL and KS coordinates will be highly helpful for understanding physics in BZ process. This paper is organized as follows. In Section 2, we explain our formulation of general relativistic electrodynamics, set generic assumptions for Kerr BH magnetosphere, and review the recent analytical understandings given by K04 and TT14. Section 3 concentrates on the field lines threading the equatorial plane, for which we show the flux production mechanism and the role of the negative energy of particles. In Section 4, we explain differences between the equatorial plane and the horizon, and then we focus on the field lines threading the horizon, discussing differences of the electromagnetic structures as seen in the BL and KS coordinates and the role of the negative electromagnetic energy density. In Section 5, we discuss the time-dependent process towards the steady state. Section 6 is devoted to conclusion.
