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The transition which connects the chirp to the ÿnal black hole state remains highly uncertain— here the gravitational radiation emission process is most nonlinear and potentially most interesting. , 1991; Hello, 1997). In neutron star–black hole coalescence, on the other hand, a black hole–torus state is expected if the black hole spins rapidly (PaczyÃnski, 1991). The gravitational wave emissions in this state will be di erent—quiescent or steady within the frequency range of its Keplerian motion.
1998). Long-term calculations of the spiral-in chirps remain a formidable enterprise, in no small measure due to the lack of dimensional reductions in these inherently three-dimensional problems, the two-fold nature of numerical implementation—Einstein equations and horizon boundary conditions of evolving black holes—and the presence of constraints, notably so conservation of energy and angular momentum. The latter impose strong conditions on formal and numerical well-posedness of the initial value problem.
Since n± derive from electrical dissipation in the gap, the associated local charge density satisÿes j =j [V ]z−h=2 − [V ]h=2 z [V ]h=2 −h=2 ; (51) where E = −V (z) is the electric ÿeld in terms of the electrostatic potential V . V shall denote h=2 [V ]h=2 −h=2 = [ ]A 6 [ÿ]h=2 A , as in (43). Thus, E satisÿes Poisson’s equation E = 4 ( + j ); where (z) = − e (z): In view of (50) and (51), we have j ∼ 2jz=h (−h=2¡z¡h=2) : (52) No new net charges are created and, in the linear regime (50), the net charge within the inversion layer remains zero.