By J. A. H. Futterman
ISBN-10: 0521112109
ISBN-13: 9780521112109
This booklet investigates the propagation of waves within the presence of black holes. Astrophysical black holes may possibly finally be probed via those strategies. The authors emphasise intuitive actual considering of their therapy of the ideas of research of scattering, yet trade this with chapters at the rigourous mathematical improvement of the topic. low and high power restricting situations are taken care of generally and semi-classical effects also are bought. The analogy among Newtonian gravitational scattering and Coulomb quantum mechanical scattering is absolutely exploited. The booklet introduces the options of scattering via contemplating the best, scalar wave case of scattering through a round black gap. It then develops the formalism of spin-weighted spheroidal harmonics and of airplane wave representations for neutrino, electromagnetic and gravitational scattering. examine employees and graduate and complex undergraduate scholars in scattering concept, wave propagation and relativity will locate this a complete therapy of the subject.
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Additional info for Scattering from Black Holes
Sample text
O is not possible. 4 Scalar waves, Kerr background, arbitrary incidence Our approach here will be to compute the angular decomposition in terms of spheroidal functions for an off-axis plane wave in flat space and then introduce r* for r as in the procedures described above. 20) which represents a wave of frequency a> and amplitude b travelling along a ray inclined by an angle y with respect to the z-axis. 3, c/> may be expanded in oblate spheroidal harmonics of spin-weight zero: E ; ™ > ) . 21) lm Where now we must include nonzero m, because of the explicit
I) m+ \STir,a&)d(co - a>) + eiMr(i)m+ \ST{n - T, a&)d(oi + <»)]. 35) yields (valid for s= +1) SA = -{S+l) ^An I X l e - ^ - K - i ) m + \ S T ( y ; -aco)sZT(e,cf>; -aco) icor im n - y; 2 + i<0(r+t) e icor -<'-<>(- i f + i ^ y ; aco)sZr(0, (/>; aco) (i) m + 1 I ST(7r - y; - aco) s Zr(0, (6; - aco)]. 40) is the relation we seek. 41) to obtain a result valid for the Kerr background. Then match the expansions for the incident plane wave above with the asymptotic limits of expansions of the ingoing (dn) and outgoing (up) portions of the vector potential in terms of the normal modes of the electromagnetic field.
Furthermore the separated Teukolsky equations make no reference to parity. The parity dependence of the reference plane wave will guarantee that gravitational wave scattering is parity dependent, despite this parity independence of the Teukolsky equation. This is consistent with the behavior in the Schwarzschild case for metric perturbations, where Zerilli (1970) and Moncrief (1975) have shown that the equations obeyed by the metric perturbations do depend on parity. We have just seen that the plane-wave metric perturbations themselves depend only trivially on the parity.
Scattering from Black Holes by J. A. H. Futterman
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