In the first part of the paperwe construct the metric of a tidally deformed, nonrotating black hole. The metric is presented as an expansion in powers of r/b 1, in which r is the distance to the black hole and b the characteristic length scale of the tidal field—the typical distance to the remote bodies responsible for the tidal environment. The metric is expanded through order (r/b)~4 and written in terms of a number of tidal multipole moments, the gravitoelectric moments ε_(ab), ε_(abc), ε_(abcd), and the gravitomagnetic moments B_(ab), B_(abc), B_(abcd). It differs fromthe similar construction of Poisson and Vlasov in that the tidal perturbation is presented in Regge- Wheeler gauge instead of the light-cone gauge employed previously. In the second part of the paper we determine the tidal moments by matching the black-hole metric to a post-Newtonian metric that describes a system of bodies with weak mutual gravity. This extends the previous work of Taylor and Poisson (Paper I in this sequence), which computed only the leading-order tidal moments, ε_(ab) and B_(ab). The matching is greatly facilitated by the Regge-Wheeler form of the black-hole metric, and this motivates the work carried out in the first part of the paper. The tidal moments are calculated accurately through the first post-Newtonian approximation, and at this order they are independent of the precise nature of the compact body. The moments therefore apply equally well to a rotating black hole, or to a (rotating or nonrotating) neutron star. As an application of this formalism, we examine the intrinsic geometry of a tidally deformed event horizon and describe it in terms of a deformation function that represents a quadrupolar and octupolar tidal bulge.
展开▼
