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Distorted black holes in terms of multipole moments
Phys. Rev. D 34, 3633 – Published 15 December, 1986
DOI: https://doi.org/10.1103/PhysRevD.34.3633
Abstract
In terms of a multipole-moment formalism previously developed for non-asymptotically-flat systems in general relativity, the metric of a Schwarzschild black hole in an external quadrupolar gravitational field is studied. Among other results, we find that the black hole develops an induced quadrupole moment, which in turn generates a tidal field opposing the applied field. This effect, plus the fact that the horizon cannot expand when a quasistatic tidal force is applied, can be described in terms of effective 2-dimensional elastic moduli for the black-hole horizon. The bulk modulus is κ̃=∞, and the shear modulus is μ̃=-63/(20πM), where M is the hole’s mass.
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