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Membrane viewpoint on black holes: Gravitational perturbations of the horizon.

This paper is part of a series of papers which develop and illustrate the ''membrane'' formalism for black holes. In this formalism, described in earlier papers, the role of the absolute event horizon is played by a two-dimensional surface endowed with electrical, mechanical, and thermodynamic properties. The present paper deals with gravitational perturbations of holes and presents and discusses model problems that illustrate the effects of tidal gravitational fields on stationary holes. The first of these problems demonstrates the use of the Rindler approximation to Schwarzschild spacetime in the case of a static perturbing point mass and clarifies the contribution to the horizon distortion due to forces constraining the motion of the mass point. Subsequent model problems use the Rindler approximation to compute the evolution of distortions of the Schwarzschild or Kerr horizon due to mass points in motion near the horizon.