  The metric of a nonrotating black hole deformed by a tidal interaction is
calculated and expressed as an expansion in the strength of the tidal coupling.
The expansion parameter is the inverse length scale R^{-1}, where R is the
radius of curvature of the external spacetime in which the black hole moves.
The expansion begins at order R^{-2}, and it is carried out through order
R^{-4}. The metric is parameterized by a number of tidal multipole moments,
which specify the black hole's tidal environment. The tidal moments are
freely-specifiable functions of time that are related to the Weyl tensor of the
external spacetime. The metric is presented in a light-cone coordinate system
that possesses a clear geometrical meaning: The advanced-time coordinate $v$ is
constant on past light cones that converge toward the black hole; the angles
theta and phi are constant on the null generators of each light cone; and the
radial coordinate r is an affine parameter on each generator, which decreases
as the light cones converge toward the black hole. The coordinates are
well-behaved on the black-hole horizon, and they are adjusted so that the
coordinate description of the horizon is the same as in the Schwarzschild
geometry: r = 2M. At the order of accuracy maintained in this work, the horizon
is a stationary null hypersurface foliated by apparent horizons; it is an
isolated horizon in the sense of Ashtekar and Krishnan. As an application of
our results we examine the induced geometry and dynamics of the horizon, and
calculate the rate at which the black-hole surface area increases as a result
of the tidal interaction.
