  The attractor mechanism governs the near-horizon geometry of extremal black
holes in ungauged 4D N=2 supergravity theories and in Calabi-Yau
compactifications of string theory. In this paper, we study a natural
generalization of this mechanism to solutions of arbitrary 4D N=2 gauged
supergravities. We define generalized attractor points as solutions of an
ansatz which reduces the Einstein, gauge field, and scalar equations of motion
to algebraic equations. The simplest generalized attractor geometries are
characterized by non-vanishing constant anholonomy coefficients in an
orthonormal frame. Basic examples include Lifshitz and Schrodinger solutions,
as well as AdS and dS vacua. There is a generalized attractor potential whose
critical points are the attractor points, and its extremization explains the
algebraic nature of the equations governing both supersymmetric and
non-supersymmetric attractors.
