  We discuss phantom metrics admitting Killing spinors in fake N=2, D=4
supergravity coupled to vector multiplets. The Abelian U(1) gauge fields in the
fake theory have kinetic terms with the wrong sign. We solve the Killing spinor
equations for the standard and fake theories in a unified fashion by
introducing a parameter which distinguishes between the two theories. The
solutions found are fully determined in terms of algebraic conditions, the
so-called stabilisation equations, in which the symplectic sections are related
to a set of functions. These functions are harmonic in the case of the standard
supergravity theory and satisfy the wave-equation in flat (2+1)-space-time in
the fake theory. Explicit examples are given for the minimal models with
quadratic prepotentials.
