  The aperiodic variability ubiquitously observed from accreting black hole
X-ray binary systems is generally analysed within the framework of the
so-called ``theory of propagating fluctuations''. In this paper we derive the
Fourier transforms of the Green's function solutions of the thin disc
equations. These solutions suffice to describe all possible solutions through
standard convolution techniques. Solutions are found for both Newtonian discs
and general relativistic solutions with a vanishing ISCO stress. We use this
new relativistic theory to highlight the Kerr black hole spin dependence of a
number of observable variability properties of black hole discs. The phase
lags, coherence, and power density spectra of Kerr discs are shown to be strong
functions of black hole spin. Observations of the aperiodic variability of
black hole accretion sources may now, at least in principle, offer a new avenue
to directly constrain black hole spins.
