  Accreting black hole sources show a wide variety of rapid time variability,
including the manifestation of time lags during X-ray transients, in which a
delay (phase shift) is observed between the Fourier components of the hard and
soft spectra. Despite a large body of observational evidence for time lags, no
fundamental physical explanation for the origin of this phenomenon has been
presented. We develop a new theoretical model for the production of X-ray time
lags based on an exact analytical solution for the Fourier transform describing
the diffusion and Comptonization of seed photons propagating through a
spherical corona. The resulting Green's function can be convolved with any
source distribution to compute the associated Fourier transform and time lags,
hence allowing us to explore a wide variety of injection scenarios. We show
that thermal Comptonization is able to self-consistently explain both the X-ray
time lags and the steady-state (quiescent) X-ray spectrum observed in the
low-hard state of Cyg X-1. The reprocessing of bremsstrahlung seed photons
produces X-ray time lags that diminish with increasing Fourier frequency, in
agreement with the observations for a wide range of sources.
