  The static and stationary C-metric are revisited in a generic framework and
their interpretations studied in some detail. Specially those with two event
horizons, one for the black hole and another for the acceleration. We found
that: i) The spacetime of an accelerated static black hole is plagued by either
conical singularities or lack of smoothness and compactness of the black hole
horizon; ii) By using standard black hole thermodynamics we show that
accelerated black holes have higher Hawking temperature than Unruh temperature
of the accelerated frame; iii) The usual upper bound on the product of the mass
and acceleration parameters <1/sqrt(27) is just a coordinate artifact. The main
results are extended to accelerated rotating black holes with no significant
changes.
