The static and stationary C metric are examined in a generic framework and
their interpretations studied in some detail, especially those with two eve
nt horizons, one for the black hole and another for the acceleration. We fi
nd that (i) the spacetime of an accelerated static black hole is plagued by
either conical singularities or a lack of smoothness and compactness of th
e black hole horizon, (ii) by using standard black hole thermodynamics we s
how that accelerated black holes have a higher Hawking temperature than Unr
uh temperature of the accelerated frame, and (iii) the usual upper bound on
the product of the mass and acceleration parameters (<1/<root>27) is just
a coordinate artifact. The main results are extended to accelerated rotatin
g black holes with no significant changes.