We present high spatial resolution near-infrared spectra and images of the
nucleus of Centaurus A (NGC 5128) obtained with NAOS-CONICA at the VLT. The
adaptive optics corrected data have a spatial resolution of 0.06" (FWHM) in K-
and 0.11" in H-band, four times higher than previous studies. The observed gas
motions suggest a kinematically hot disk which is orbiting a central object and
is oriented nearly perpendicular to the nuclear jet. We model the central
rotation and velocity dispersion curves of the [FeII] gas orbiting in the
combined potential of the stellar mass and the (dominant) black hole. Our
physically most plausible model, a dynamically hot and geometrically thin gas
disk, yields a black hole mass of M_bh = (6.1 +0.6/-0.8) 10^7 M_sun. As the
physical state of the gas is not well understood, we also consider two limiting
cases: first a cold disk model, which completely neglects the velocity
dispersion; it yields an M_bh estimate that is almost two times lower. The
other extreme case is to model a spherical gas distribution in hydrostatic
equilibrium through Jeans equation. Compared to the hot disk model the best-fit
black hole mass increases by a factor of 1.5. This wide mass range spanned by
the limiting cases shows how important the gas physics is even for high
resolution data. Our overall best-fitting black hole mass is a factor of 2-4
lower than previous measurements. With our revised M_bh estimate, Cen A's
offset from the M_bh-sigma relation is significantly reduced; it falls above
this relation by a factor of ~2, which is close to the intrinsic scatter of
this relation. (Abridged)Comment: 12 pages, 14 figures, including minor changes following the referee
report; accepted for publication in The Astrophysical Journa