  Abbreviated Abstract: The near-infrared study of the Carina Nebula in this
paper builds on the results of the Chandra Carina Complex Project (CCCP), that
detected 14368 X-ray sources in the 1.4 square-degree survey region, an
automatic source classification study that classified 10714 of these as very
likely young stars in Carina, and an analysis of their clustering properties.
We used HAWK-I at the ESO VLT to conduct a very deep near-IR survey with
sub-arcsecond angular resolution, covering about 1280 square-arcminutes. The
HAWK-I images reveal more than 600000 individual infrared sources, whereby
objects as faint as J ~ 23, H ~ 22, and Ks ~ 21 are detected at S/N >= 3. While
less than half of the Chandra X-ray sources have counterparts in the 2MASS
catalog, the ~5 mag deeper HAWK-I data reveal infrared counterparts to 6636 (=
88.8%) of the 7472 Chandra X-ray sources in the HAWK-I field. We analyze
near-infrared color-color and color-magnitude diagrams to derive information
about the extinctions, infrared excesses, ages, and masses of the X-ray
selected objects. The near-infrared properties agree well with the results of
the automatic X-ray source classification. The shape of the K-band luminosity
function of the X-ray selected Carina members agrees well with that derived for
the Orion Nebula Cluster, suggesting that, down to the X-ray detection limit
around 0.5-1 Msun, the shape of the IMF in Carina is consistent with that in
Orion (and thus the field IMF). The fraction of stars with near-infrared
excesses is rather small, <=10%, but shows considerable variations between
individual parts of the complex. The distribution of extinctions for the
diskless stars ranges from ~1.6 mag to ~6.2 mag (central 80th percentile),
clearly showing a considerable range of differential extinction between
individual stars in the complex.
