We report molecular line observations, made with ASTE and SEST, and dust continuum observations at 0.87 mm, made with APEX, towards the cold dust core G305.136+0.068. The molecular observations show that the core is isolated and roughly circularly symmetric and imply that it has a mass of $1.1times10^3~M_odot$. A simultaneous model fitting of the spectra observed in four transitions of CS, using a non-LTE radiative transfer code, indicates that the core is centrally condensed, with the density decreasing with radius as $r^{-1.8}$, and that the turbulent velocity increases towards the center. The dust observations also indicate that the core is highly centrally condensed and that the average column density is 1.1 g cm$^{-2}$, value slightly above the theoretical threshold required for the formation of high mass stars. A fit to the spectral energy distribution of the emission from the core indicates a dust temperature of $17pm2$ K, confirming that the core is cold. Spitzer images show that the core is seen in silhouette from 3.6 to 24.0 $mu$m and that is surrounded by an envelope of emission, presumably tracing an externally excited photo-dissociated region. We found two embedded sources within a region of 20 centered at the peak of the core, one of which is young, has a luminosity of $66~L_odot$ and is accreting mass with a high accretion rate, of $sim1times10^{-4}~M_odot$ yr$^{-1}$. We suggest that this object corresponds to the seed of a high mass protostar still in the process of formation. The present observations support the hypothesis that G305.136+0.068 is a massive and dense cold core in an early stage of evolution, in which the formation of a high mass star has just started.
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