We aim at characterising dense cores in the clustered environments associated with massive star-forming regions. For this, we present an uniform analysis of VLA NH3(1,1) and (2,2) observations towards a sample of 15 massive star-forming regions, where we identify a total of 73 cores, classify them as protostellar, quiescent starless, or perturbed starless, and derive some physical properties. The average sizes and ammonia column densities are 0.06 pc and 10^15 cm^-2, respectively, with no significant differences between the starless and protostellar cores, while the linewidth and rotational temperature of quiescent starless cores are smaller, 1.0 km/s and 16 K, than those of protostellar (1.8 km/s, 21 K), and perturbed starless (1.4 km/s, 19 K) cores. Such linewidths and temperatures for these quiescent starless cores in the surroundings of massive stars are still significantly larger than the typical values measured in starless cores of low-mass star-forming regions, implying an important non-thermal component. We confirm at high angular resolutions the correlations previously found with single-dish telescopes between the linewidth, the temperature of the cores, and the bolometric luminosity. In addition, we find a correlation between the temperature of each core and the incident flux from the most massive star in the cluster, suggesting that the large temperatures measured in the starless cores of our sample could be due to heating from the nearby massive star. A simple virial equilibrium analysis seems to suggest a scenario of a self-similar, self-graviting, turbulent, virialised hierarchy of structures from clumps (0.1-10 pc) to cores (0.05 pc). A closer inspection of the dynamical state taking into account external pressure effects, reveal that relatively strong magnetic field support may be needed to stabilise the cores, or that they are unstable and thus on the verge of collapse.
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