Aims. We compile and analyze an extended database of light curve parameters scattered in the literature to search for correlations and study physical properties, including internal structure constraints. Methods. We analyze a vast light curve database by obtaining mean rotational properties of the entire sample, determining the spin frequency distribution and comparing those data with a simple model based on hydrostatic equilibrium. Results. For the rotation periods, the mean value obtained is 6.95 h for the whole sample, 6.88 h for the Trans-neptunian objects (TNOs) alone and 6.75 h for the Centaurs. From Maxwellian fits to the rotational frequencies distribution the mean rotation rates are 7.35 h for the entire sample, 7.71 h for the TNOs alone and 8.95 h for the Centaurs. These results are obtained by taking into account the criteria of considering a single-peak light curve for objects with amplitudes lower than 0.15 mag and a double-peak light curve for objects with variability >0.15 mag. We investigate the effect of using different values other than 0.15 mag for the transition threshold from albedo-caused light curves to shape-caused light curves. The best Maxwellian fits were obtained with the threshold between 0.10 and 0.15 mag. The mean light-curve amplitude for the entire sample is 0.26 mag, 0.25 mag for TNOs only, and 0.26 mag for the Centaurs. The Period versus $B-V$ color shows a correlation that suggests that objects with shorter rotation periods may have suffered more collisions than objects with larger ones. The amplitude versus Hv correlation clearly indicates that the smaller (and collisionally evolved) objects are more elongated than the bigger ones. Conclusions. From the model results, it appears that hydrostatic equilibrium can explain the statistical results of almost the entire sample, which means hydrostatic equilibrium is probably reached by almost all TNOs in the H range -1,7 . This implies that for plausible albedos of 0.04 to 0.20, objects with diameters from 300 km to even 100 km would likely be in equilibrium. Thus, the great majority of objects would qualify as being dwarf planets because they would meet the hydrostatic equilibrium condition. The best model density corresponds to 1100 kg/m3.