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We study the impact of the capture and annihilation of weakly interacting massive particles (WIMPs) on the evolution of Population III stars. With a suitable modification of the Geneva stellar evolution code, we study the evolution of 20 and 200M_ stars in dark matter halos with densities between 10^8 and 10^11 GeV/cm^3 during the core H-burning phase, and, for selected cases, until the end of the core He-burning phase. We find that for WIMP densities higher than 5. 3 10^10 (^SD/10^-38 cm^2) ^-1 GeV cm^-3 the core H-burning lifetime of 20M_ and 200M_ stars exceeds the age of the Universe, and stars are sustained only by WIMP annihilations. We determine the observational properties of these ``frozen'' objects and show that they can be searched for in the local Universe thanks to their anomalous mass-radius relation, which should allow unambiguous discrimination from normal stars.
Taoso et al. (Thu,) studied this question.