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Regular magnetic monopoles in the non-Abelian Born-Infeld-Higgs theory areknown to exist in the region of the field strength parameter $\beta>\beta_{{\rmcr}}$, bounded from below. Beyond this region, only pointlike (embeddedabelian) monopoles exist, and we show that the transition from the regular tosingular structure is reminiscent of gravitational collapse. Near the thresholdbehavior is characterized by the rapidly increasing negative pressure, whichtypically arises in the high density NBI matter. Another feature, shared boththe NBI and gravitating monopoles, is the existence of excited states, whichcan be thought of as bound states of monopoles and sphalerons. These arelabeled by the number $N$ of nodes of the Yang-Mills function. Their masses aregreater than the mass of the ground state monopole, and they are expected to beunstable. The sequence of masses $M_N$ rapidly converges to the mass of theembedded Abelian solution with constant Higgs. The ratio of the sphaleron sizeto that of the monopole grows with decreasing $\beta$, and, at the same time,both fall down until the solutions cease to exist, again exhibiting collapse tothe pointlike monopole. The results are presented and compared both for theordinary and the symmetrized trace NBI actions.Comment: latex, 15 pages, 6 figure

Monopoles in non-Abelian Born-Infeld-Higgs theory and Born-Infeld collapse