Solitons and black holes in Einstein-Born-Infeld-dilaton theory - art. no.124013

Static spherically symmetric asymptotically flat solutions to the U(1) Born -Infeld theory coupled to gravity and to a dilaton are investigated. The di laton enters in such a way that the theory is SL(2,R) symmetric for a unit value of the dilaton coupling constant. We find globally regular solutions for any value of the effective coupling which is the ratio of the gravitati onal and dilaton couplings; they form a continuous sequence labeled by the sole free parameter of the local solution near the origin. The allowed valu es of this parameter are bounded from below, and, as the limiting value is approached, the mass and the dilaton charge rise indefinitely and tend to a strict equality tin suitable units). Together with the electric charge the y saturate the BPS bound of the corresponding linear U(1) theory. Beyond th is boundary the solutions become compact (singular), while the limiting sol ution at the exact boundary value is noncompact and nonasymptotically flat. The black holes in this theory exist for any value of the event horizon ra dius and also form a sequence labeled by a continuously varying parameter r estricted to a finite interval. The singularity inside the black hole exhib its a power-law mass inflation.