Multidimensional extremal dilatonic black holes in string-like model with cosmological term

A string-like model with the “cosmological constant” Λ is considered. The Maki-Shiraishi multi-black-hole solution [T. Maki and K. Shiraishi, Progress of Theoretical Physics 90 (1993) 1259] is generalized to space-times with a Ricci-flat internal space. For Λ = 0 the obtained solution in the one-black-hole case is shown to coincide with the extreme limit of the charged dilatonic black hole solution [U. Bleyer and V.D. Ivashchuk, Phys. Lett. B 332 (1994) 282; U. Bleyer, K.A. Bronnikov, S.B. Fadeev and V.N. Melnikov, Astron. Nachr. 315 (1994) 393; K.A. Bronnikov and V.N. Melnikov, Annals of Physics (N.Y.) 239 (1995) 40; K.A. Bronnikov, Gravitation and Cosmology 1 (1995) 67]. The Hawking temperature TH for the solution [U. Bleyer and V.D. Ivashchuk, Phys. Lett. B 332 (1994) 292; U. Bleyer, K.A. Bronnikov, S.B. Fadeev and V.N. Melnikov, Astron. Nachr. 315 (1994) 393; K.A. Bronnikov and V.N. Melnikov, Annals of Physics (N.Y.) 239 (1995) 40; K.A. Bronnikov, Gravitation and Cosmology 1 (1995) 67] is presented and its extreme limit is considered. For the string value of dilatonic coupling the temperature TH does not depend upon the internal space dimension.