Abstract. We consider Maxwell and Yang–Mills (YM) fields together, interacting through gravity both in Einstein and in Gauss–Bonnet (GB) theories. For this purpose we choose two different sets of Maxwell and metric ansätze. In our first ansatz, asymptotically for r → 0 (and N > 4) the Maxwell field dominates over the YM field. In the other asymptotic region, r → ∞, however, the YM field becomes dominant. For N = 3 and 4, where the GB term is absent, we recover the well-known Bañados–Teitelboim–Zanelli and Reissner–Nordström metrics, respectively. The second ansatz corresponds to the case of constant radius function for the S^N−2 part in the metric. This leads to the maximally symmetrical, everywhere regular, Bertotti–Robinson type of solutions for representing our cosmos both at large and small scales.

Key words: black holes; extra dimensions; gravity

Received 10 November 2008, accepted for publication 12 November 2008
Published 2 December 2008