Black hole solutions in Einstein–Maxwell–Yang–Mills–Gauss–Bonnet theory

Abstract

We consider Maxwell and Yang–Mills (YM) fields together, interacting through gravityboth in Einstein and in Gauss–Bonnet (GB) theories. For this purpose we choose twodifferent sets of Maxwell and metric ansätze. In our first ansatz, asymptotically forr → 0 (and N > 4) the Maxwell field dominates over the YM field. In the other asymptotic region,r → ∞, however, the YM field becomes dominant. ForN = 3 and4, wherethe GB term is absent, we recover the well-known Bañados–Teitelboim–Zanelli and Reissner–Nordströmmetrics, respectively. The second ansatz corresponds to the case of constant radius function for theSN−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 smallscales.