We have investigated the classical stability of magnetically charged black p-brane solutions for string theories that include the case studied by Gregory and Laflamme. It turns out that the stability behaves very differently depending on a coupling parameter between dilaton and gauge fields. In the case of Gregory and Laflamme, it has been known that the black brane instability decreases monoto...

for fixed nonzero integers (r, s) with r > 0 and (r, s) = 1. It shows there are finitely many solutions in positive integers qi ≥ 1, and obtains sharp bounds on the maximal size of solutions for almost all (r, s). The extremal solutions for r = s = 1 are related to Sylvester’s sequence 2, 3, 7, 43, 1807, .... If the positivity condition on the integers qi is dropped, then for r = 1 these system...

We construct static axially symmetric solutions of SU(2) Einstein-Yang-Millsdilaton theory. Like their spherically symmetric counterparts, these solutions are nonsingular and asymptotically flat. The solutions are characterized by the winding number n and the node number k of the gauge field functions. For fixed n with increasing k the solutions tend to “extremal” Einstein-Maxwell-dilaton black...