  We construct holographic backgrounds that are dual by the AdS/CFT
correspondence to Euclidean conformal field theories on products of spheres
$S^{d_1}\times S^{d_2}$, for conformal field theories whose dual may be
approximated by classical Einstein gravity (typically these are large $N$
strongly coupled theories). For $d_2=1$ these backgrounds correspond to thermal
field theories on $S^{d_1}$, and Hawking and Page found that there are several
possible bulk solutions, with two different topologies, that compete with each
other, leading to a phase transition as the relative size of the spheres is
modified. By numerically solving the Einstein equations we find similar results
also for $d_2>1$, with bulk solutions in which either one or the other sphere
shrinks to zero smoothly at a minimal value of the radial coordinate, and with
a first order phase transition (for $d_1+d_2 < 9$) between solutions of two
different topologies as the relative radius changes. For a critical ratio of
the radii there is a (sub-dominant) singular solution where both spheres
shrink, and we analytically analyze the behavior near this radius. For $d_1+d_2
< 9$ the number of solutions grows to infinity as the critical ratio is
approached.
