We consider solutions of d = 11 supergravity describing a product of a four-dimensional Schwarzschild geometry and a seven-sphere whose radius R does depend on r. Three cases are studied as follows. \ud \ud 1. (i) Vanishing photon fields: an exact solution with r-dependent R(r) is presented which exhibits a horizon.\ud \ud 2. (ii) Freund-Rubin asymptotics: Numerical results show that in this case solutions exist without a horizon at a finite value of r, but with R(0) = ∞.\ud \ud 3. (iii) Englert asymptotics: a striking analogy with the 't Hooft-Polyakov monopole is found which suggests the existence of a completely regular solution which interpolates between the Englert solution at r = ∞ and the Freund-Rubin solution at r = 0
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