New black holes in the brane world?

It is known that the Einstein field equations in five dimensions admit more general spherically symmetric black holes on the brane than four-dimensional general relativity. We propose two families of analytic solutions (with ${g}_{\mathrm{tt}}\ensuremath{\ne}\ensuremath{-}{g}_{\mathrm{rr}}^{\ensuremath{-}1}),$ parametrized by the Arnowitt-Deser-Misner mass and the parametrized post-Newtonian parameter $\ensuremath{\beta},$ which reduce to Schwarzschild for $\ensuremath{\beta}=1.$ Agreement with observations requires $|\ensuremath{\beta}\ensuremath{-}1|\ensuremath{\sim}|\ensuremath{\eta}|\ensuremath{\ll}1.$ The sign of $\ensuremath{\eta}$ plays a key role in the global causal structure, separating metrics which behave like Schwarzschild $(\ensuremath{\eta}<0)$ from those similar to Reissner-Nordstr\"om spare-time $(\ensuremath{\eta}>0).$ In the latter case, we find a family of black hole space-times completely regular.

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