New black holes in the brane world?

Abstract

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.