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 gtt = −g −1 rr ), parameterized by the ADM mass and the PPN parameter β, which reduce to Schwarzschild for β = 1. Agreement with observations requires |β − 1| ∼ |η| 1. The sign of η plays a key role in the global causal structure, separating metrics which behave like Schwarzschild (η < 0) from those similar to Reissner-Nordström (η > 0). In the latter case, we find a family of black hole space-times completely regular. 04.70.Bw, 04.50.+h In recent years there has been a renewed interest in models with extra dimensions in which the standard model fields are confined to our four-dimensional world viewed as a (infinitely thin) hypersurface (the brane) embedded in the higher-dimensional space-time (the bulk) where (only) gravity can propagate. Of particular interest are cases where the extra dimensions are infinitely extended but "warped" by the presence of a non-vanishing bulk cosmological constant Λ related to the (singular) vacuum energy density of the brane [1,2] by the standard junction equations [3].In D + 1 space-time dimensions a vacuum solution must satisfy (µ, ν = 0, . . . , D)On projecting the above equation on a time-like manifold of codimension one (the brane) and introducing Gaussian normal coordinates x i (i = 0, . . . , D − 1) and z (z = 0 on the brane), one obtains the constraints (at z = 0)where R is the D-dimensional Ricci scalar, λ the cosmological constant on the brane (we shall set λ = 0 from now on, equivalently to the fine tuning between Λ and the brane tension [1]) and use has been made of the necessary junction equations [3]. For static solutions, one can view Eqs. (2) as the analogs of the momentum and Hamiltonian constraints in the ADM decomposition of the metric and their role is therefore to select out admissible field configurations along hypersurfaces of constant z. Such field configurations will then be "propagated" off-brane by the remaining Einstein Eqs.(1). It is clear that the above "Hamiltonian" constraint is a weaker requirement than the purely D-dimensional vacuum equations R ij = 0 and, in fact, it is equivalent to R ij = E ij where E ij is (proportional to) the (traceless) projection of the D + 1-dimensional Weyl tensor on the brane [4]. In the present letter we investigate spherically symmetric solutions to Eqs. (2) with D = 4 of the formwith dΩ 2 = dθ 2 + sin 2 θ dφ 2 , which might represent black holes in the brane-world [5][6][7][8][9]. First of all, let us recall that the Schwarzschild four-dimensional metric (3) with 4) and N = 1 − 2 M/r is ruled out as a physical candidate since its unique propagation in the bulk is a black string with the central singularity extending all along the extra dimension and making the AdS horizon singular [5]. Further, this case is also unstable under linear perturbations [10]. A few different cases have been recen...

We propose a method to extend to the bulk asymptotically flat static spherically symmetric brane-world metrics. We employ the multipole (1/r) expansion in order to allow the exact integration of the relevant equations along the (fifth) extra coordinate and make contact with the parametrized post-Newtonian formalism. We apply our method to three families of solutions previously appeared as candidates of black holes in the brane world and show that the shape of the horizon is very likely a flat "pancake" for astrophysical sources.

In a one parameter family of dilaton gravity theories which allow the coupling of the dilaton to gravity and to a U (1) gauge field to differ, we have found the existence of everywhere regular spacetimes describing black holes hiding expanding universes inside their horizon.