Alternative for black hole paradoxes

Abstract

In this paper, we investigate the exact time-dependent black hole solution on a warped five-dimensional Randall–Sundrum space–time in conformal dilaton gravity. The zeroes of the model are described by a meromorphic quintic polynomial, which has no essential singularities. The quintic equation can be reduced to the Brioschi form by means of the Weierstrass elliptic curve over [Formula: see text]. The model fits the antipodal boundary condition, i.e. antipodal points in the projected space are identified using the embedding of a Klein surface in [Formula: see text], using the [Formula: see text] symmetry on the two sides of the brane. If one writes [Formula: see text], [Formula: see text], with [Formula: see text] the normal to the brane and [Formula: see text] the dilaton field, then [Formula: see text] is conformally flat. It is the contribution from the bulk which determines the real pole on the effective four-dimensional space–time. There is no objection applying ’t Hooft’s back reaction method in constructing the unitary S-matrix for the Hawking radiation. Again, there is no “inside” of the black hole. The zeroes can also be analyzed by the icosahedron equation and by the Hopf-fibration of the Klein surface.