Alternative for Black Hole Paradoxes

Abstract: A throughout investigation is made of the exact black hole solution in five-dimensional warped conformal dilaton gravity, found in an earlier investigation. The singularities of the dynamical black hole spacetime are determined by the zeros of a meromorphic quintic polynomial, which has no essential singularities. The solutions of the polynomial are analyzed in the complex plane in relation to the icosahedron group and by the Hopf-fibrations of the Klein surface. 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 $\mathds{C}^2$, using the $\mathds{Z}2$ symmetry on the two sides of the brane. If one writes $^{(5)}g{\mu\nu}=\omega^{4/3}{^{(5)}}{\tilde g_{\mu\nu}}, {^{(5)}}{\tilde g_{\mu\nu}}={^{(4)}}{\tilde g_{\mu\nu}}+n_\mu n_\nu$, $ ^{(4)}\tilde g_{\mu\nu}=\bar\omega^2 {^{(4)}}\bar g_{\mu\nu}$, with $n_\mu$ the normal to the brane and $\omega$ the dilaton field, then ${^{(4)}}\bar g_{\mu\nu}$ is conformally flat. It is the contribution from the bulk which determines the real pole on the effective four-dimensional spacetime. 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.