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A thorough investigation is presented of the exact black hole solution on awarped five-dimensional spacetime in conformal dilaton gravity (CDG), found inearlier work. Summarized, we will prove: The black hole solution in the CDGmodel on a warped 5D spacetime: 1. It is an exact solution for the metriccomponents as well as for the dilaton field. 2.The quintic polynomialdescribing the zero's of the model, has no essential singularities. 3.If wewrite $^{(5)}g_{\mu\nu}=\omega^{4/3}{^{(5)}}{\tilde g_{\mu\nu}}, ^{(5)}\tildeg_{\mu\nu}=^{(4)}\tilde g_{\mu\nu}+n_\mu n_\nu, ^{(4)}\tildeg_{\mu\nu}=\bar\omega^2 {^{(4)}}\bar g{\mu\nu}$ then ${^{(4)}}\bar g{\mu\nu}$is conformally flat and with $n_\mu$ the normal to the brane. 4. It fits theantipodal boundary condition, i.e., antipodal points in the projected space areidentified using the embedding of a Klein surface in $\mathbb{C}^4$. 5. One canapply 't Hooft's back reaction method in constructing the unitary S-matrix andthere is no "inside" of the black hole. 6. The contribution from the bulkdetermines the poles on the effective 4D spacetime. 7. The zeros of the quinticresolvent can analytically described by the icosahedral equation, i.e., interms of hypergeometric functions and elliptic modular functions. 8. The Hopffibration of the Klein bottle can be applied.

The Dilaton Black Hole on a Conformal Invariant Five Dimensional Warped Spacetime: Paradoxes Possibly Resolved?