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.

arXiv commentVersion 2. Some minor changes. Comment welcome. 10 figures. 25 pages. To be presented at the 4-th Information Universe Conference, Groningen, The Netherlands. June 2022

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