Alternative for Black Hole Paradoxes

TL;DR

This paper investigates a five-dimensional warped conformal dilaton gravity black hole solution, analyzing its singularities, boundary conditions, and implications for black hole paradoxes, suggesting no inside region and supporting unitarity in Hawking radiation.

Contribution

It provides a detailed analysis of a novel exact black hole solution in higher-dimensional gravity, connecting complex polynomial roots, geometric structures, and boundary conditions to address black hole paradoxes.

Findings

Singularities determined by zeros of a meromorphic quintic polynomial.

Model satisfies antipodal boundary conditions via Klein surface embedding.

Supports unitarity of Hawking radiation without an inside black hole region.

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.