Research PaperNo Access

ASFYON, Astronomisch Fysisch Onderzoek Nederland, University of Amsterdam, The Netherlands

https://doi.org/10.1142/S0217751X22501767Cited by:4 (Source: Crossref)

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 $ℚ$ . 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 $ℂ^{2}$ , using the $ℤ_{2}$ symmetry on the two sides of the brane. If one writes $^{(5)} g_{μ ν} = ω^{4 ∕ 3}^{(5)} {\tilde{g}}_{μ ν},^{(5)} {\tilde{g}}_{μ ν} =^{(4)} {\tilde{g}}_{μ ν} + n_{μ} n_{ν}$ , $^{(4)} {\tilde{g}}_{μ ν} = {\bar{ω}}^{2}^{(4)} ḡ_{μ ν}$ , with $n_{μ}$ the normal to the brane and $ω$ the dilaton field, then $^{(4)} ḡ_{μ ν}$ 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.

Keywords:

PACS: 03.65.Pm, 03.65.Ud, 04.20.-q, 04.20.Jb, 04.50.Kd, 04.60.Bc, 04.70.-s

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