Conformal dilaton gravity, antipodal mapping and black hole physics on a warped spacetime

Abstract

An exact time-dependent solution of a black hole is found in a conformally invariant gravity model on a warped Randall-Sundrum spacetime, by writing the metric gμν = ω 4 n−2 g̃μν . Here g̃μν represents the ”un-physical” spacetime and ω the dilaton field, which will be treated on equal footing as any renormalizable scalar field. It is remarkable that the 5D and 4D effective field equations for the metric components and dilaton fields can be written in general dimension n = 4, 5. The location of the horizon(s) are determined by a quintic polynomial. This polynomial is related to the symmetry group of the icosahedron, isomorphic with the Galois group A5. We applied the antipodal mapping on the axially symmetric black hole spacetime and make some connection with the information and firewall paradoxes. The dilaton field can be used to describe the different notion the in-going and outside observers have of the Hawking radiation by using different conformal gauge freedom. The disagreement about the interior of the black hole is explained by the antipodal map of points on the horizon. The free parameters of the solution can be chosen in such a way that ḡμν is singular-free and topologically regular, even for ω → 0.