Conformal Dilaton-Higgs Gravity on Warped Spacetimes: Black Hole Paradoxes revisited

TL;DR

This paper explores a conformal dilaton-Higgs gravity model on warped spacetimes, providing new insights into black hole solutions, antipodal boundary conditions, and their implications for the information paradox, with potential advantages in describing Hawking radiation.

Contribution

It introduces a novel Kerr-like black hole solution in a conformal dilaton-Higgs gravity framework on warped spacetimes, emphasizing antipodal boundary conditions and their role in black hole information paradoxes.

Findings

Effective 4D brane spacetime derived from 5D manifold

Antipodal boundary condition maintains symmetry without quantum cloning

Relation established between Klein surface embedding and information paradox

Abstract

We investigate on a Randall-Sundrum warped spacetime, a Kerr-like black hole in the conformal dilaton-Higgs $(\omega,\Phi)$ gravity model. We applied the antipodal boundary condition on the Klein surface using the $\mathds{Z}_2$-symmetry in the "large" (bulk) extra dimension. It turns out that the pseudo-Riemannian 5D manifold can be written as an effective 4D Riemannian brane spacetime, $\mathds{R}^2_+\times\mathds{R}^1\times S^1$, where $\mathds{R}^2_+$ is conformally flat. The solution in valid on both manifolds. So the solution can equally well described by an instanton solution. An advantage is that antipodicity can be maintained without a "cut-and-past" method or to rely on quantum cloning, when treating the scattering description of the evaporation process of the Hawking radiation. We need only the windingnumber as quantum number. Moreover, the equations are invariant under time reversal. The problem of finding the matching condition of the near-horizon approximation and the far-away Regge-Wheeler approximation, can possibly be solved by splitting the spacetime in a dilaton field times an "un-physical" spacetime, which is conformally flat. In the case of a constant gauge field, we find that the conform invariant mass term $\sim \Phi^2\omega^2$ in the Lagrangian follows directly from the superfluous dilaton equation by suitable choice of the scale of the extra dimension.Finally, we bring forward the relation between the embedded Klein surface in $\mathds{R}^4$ and the quantum mechanical information paradox.