Abstract
We study the information paradox for the eternal black hole with charges on a doubly-holographic model in general dimensions, where the charged black hole on a Planck brane is coupled to the baths on the conformal boundaries. In the case of weak tension, the brane can be treated as a probe such that its backreaction to the bulk is negligible. We analytically calculate the entanglement entropy of the radiation and obtain the Page curve with the presence of an island on the brane. For the near-extremal black holes, the growth rate is linear in the temperature. Taking both Dvali-Gabadadze-Porrati term and nonzero tension into account, we obtain the numerical solution with backreaction in four-dimensional spacetime and find the quantum extremal surface at t = 0. To guarantee that a Page curve can be obtained in general cases, we propose two strategies to impose enough degrees of freedom on the brane such that the black hole information paradox can be properly described by the doubly-holographic setup.
Highlights
Motivated by the Ryu-Takayanagi formula and its generalization [10, 11], the finegrained entropy of a system is calculated by the quantum extremal surface (QES) [12]
We study the information paradox for the eternal black hole with charges on a doubly-holographic model in general dimensions, where the charged black hole on a Planck brane is coupled to the baths on the conformal boundaries
To guarantee that a Page curve can be obtained in general cases, we propose two strategies to impose enough degrees of freedom on the brane such that the black hole information paradox can be properly described by the doubly-holographic setup
Summary
We will present the general setup for the island within the charged eternal black hole. We consider a d-dimensional charged eternal black hole in AdSd coupled to two flat baths on each side, with the strongly coupled conformal matter living in the bulk, as shown in figure 1(a). At σ = 0, we glue the conformal boundary of the AdSd and flat spacetime together and impose the transparent boundary condition on the matter sector. The above description can be equivalently pushed forward into a doubly-holographic setup, where the matter sector is dual to a (d + 1)-dimensional spacetime and the ddimensional black hole is described by a Planck brane pl in the bulk, as shown in figure 1(b). K∂ is the extrinsic curvature on the conformal boundary ∂. Where T is the trace of the energy-stress tensor Tμν
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