Fuzzball models with stretched horizons modify or eliminate entanglement islands depending on boundary conditions and cap geometry, producing information paradox analogues in some cases.
Entanglement entropy of asymptotically flat non-extremal and extremal black holes with an island
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abstract
The island rule for the entanglement entropy is applied to an eternal Reissner-Nordstr\"om black hole. The key ingredient is that the black hole is assumed to be in thermal equilibrium with a heat bath of an arbitrary temperature and so the generalized entropy is treated as being off-shell. Taking the on-shell condition to the off-shell generalized entropy, we find the generalized entropy and then obtain the entanglement entropy following the island rule. For the non-extremal black hole, the entanglement entropy grows linearly in time and can be saturated after the Page time as expected. The entanglement entropy also has a well-defined Schwarzschild limit. In the extremal black hole, the island prescription provides a logarithmically growing entanglement entropy in time and a constant entanglement entropy after the Page time. In the extremal black hole, the boundary of the island hits the curvature singularity where the semi-classical approximations appear invalid. To avoid encountering the curvature singularity, we apply this procedure to the Hayward black hole regular at the origin. Consequently, the presence of the island in extremal black holes can provide a finite entanglement entropy, which might imply non-trivial vacuum configurations of extremal black holes.
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A rotating regular black hole leaves a remnant because the correction term in the generalized entropy of Hawking radiation vanishes at a finite mass above the extremal limit.
citing papers explorer
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Entanglement islands, fuzzballs and stretched horizons
Fuzzball models with stretched horizons modify or eliminate entanglement islands depending on boundary conditions and cap geometry, producing information paradox analogues in some cases.
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The Remnant of an Evaporating Rotating Regular Black Hole from the Generalized Entropy in the Final Stage of Evaporation
A rotating regular black hole leaves a remnant because the correction term in the generalized entropy of Hawking radiation vanishes at a finite mass above the extremal limit.