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ER = EPR revisited: On the Entropy of an Einstein-Rosen Bridge
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abstract
We propose a new link between entropy and area: an eternal black hole with an ER bridge with cross-section $A$ can carry a macroscopic amount of quantum information, or be in a mixed state, with entropy bounded by $S \leq A/4G_N$. We substantiate our proposal in the context of AdS3 and JT gravity, by using the Island prescription and replica wormhole method for computing the black hole entropy. We argue that the typical mixed state of a two sided black hole takes the form of an entangled `thermo-mixed double' state with only classical correlations between the two sides. Our result for the von Neumann entropy of a post-Page time two-sided black hole is smaller by a factor of two from previous answers. Our reasoning implies that black hole quantum information is topologically protected, similar to the information stored inside a topological quantum memory.
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Page Curve for an Evaporating Schwarzschild Black Hole in Dimensionally-Reduced Model of Dilaton Gravity
In a dimensionally-reduced dilaton-gravity model, the island formula produces a Page curve for an evaporating Schwarzschild black hole, with the entropy vanishing at the endpoint.
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