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arXiv · 2410.23886

Notes on the Factorisation of the Hilbert Space for Two-Sided Black Holes in Higher Dimensions

Pan Li
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Abstract

In this paper, we investigate the Hilbert space factorisation problem of two-sided black holes in high dimensions. We demonstrate that the Hilbert space of two-sided black holes can be factorized into the tensor product of two one-sided bulk Hilbert spaces when the effect of non-perturbative replica wormholes is taken into account. We further interpret the one-sided bulk Hilbert space as the Hilbert space of a one-sided black hole. Therefore, since the Hilbert space of a two-sided black hole can be obtained from the tensor product of two single-sided black hole Hilbert spaces, we consider this as an embodiment of the ER=EPR conjecture, and we show when the entanglement between the two single-sided black holes is sufficiently strong, the (Lorentzian) geometry of a two-sided black hole will emerge.

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Pan Li. 2025-01-14. Notes on the Factorisation of the Hilbert Space for Two-Sided Black Holes in Higher Dimensions. https://arxiv.org/abs/2410.23886

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