Krishnan, C and Mohan, V (2024) State-independent black hole interiors from the crossed product. In: Journal of High Energy Physics, 2024 (5).
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Abstract
Opinion is divided about the nature of state dependence in the black hole interior. Some argue that it is a necessary feature, while others argue it is a bug. In this paper, we consider the extended half-sided modular translation U (s0) (with s0 > 0) of Leutheusser and Liu that takes us inside the horizon. We note that we can use this operator to construct a modular Hamiltonian H and a conjugation J on the infalling time-evolved wedges. The original thermofield double translates to a new cyclic and separating vector in the shifted algebra. We use these objects and the Connes� cocycle to repeat Witten�s crossed product construction in this new setting, and to obtain a Type II� algebra that is independent of the various choices, in particular that of the cyclic separating vector. Our emergent times are implicitly boundary-dressed. But if one admits an �extra� observer in the interior, we argue that the (state-independent) algebra can be Type I or Type II1 instead of Type II�, depending on whether the observer�s light cone contains an entire Cauchy slice or not. Along with these general considerations, we present some specific calculations in the setting of the Poincare BTZ black hole. We identify a specific pointwise (as opposed to non-local) modular translation in BTZ-Kruskal coordinates that is analytically tractable, exploiting a connection with AdS-Rindler. This modular translation can reach the singularity. © The Author(s) 2024.
| Item Type: | Journal Article |
|---|---|
| Publication: | Journal of High Energy Physics |
| Publisher: | Springer Science and Business Media Deutschland GmbH |
| Additional Information: | The copyright for this article belongs to Authors. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Centre for High Energy Physics |
| Date Deposited: | 06 Aug 2024 13:14 |
| Last Modified: | 06 Aug 2024 13:14 |
| URI: | http://eprints.iisc.ac.in/id/eprint/85251 |
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