Journey to the Center of a Black Hole
Abstract
An infalling two-point function of a scalar field in a three-dimensional BTZ black hole, with one operator inserted in the exterior and the other inserted along a timelike geodesic, diverges when the infalling insertion point reaches the black hole singularity. In the boundary description, this divergence is tied to the exchange of double-twist operators rather than to the multi-stress-tensor sector that encodes curvature singularities in higher dimensions. We show that the inclusion of a tower of massive particles with Hagedorn growth gives rise to loop corrections that become important near the singularity, where they trigger a Hagedorn transition that renders the tree-level divergence untrustworthy. In the boundary theory, the corresponding tower of primary operators leads to a breakdown of the generalized free field description of the probe operator in the black hole state. In a large black hole, these corrections become important only near the singularity and remain exponentially suppressed at the horizon. The region where these corrections dominate is therefore parametrically separated from the horizon, as anticipated by the principle of black hole complementarity.
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BibTeX
@misc{mohan2026journey,
title = {{Journey to the Center of a Black Hole}},
author = {Vyshnav Mohan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.35705},
eprint = {2609.35705},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35705},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Journey to the Center of a Black Hole
AU - Vyshnav Mohan
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2609.35705
UR - https://arxiv.org/abs/2609.35705
AB - An infalling two-point function of a scalar field in a three-dimensional BTZ black hole, with one operator inserted in the exterior and the other inserted along a timelike geodesic, diverges when the infalling insertion point reaches the black hole singularity. In the boundary description, this divergence is tied to the exchange of double-twist operators rather than to the multi-stress-tensor sector that encodes curvature singularities in higher dimensions. We show that the inclusion of a tower of massive particles with Hagedorn growth gives rise to loop corrections that become important near the singularity, where they trigger a Hagedorn transition that renders the tree-level divergence untrustworthy. In the boundary theory, the corresponding tower of primary operators leads to a breakdown of the generalized free field description of the probe operator in the black hole state. In a large black hole, these corrections become important only near the singularity and remain exponentially suppressed at the horizon. The region where these corrections dominate is therefore parametrically separated from the horizon, as anticipated by the principle of black hole complementarity.
ER -