Holographic Pseudo Entropy from the Rindler Method in AdS and Flat Space
Abstract
Via the Rindler method, we study holographic timelike entanglement entropy (TEE) for a general timelike interval in AdS3/CFT2 and flat3/CCFT2. The TEE is the pseudo entropy of a timelike interval. In the bulk, the imaginary part of the TEE comes from a timelike geodesic, but in the Rindler picture this geodesic has not been identified. After a Rindler transformation to a rotating BTZ black hole, the two spacelike extremal curves lie on the inner and outer horizons, and exchanging lu↔ ℓ lϕ takes one to the other. We find the geometric meaning of the timelike extremal curve: a geodesic stretched between the two horizons. Its length, iπℓ, is independent of the interval, and it alone produces the imaginary part iπc/6. We follow the same procedure in flat space holography, where the spacelike curve sits on the cosmological horizon and the timelike curve lies between the cosmological horizon and timelike infinity. Evaluating the holographic TEE for a timelike interval in CCFT2 on the plane, we find that, in contrast with the cylinder, the real and imaginary parts are equal.
Related
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BibTeX
@misc{shalamzari2026holographic,
title = {{Holographic Pseudo Entropy from the Rindler Method in AdS and Flat Space}},
author = {Mehdi Hakami Shalamzari and Zahra Paygozar and Mahdi Kord Zangeneh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17239},
eprint = {2610.17239},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17239},
}
RIS
TY - UNPB
TI - Holographic Pseudo Entropy from the Rindler Method in AdS and Flat Space
AU - Mehdi Hakami Shalamzari
AU - Zahra Paygozar
AU - Mahdi Kord Zangeneh
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17239
UR - https://arxiv.org/abs/2610.17239
AB - Via the Rindler method, we study holographic timelike entanglement entropy (TEE) for a general timelike interval in AdS_3/CFT_2 and flat_3/CCFT_2. The TEE is the pseudo entropy of a timelike interval. In the bulk, the imaginary part of the TEE comes from a timelike geodesic, but in the Rindler picture this geodesic has not been identified. After a Rindler transformation to a rotating BTZ black hole, the two spacelike extremal curves lie on the inner and outer horizons, and exchanging l_u↔ ℓ l_ϕ takes one to the other. We find the geometric meaning of the timelike extremal curve: a geodesic stretched between the two horizons. Its length, iπℓ, is independent of the interval, and it alone produces the imaginary part iπc/6. We follow the same procedure in flat space holography, where the spacelike curve sits on the cosmological horizon and the timelike curve lies between the cosmological horizon and timelike infinity. Evaluating the holographic TEE for a timelike interval in CCFT_2 on the plane, we find that, in contrast with the cylinder, the real and imaginary parts are equal.
ER -