Analytic Holographic Pseudo-Entropy in a Boosted BTZ Geometry
Abstract
We investigate holographic entanglement entropy and its generalization to pseudo-entropy in a boosted BTZ black hole geometry, which is holographically dual to a moving strongly coupled plasma. By solving the extremal surface equation, we derive an {\it exact closed-form expression} for the holographic entanglement entropy as a function of the boundary interval length, boost velocity, temperature, and conserved quantities. The resulting exact analytic formula correctly reproduces the standard thermal BTZ entanglement entropy in the vanishing-boost limit and smoothly reduces to the vacuum conformal result at zero temperature, thereby providing robust consistency checks. Motivated by the off-diagonal structure of the boosted metric arising from the Lorentz transformation, we then study two families of analytic continuations to Euclidean signature. Both require a simultaneous continuation of the time coordinate and the boost parameter so that the Euclidean metric remains real. If only these two parameters are continued, the boundary interval becomes imaginary and the analytically continued holographic entanglement entropy is complex-valued; we interpret this complex entropy as the holographic dual of pseudo-entropy for the boosted thermal state. If, in addition, a conserved charge is also continued, the boundary interval remains real and the resulting entropy is real. Our construction establishes a direct connection between boosted HEE and holographic pseudo-entropy, extending previous analytic frameworks developed for rotating BTZ geometries to Lorentz-boosted spacetimes.
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BibTeX
@misc{goki2026analytic,
title = {{Analytic Holographic Pseudo-Entropy in a Boosted BTZ Geometry}},
author = {M. M. Daryaei Goki and M. Ali-Akbari},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29710},
eprint = {2609.29710},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29710},
note = {CC0},
}
RIS
TY - UNPB
TI - Analytic Holographic Pseudo-Entropy in a Boosted BTZ Geometry
AU - M. M. Daryaei Goki
AU - M. Ali-Akbari
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.29710
UR - https://arxiv.org/abs/2609.29710
AB - We investigate holographic entanglement entropy and its generalization to pseudo-entropy in a boosted BTZ black hole geometry, which is holographically dual to a moving strongly coupled plasma. By solving the extremal surface equation, we derive an {\it exact closed-form expression} for the holographic entanglement entropy as a function of the boundary interval length, boost velocity, temperature, and conserved quantities. The resulting exact analytic formula correctly reproduces the standard thermal BTZ entanglement entropy in the vanishing-boost limit and smoothly reduces to the vacuum conformal result at zero temperature, thereby providing robust consistency checks. Motivated by the off-diagonal structure of the boosted metric arising from the Lorentz transformation, we then study two families of analytic continuations to Euclidean signature. Both require a simultaneous continuation of the time coordinate and the boost parameter so that the Euclidean metric remains real. If only these two parameters are continued, the boundary interval becomes imaginary and the analytically continued holographic entanglement entropy is complex-valued; we interpret this complex entropy as the holographic dual of pseudo-entropy for the boosted thermal state. If, in addition, a conserved charge is also continued, the boundary interval remains real and the resulting entropy is real. Our construction establishes a direct connection between boosted HEE and holographic pseudo-entropy, extending previous analytic frameworks developed for rotating BTZ geometries to Lorentz-boosted spacetimes.
ER -