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arXiv · 2601.09397

Geodesics, One Point Functions and Black Hole Perturbations

Parijat Dey·Arundhati Goldar·Nirmalya Kajuri
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Abstract

Holographic black holes exhibit a striking relation between thermal boundary one-point functions and bulk geodesic lengths. In the large conformal-dimension limit, the one-point function of a primary operator is given by the exponential of the geodesic length from its boundary insertion point to the horizon. We test the robustness of this relation under perturbations by considering a class of deformations of an Euclidean BTZ black hole and working to first order in the perturbation.We find that, at leading order in the large conformal-dimension limit and to first order in the radial horizon-preserving perturbation, the logarithmic variation of the one-point function is governed by the variation of the renormalized boundary-to-horizon geodesic length. The result is established using WKB and saddle-point methods, and WKB expressions at large conformal dimension are checked against the exact Green function and bulk-boundary propagator.

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Parijat Dey, Arundhati Goldar, Nirmalya Kajuri. 2026-01-14. Geodesics, One Point Functions and Black Hole Perturbations. https://arxiv.org/abs/2601.09397

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