arXiv subjects

Zhenkang Lu

Publications and source records attributed to Zhenkang Lu.

4 recordsLinked to original sources

arXiv2026

Probing bulk geometry via pole skipping: from static to rotating spacetimes

We investigate an analytical framework for reconstructing bulk geometries from pole-skipping data. Previously, this method enabled the recursive recovery of near-horizon metric derivatives in static, planar-symmetric black holes. Building on this framework, we systematically extend it to more intricate geometries, specifically static topological black holes and rotating black holes. For three-dimensional rotating black holes, we demonstrate that the metric can be fully reconstructed from boundary pole-skipping data. For four-dimensional rotating spacetimes admitting a separable coordinate system (such as the Kerr family), standard near-horizon pole-skipping successfully reconstructs the purely radial metric functions. To recover the remaining angular metric functions, we introduce a mathematical counterpart termed "angular pole-skipping," defined via a near-axis analysis. Although its precise holographic dictionary remains an open question, this bulk-side formalism completes the geometric reconstruction algorithm. Furthermore, we demonstrate that the vacuum Einstein equations can be recast as a set of algebraic equations governing the pole-skipping data and that the null energy condition imposes algebraic inequalities on this boundary data. Finally, we establish general polynomial constraints dictated by the overdetermined nature of the metric reconstruction, highlighting the highly redundant encoding of bulk geometry in boundary data.

gr-qc↗

arXiv2026

Bulk Spacetime Encoding via Boundary Ambiguities

We propose a method to reconstruct the metric and its arbitrary-order derivatives at the horizon for any static, planar-symmetric black hole, using an infinite set of discrete pole-skipping points in momentum space where the boundary Green's function becomes ambiguous. This method is fully analytical and involves solving only linear equations. The near-horizon reconstruction can extend either inside or outside the horizon until reaching the nearest singularity in the complex radial plane. It further enables a reinterpretation of any pure gravitational field equation in pole-skipping data. Moreover, our method reveals that the pole-skipping points are redundant: only a subset is independent, while the rest are fixed by an equal number of homogeneous polynomial constraints. These identities are universal, independent of the details of the bulk geometry, including its dimensionality, asymptotic behavior, or the existence of a holographic duality.

hep-th↗

arXiv2026

The Algebraic Structure Underlying Pole-Skipping Points

The holographic Green's function becomes ambiguous, taking the indeterminate form `$0/0$', at an infinite set of special frequencies and momenta known as ``pole-skipping points''. In this work, we propose that these pole-skipping points can be used to reconstruct both the interior and exterior geometry of a static, planar-symmetric black hole in the bulk. The entire reconstruction procedure is fully analytical and only involves solving a system of linear equations. We demonstrate its effectiveness across various backgrounds, including the BTZ black hole, its $T\bar{T}$-deformed counterparts, as well as geometries with Lifshitz scaling and hyperscaling-violation. Within this framework, other geometric quantities, such as the vacuum Einstein equations, can also be reinterpreted directly in terms of pole-skipping data. Moreover, our approach reveals a hidden algebraic structure governing the pole-skipping points of Klein-Gordon equations of the form $(\nabla^{2} + V(r))ϕ(r) = 0$: only a subset of these points is independent, while the remainder is constrained by an equal number of homogeneous polynomial identities in the pole-skipping momenta. These identities are universal, as confirmed by their validity across a broad class of bulk geometries with varying dimensionality, boundary asymptotics, and perturbation modes.

hep-th↗

arXiv2022

Aspects of univalence in holographic axion models

Univalent functions are complex, analytic (holomorphic) and injective functions that have been widely discussed in complex analysis. It was recently proposed that the stringent constraints that univalence imposes on the growth of functions combined with sufficient analyticity conditions could be used to derive rigorous lower and upper bounds on hydrodynamic dispersion relation, i.e., on all terms appearing in their convergent series representations. The results are exact bounds on physical quantities such as the diffusivity and the speed of sound. The purpose of this paper is to further explore these ideas, investigate them in concrete holographic examples, and work towards a better intuitive understanding of the role of univalence in physics. More concretely, we study diffusive and sound modes in a family of holographic axion models and offer a set of observations, arguments and tests that support the applicability of univalence methods for bounding physical observables described in terms of effective field theories. Our work provides insight into expected `typical' regions of univalence, comparisons between the tightness of bounds and the corresponding exact values of certain quantities characterizing transport, tests of relations between diffusion and bounds that involve chaotic pole-skipping, as well as tests of a condition that implies the conformal bound on the speed of sound and a complementary condition that implies its violation.

hep-th↗