Resolved core Stokes graphs

Interactive companion to Expiscating the black hole singularity in holography.

Planar Schwarzschild–AdS and RNAdS₅ · full sphere and core magnification · fixed physical ζ

ϑ (radians)

Drag a sphere to rotate the matching views. Arrow keys rotate a focused sphere.

Outer horizon H₊ H₁ H₂ (d = 6) Root connection / return Ordinary closed leaf Boundary → H₊

Schwarzschild–AdS₅ · d = 4

Full sphere

SAdS5 full sphere.

Core magnification

SAdS5 core magnification.

Turning-point names and coordinates
Pointu

Schwarzschild–AdS₇ · d = 6

Full sphere

SAdS7 full sphere.

Core magnification

SAdS7 core magnification.

Turning-point names and coordinates
Pointu

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Turning points. Blue open circles carry the core tags b₀, b₁, …; pale crosses mark primary WKB roots j₀, j₁, …. The extra turning point near the boundary B is separate from the core family. Expand a coordinate table or select an emitter to identify a root and its arms.

Reading the sphere. The two views show the same finite-frequency Stokes graph. B is the AdS boundary at u = 0, H₊ the outer horizon at u = 1, and S (neutral) or O (RN) the origin at u = 2. Solid and faint dashed curves distinguish front and rear hemispheres. The sphere compactifies the base coordinate.

Neutral core print atlas · Coordinates and conventions · Print atlases