What question did this study set out to answer?

This research aims to extend the D3 evaporation invariant to Anti-de Sitter black holes and interpret it through holographic principles.

June 8, 2026Open Access

Information-Geometry of AdS-Schwarzschild Black Holes: An Exact AdS Correction to the D3 Evaporation Invariant and its Holographic CFT Interpretation

Key Points

This research aims to extend the D3 evaporation invariant to Anti-de Sitter black holes and interpret it through holographic principles.
Extended the D3 evaporation invariant to AdS black holes using mathematical formulations.
Analyzed the thermal and vacuum contributions for understanding their holographic meanings.
Validated findings through numerical methods to four significant figures.
The total D3 displacement is quantified as R_total(AdS) = r_s·(1+(r_s/L)²).
At the Hawking-Page transition, R_total equals 2r_s, indicating equal costs for thermal and vacuum information.
The correction factor φ(x) = 1 + x² introduces a new observable for measuring the information cost ratio.

Abstract

We extend the D3 evaporation invariant to Anti-de Sitter (AdS) black holes. The total D3 displacement is Rₜotal (AdS) = rₛ· (1+ (rₛ/L) ²). The two terms have distinct holographic meanings: rₛ is the vacuum (T=0) contribution; rₛ³/L² is the thermal contribution scaling as T³CFT — the Stefan-Boltzmann law of a 3D CFT. At the Hawking-Page transition (rₛ=L): Rₜotal=2rₛ exactly — thermal and vacuum information-geometry costs are equal. The correction factor φ (x) =1+x² is a new holographic observable measuring total-to-vacuum information cost ratio. This is the first D3 result with a complete AdS/CFT interpretation. Verified numerically to four significant figures.

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