What question did this study set out to answer?

The aim is to extend the evaporation invariant to rotating Kerr black holes and unify prior research on D3 displacements.

June 7, 2026Open Access

Spin-Suppressed Evaporation Invariant: Total D3 Displacement for Kerr Black Holes and Unification of the D3 Research Series

Key Points

The aim is to extend the evaporation invariant to rotating Kerr black holes and unify prior research on D3 displacements.
Analyzed total D3 displacement during complete Hawking evaporation for Kerr black holes.
Derived the spin-suppression factor f(χ) to explore its role in displacement.
Verified findings across multiple mass decades and spin values, including notable black holes like GW150914.
Determined R_total(Kerr) = f(χ)·r_s(M₀), showcasing the impact of spin on black hole evaporation.
Confirmed that constants M, ℏ, k_B, ln2, π cancel during the analysis, leading to a simplified equation.
Achieved a unification of the D3 research series with clear limits for Schwarzschild and Kerr cases.

Abstract

We extend the evaporation invariant to rotating (Kerr) black holes. The total D3 information-geometry displacement over complete Hawking evaporation is Rₜotal (Kerr) = f (χ) ·rₛ (M₀), where f (χ) = 2√ (1−χ²) / (1+√ (1−χ²) ) is the spin-suppression factor. Five constants cancel (M, ℏ, kB, ln2, π) — only G, c, and f (χ) survive. This unifies all four papers: at χ=0 the Schwarzschild invariant is recovered; at χ→1, Rₜotal→0. Verified across four mass decades and seven spin values including GW150914, GRS 1915+105, and Sgr A*.

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