What question did this study set out to answer?

The research aims to establish that the D3 evaporation invariant R_total = r_s is valid in all spacetime dimensions from d ≥ 4.

June 8, 2026Open Access

The D3 Evaporation Invariant in All Spacetime Dimensions: Rₜotal = rₛ is Dimension-Independent

Key Points

The research aims to establish that the D3 evaporation invariant R_total = r_s is valid in all spacetime dimensions from d ≥ 4.
Proof of R_total = r_s across dimensions d ≥ 4
Analysis of scaling laws for D3_d and Bekenstein bit-loss rate
Application of the black hole thermodynamics first law
D3_d scales as M^(−1/(d−3)) and Bekenstein bit-loss rate scales as M^(+1/(d−3))
Their product yields a constant, M⁰, independent of M and d
The findings are applicable to d=4 (GR), d=10 (string theory), and d=11 (M-theory).

Abstract

We prove that the D3 evaporation invariant Rₜotal = rₛ holds in all spacetime dimensions d ≥ 4. In d dimensions, D3d scales as M^ (−1/ (d−3) ) while the Bekenstein bit-loss rate scales as M^ (+1/ (d−3) ). Their product is M⁰ — a constant independent of M and d. This dimension-independent cancellation follows directly from the first law of black hole thermodynamics dM = TH·dS in d dimensions. The result holds for d=4 (standard GR), d=10 (string theory), d=11 (M-theory), and any d ≥ 4. Paper 3 is therefore not a 4D coincidence but a universal property of the D3 framework.

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