We prove the D3 evaporation invariant is consistent across various spacetime dimensions, indicating its universal nature.
We prove that the D3 evaporation invariant R_total = r_s holds in all spacetime dimensions d ≥ 4. In d dimensions, D3_d 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 = T_H·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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Bharat Bhushan sharma (2026) studied this question.
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