What must be specified

A prospective semiclassical calculation must state an action, state, renormalization prescription, and domain. For example, a matter action may be declared as

A corresponding gravitational effective action may include

These are possible interface declarations, not a choice of a completed microscopic theory, and no coefficient in (eq:eftaction) is calculated here. Low-energy gravitational EFT and ultraviolet completion are different claims Donoghue.

With inverse-metric variation, define

The mean-field target equation is

For the Einstein–Hilbert term alone, this convention yields $G_{ab}+\Lambda g_{ab}=8\pi G⟨T_{ab}{⟩}_{\mathrm{ren}}$.

A point-splitting prescription must identify the Hadamard subtraction, local curvature freedom, conservation condition, and state dependence. Local covariant Wick and time-ordered constructions provide relevant frameworks, not solutions of (eq:semiclassical) for the present evaporation problem HollandsWald2001,HollandsWald2002. If stress-energy fluctuations matter in the claimed regime, their effect must also be controlled; mean-field self-consistency alone does not supply that control HuVerdaguer.

A useful spherical metric interface is

Both $m(v,r)$ and $\psi (v,r)$ are unknowns. One function $M(u)$ cannot stand in for all components of (eq:semiclassical). Advanced coordinate $v$ and asymptotic retarded coordinate $u$ must not be silently identified.

boundary. The preprint of del Río and Marañón-González, submitted July 13, 2026, reports a four-dimensional quasi-stationary semiclassical backreaction construction delRio2026. It is a relevant comparison, not a premise of any theorem here. The present paper makes no universal claim that four-dimensional semiclassical backreaction has never been constructed. Its narrower point is that the supplied source records do not derive the microscopic code-transfer law.