Quantum enforcement of strong cosmic censorship

Abstract

We show that the trace anomaly of quantum field theory is sufficient to enforce strong cosmic censorship in any stationary spacetime with an inner horizon of nonzero surface gravity. In the two-dimensional dilaton reduction of four-dimensional Einstein-Maxwell theory coupled to $N$ conformal fields, the anomaly-induced Polyakov term yields a finite $\langle T_{vv}\rangle \to \frac{N}{48π}κ_-^2$ near the Cauchy horizon, while the affine-frame energy grows as $T_{kk}\propto e^{2κ_- v}$. The resulting tidal blow-up converts the inner horizon into a null, Tipler-strong singularity. The mechanism is local, universal, and state-independent, and extends to Kerr/Kerr-Newman, $Λ>0$, and nonsingular interiors. Thus, the trace anomaly is the minimal quantum ingredient restoring strong cosmic censorship.

Figures (1)

• Figure 1: Causal structure of the Reissner–Nordström interior. A timelike geodesic $P$ from initial data on a complete Cauchy surface $S$ crosses the classical Cauchy horizon $r_-$ in finite proper time without curvature blow-up, leading to loss of predictability. Including the trace anomaly, the inner horizon becomes a null singularity, thereby restoring strong cosmic censorship.