Real-Time Claims, Horizons, and Validity Limits

Every real-time holographic conclusion carries a causal contract: state-preparation contour, operator ordering, horizon or interior condition, fluctuation channel, coupling expansion, and time window. A regular classical event horizon supports infalling linear response and quasinormal decay in its saddle. An apparent horizon, a transient trapped region, or a horizonless microstate does not inherit all of those conclusions automatically.

Required background. Schwinger–Keldysh Contours and Real-Time Bulk Geometries fixes the state and ordering, and Quasinormal Modes, Poles, and Spectral Response fixes saddle relaxation.

Helpful background. Semiclassical Breakdown Diagnostics and Causal, Killing, Trapping, and Apparent Horizons: The QFT Interface supply gravitational limits. Finite Size, Symmetry Sectors, and Scrambling False Positives and Scrambling Evidence and Claim-Status Matrix supply finite-system controls.

Horizon-dependent real-time statements

Claimed result	Required bulk input	Principal limitation
Retarded absorption	Future-horizon regularity in the prepared state	A horizonless interior requires a different boundary condition
Quasinormal decay	Stationary saddle and linearized channel	Intermediate-time saddle response, not exact finite-$N$ decay
Thermalization	Dynamical solution and observable comparison	Apparent-horizon formation is neither necessary nor sufficient for every probe
Hydrodynamization	Long-wavelength stress tensor and small residual	Does not require isotropy; depends on tolerance and frame-invariant observables
OTOC growth	Regulated contour, elastic eikonal regime, factorization	Ends before or at scrambling and is operator-dependent

The infalling retarded prescription is justified by future-horizon regularity in the selected thermal state Son and Starinets 2002. It is not a local rule that can be pasted onto any geometry containing a surface called a horizon.

A correlator across four time regimes

For a black-brane retarded correlator, separate:

1. Early transients: source shape and high-frequency response matter.

2. Quasinormal window: a few poles approximate the classical response,

   $$G_R(t,\mathbf k) \simeq-i\theta(t)\sum_nR_n(\mathbf k)e^{-i\omega_n t}.$$

3. Nonlinear or nonperturbative crossover: mode coupling, loops, or exponentially small saddles become comparable to the decayed leading term.

4. Finite-$N$ late time: discreteness, noise, and recurrences invalidate exact exponential decay.

The transition between 2 and 3 is observable-dependent. If the leading pole has damping rate $\Gamma$ and an omitted correction has size $e^{-S}$, equality occurs parametrically near

$$t_{\mathrm{cross}}\sim\frac{S}{\Gamma},$$

not at a universal geometric time. This estimate assumes the omitted contribution is approximately stationary; a growing secular term gives a different crossover.

Horizon-replacement adversary

Replace the stationary event horizon by a transient apparent horizon. The local geometry may still absorb over a finite interval, but stationarity and a global frequency-domain pole expansion are absent. Replace it instead by a smooth horizonless interior. The radial problem can have real normal modes or extremely narrow resonances rather than quasinormal absorption.

Each claim must be rederived:

• causal retarded response follows from the full contour and interior condition;
• decay follows only over the interval in which leakage or coarse graining is effective;
• thermality requires an observable comparison, not a trapped surface alone;
• exact unitarity cannot be inferred from a classical causal diagram.

The time-dependent numerical framework of Chesler and Yaffe 2014 illustrates why constraints, slicing, and boundary one-point functions must be tracked together.

Evidence ceiling and handoff

Evidence cutoff: 25 July 2026. Classical horizons robustly organize leading retarded response, hydrodynamics, and chaos in controlled top-down or EFT saddles. They do not determine exact finite-$N$ late time or prove that a different interior with similar coarse exterior observables has the same microscopic response.

Curved-spacetime QFT owns horizon taxonomy and semiclassical validity; Thermal and Nonequilibrium QFT owns general real-time methods. The next page treats exact spectral discreteness.

The chapter overview contains the structure diagram and validity and failure diagram. They are embedded there once so that their shared chapter-level context is not repeated on every article.

For the chapter-wide comparison of assumptions, counterevidence, falsifiers, and claim ceilings, see the claim-domain table.

References

• Chesler, Paul M., and Laurence G. Yaffe. “Numerical Solution of Gravitational Dynamics in Asymptotically Anti-de Sitter Spacetimes.” Journal of High Energy Physics 2014, 086 (2014). doi:10.1007/JHEP07(2014)086.
• Son, Dam T., and Andrei O. Starinets. “Minkowski-Space Correlators in AdS/CFT Correspondence: Recipe and Applications.” Journal of High Energy Physics 2002, 042 (2002). doi:10.1088/1126-6708/2002/09/042.