Persistence of findings beyond the Hadad–Zakharov reduction

Determine whether the numerical and statistical findings obtained within the Hadad–Zakharov metric persist when solving the full Einstein equations without employing the Hadad–Zakharov reduction, i.e., within the full framework of General Relativity.

Background

The study interprets the Hadad–Zakharov metric as a reduction of General Relativity and demonstrates, in the weakly nonlinear wave-turbulence regime, an equivalence between certain subsets of Einstein’s equations.

However, outside these assumptions and numerically, satisfying all Einstein equations simultaneously is challenging. Thus, it remains an open issue whether the reported turbulence properties are robust in full General Relativity.

References

Finally, it remains to be determined whether these findings persist within the full framework of General Relativity, beyond the specific Hadad–Zakharov reduction employed here.

— Towards Gravitational Wave Turbulence within the Hadad-Zakharov metric  (2603.29699 - Gay et al., 31 Mar 2026) in Conclusion (Section 5)

This motivates the following working conjecture. Sufficiently weak initial data supported near the AdS boundary may possess an intermediate time interval during which their boundary response is governed predominantly by the linearized vacuum geometry. If subleading contributions decay before the evolution probes the finite-area apparent horizon present in the full bulk geometry or backreaction becomes important, the boundary stress-energy tensor will be driven toward $P_L/\varepsilon=0$. At later times, this approximation breaks down, and the full bulk geometry and dynamics drive the system toward hydrodynamization. IR-supported data need not pass through this intermediate regime. The conjecture predicts that the near-zero-$P_L$ interval should become more pronounced as the initial data are made weaker and more sharply UV-localized. Testing these predictions in nonlinear evolutions is part of the ongoing work.

— Hydrodynamic attractors  (2609.09114 - Enss et al., 8 Sep 2026) in Section 2.3, subsection “Hydrodynamic attractors in holography”