The magic of the gravitational vacuum

Abstract: The black hole information paradox challenges us to do something that is seemingly impossible: find a violation of the semiclassical approximation in a region where all curvatures are low. The vecro hypothesis proposes a structure of the gravitational vacuum that can accomplish this task. In this article we explain the hypothesis, and give a lattice model to describe the essence of its idea. The Hamiltonian of the model is completely local, but the vacuum exhibits correlations among planck scale fluctuations which fall off relatively slowly with distance. These extended-scale correlations are able to `feel around' the region where a closed trapped surface is about to form, and to react by nucleating fuzzball structure that destroys semiclassical spacetime.

• The paper demonstrates that semiclassical gravity fails to resolve black hole information loss due to extended vacuum correlations triggering a shift to fuzzball dynamics.
• A lattice model inspired by the toric code is developed to simulate vecro dynamics, illustrating how local interactions foster the formation of fuzzball microstates.
• The analysis aligns fuzzball paradigm with string theory, maintaining causality and locality while rejecting nonlocal wormhole scenarios in resolving the paradox.

Summary of "The magic of the gravitational vacuum" (2606.20334)

The Black Hole Information Paradox and Semiclassical Gravity

The paper systematically addresses the black hole information paradox, emphasizing that semiclassical gravity, even in regions of low curvature ($\mathcal{R} \ll l_p^{-2}$), is fundamentally insufficient to resolve the paradox. Semiclassical analysis predicts information loss, or the necessity of Planck-scale remnants with infinite internal entropy, neither of which is tenable given the unitarity observed in string theoretic constructions and AdS/CFT duality. The author reviews the mechanism of information loss via monotonically increasing entanglement in Hawking radiation as well as the limitations of small corrections to Hawking's calculation, referencing the small corrections theorem which shows that only $O(1)$ modifications can alter the entanglement trajectory [Mathur:2009hf].

Fuzzball Microstates and the Vecro Hypothesis

Within string theory, explicit constructions demonstrate that black hole microstates are fuzzballs: horizonless, extended quantum objects radiating from their surfaces, circumventing the usual pair-production mechanism of Hawking radiation. The challenge then shifts to explaining the dynamical formation of fuzzballs from collapsing matter within a local, causal theory, especially as classical causality prevents signals from escaping the event horizon in semiclassical collapse.

The paper introduces the Vecro Hypothesis: the gravitational vacuum contains correlations among Planck-scale fluctuations that fall off as a power law, rather than exponentially, enabling these correlations to "feel" when a region is approaching closed trapped surface formation. This structure is motivated by the existence of exponentially many fuzzball microstates, each an extended bound state analogous to mesons or benzene rings in QFT, but with a size exceeding the classical horizon.

Lattice Model for Gravitational Vacuum: Modified Toric Code

To concretize the essence of the Vecro Hypothesis, the paper develops a lattice model inspired by the toric code [Kitaev:1997wr], a local Hamiltonian whose ground state is a superposition over extended loop configurations on the dual lattice. These loops, analogous to vecros, exhibit long-range correlations, even though all interactions are strictly local. The model is dynamically modified by introducing a "gravitational field" (a local energy penalty for loops inside a region $\mathcal{S}$), resulting in suppressed loop density $P(x)$ in regions with strong gravitational fields.

When gravitational field strength exceeds a critical threshold, it becomes energetically favorable for loops to terminate on magnetic charges (monopoles) at the boundary of $\mathcal{S}$, mirroring the nucleation of fuzzballs in quantum gravity when matter compresses inside its Schwarzschild radius. The extended correlations in the vacuum are crucial to tracking the gravitational field over the entire region and facilitating transition from semiclassical to fuzzball structure in a strictly local framework.

Breakdown of the Semiclassical Approximation in Low Curvature Regimes

The author analyzes time-symmetric slices of classical black hole geometries (e.g., eternal black holes), showing that the lowest energy configuration of Planck-scale fluctuations (under vecro dynamics) necessarily develops a spike in energy density at the horizon due to infinite redshift, leading to a condensation of fuzzball structure at $r=2M$—even though curvature remains low. Only the lowest energy state, with optimal extended correlations, is permitted as a semiclassical geometry; Hartle-Hawking-like vacua are excluded for Planckian fluctuations due to their high vacuum energy density.

Implications for Black Hole Formation, Thermodynamics, and the Wormhole Paradigm

The paper clarifies that accepting the semiclassical geometry leads to information loss, and only the fuzzball paradigm, enforced by extended vacuum correlations (vecros), resolves the paradox without recourse to nonlocal Hamiltonian effects. The fuzzball construction is consistent with string theory locality and adiabatic connection to D-brane states. Furthermore, the model aligns with the universal thermodynamic properties of fuzzballs [Mathur:2023uoe, Mathur:2024mvo].

It is argued that proposals invoking wormholes (e.g., ER=EPR) to mediate information between entangled subsystems demand nonlocality incompatible with string theory's gauge-gravity duality. In fuzzball dynamics, entangled CFTs correspond to entangled fuzzballs without any Hamiltonian connection, eschewing semiclassical wormhole geometry.

Conclusion

The paper presents a robust theoretical framework, built upon local Hamiltonians with extended vacuum correlations (vecros), for dynamically resolving the black hole information paradox via the fuzzball paradigm. The Vecro Hypothesis, concretized through a lattice model, demonstrates how semiclassical approximation fails not due to high curvature, but because of a critical shift in vacuum structure induced by extended correlations. This paradigm preserves causality and locality, aligns with string theory, and avoids the pitfalls of nonlocal information transfer posited by wormhole scenarios. Future developments may refine the vecro model or explore its implications for quantum gravity, holography, and the emergence of spacetime.