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arxiv: 1907.08960 · v1 · pith:25MDU742new · submitted 2019-07-21 · ❄️ cond-mat.mes-hall · gr-qc· physics.comp-ph· quant-ph

Exploring Event Horizons and Hawking Radiation through Deformed Graphene Membranes

Tommaso Morresi , Daniele Binosi , Stefano Simonucci , Riccardo Piergallini , Stephan Roche , Nicola M. Pugno , Simone Taioli This is my paper

Pith reviewed 2026-05-24 18:43 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall gr-qcphysics.comp-phquant-ph
keywords grapheneanalogue gravityHawking radiationpseudosphereevent horizonlocal density of statescurved spacetimeDirac fermions
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The pith

Graphene deformed into pseudospheres forms analogue event horizons where the local density of states becomes thermal at tens of Kelvin.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates shaping graphene sheets into surfaces of constant negative curvature to create laboratory analogues of curved spacetime. Large-scale simulations are used to test whether such deformed membranes remain energetically stable and whether the atomic spacing permits an analogue horizon to appear. The work reports that the local density of states evaluated near this horizon follows a thermal distribution with a temperature of a few tens of Kelvin. This would open a solid-state route to studying the quantum dynamics of fields in curved geometries without relying on ultracold atomic gases.

Core claim

Shaping a graphene membrane into a Beltrami pseudosphere produces an energetically stable structure in which the ratio of carbon-carbon bond length to pseudosphere radius is small enough for an analogue event horizon to form; the local density of states near that horizon exhibits a thermal spectrum with characteristic temperatures of a few tens of Kelvin.

What carries the argument

Beltrami's pseudosphere, a surface of constant negative curvature, deforms the graphene lattice to induce an analogue event horizon for its Dirac-like electronic excitations.

If this is right

  • Energetically stable negative-curvature graphene surfaces can be realized.
  • The bond-length to radius ratio is small enough to allow horizon formation.
  • The local density of states at the horizon has a thermal character.
  • The setup provides a solid-state platform for investigating quantum many-body dynamics in curved spacetime.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Experimental fabrication of the deformed membranes would allow direct tests of the predicted thermal spectrum.
  • The tens-of-Kelvin temperature scale places the effect within reach of standard cryogenic measurement techniques.
  • The same curvature-engineering approach could be applied to other atomically thin materials to broaden the range of analogue systems.

Load-bearing premise

The ratio between the carbon-carbon bond length and the pseudosphere radius remains small enough for a horizon to form while the deformed membrane stays energetically stable.

What would settle it

A direct calculation or measurement showing that the local density of states immediately outside the proposed horizon does not follow a thermal distribution would falsify the central claim.

Figures

Figures reproduced from arXiv: 1907.08960 by Daniele Binosi, Nicola M. Pugno, Riccardo Piergallini, Simone Taioli, Stefano Simonucci, Stephan Roche, Tommaso Morresi.

Figure 1
Figure 1. Figure 1: FIG. 1. Tiling the hyperbolic plane by three-coordinated tessellations realized by an all- [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. LDOS symmetry breaking due to curvature effetcs. [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Evaluation of the LDOS through a multi-orbital TB [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Detecting the presence of an event horizon through [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Bond switch and dualization procedures. a) An example of a bond-switch trial move in a graphene lattice. Starting [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Determination of the parameters for the multi-orbital TB algorithm and corresponding reference LDOS calculations. [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

Analogue gravitational systems are becoming an increasing popular way of studying the behaviour of quantum systems in curved spacetime. Setups based on ultracold quantum gases in particular, have been recently harnessed to explore the thermal nature of Hawking's and Unruh's radiation that was theoretically predicted almost 50 years ago. For solid state implementations, a promising system is graphene, in which a link between the Dirac-like low-energy electronic excitations and relativistic quantum field theories has been unveiled soon after its discovery. Here we show that this link extends to the case of curved quantum field theory when the graphene sheet is shaped in a surface of constant negative curvature, known as Beltrami's pseudosphere. Thanks to large-scale simulations, we provide numerical evidence that energetically stable negative curvature graphene surfaces can be realized; the ratio between the carbon-carbon bond length and the pseudosphere radius is small enough to allow the formation of an horizon; and the associated Local Density Of States evaluated at horizon's proximity has a thermal nature with a characteristic temperature of few tens of Kelvin. Such findings pave the way to the realization of a solid-state system in which the curved spacetime dynamics of quantum many body systems can be investigated.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes shaping graphene into Beltrami's pseudosphere to realize an analogue of curved spacetime, claiming that large-scale simulations demonstrate energetic stability of the deformation, a sufficiently small carbon-carbon bond length to pseudosphere radius ratio to permit horizon formation and a continuum Dirac description, and a thermal local density of states (LDOS) near the horizon with temperature of a few tens of Kelvin.

Significance. If the numerical results hold under scrutiny, the work would establish a solid-state platform for investigating Hawking radiation and quantum field theory in curved spacetime, complementing ultracold-atom analogues with a potentially more accessible condensed-matter system.

major comments (2)
  1. [Abstract] Abstract: the central claims of energetic stability, horizon formation, and thermal LDOS rest on large-scale simulations, yet no error bars, convergence tests with respect to system size or discretization, or validation against known flat-graphene or analytic limits are reported, leaving the robustness of the thermal fit and the stability conclusion unassessable.
  2. [Abstract] Abstract: the key premise that the carbon-carbon bond length to pseudosphere radius ratio remains small enough for both horizon formation and a valid continuum Dirac description is invoked to support the LDOS result, but no quantitative value of this ratio, nor any check that the deformation remains stable at that ratio, is supplied.
minor comments (1)
  1. [Abstract] Abstract, line 2: 'an increasing popular way' should read 'an increasingly popular way'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each point below and will revise the manuscript to incorporate additional details on our simulations.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claims of energetic stability, horizon formation, and thermal LDOS rest on large-scale simulations, yet no error bars, convergence tests with respect to system size or discretization, or validation against known flat-graphene or analytic limits are reported, leaving the robustness of the thermal fit and the stability conclusion unassessable.

    Authors: We agree that the abstract (and associated presentation) does not explicitly report error bars, convergence tests, or validations, which limits assessability. The full manuscript describes the simulation setup, but to address this we will add explicit error bars on LDOS data, report convergence with system size and discretization, and include comparisons to flat-graphene LDOS and analytic limits. These will be presented in a dedicated methods or results subsection. revision: yes

  2. Referee: [Abstract] Abstract: the key premise that the carbon-carbon bond length to pseudosphere radius ratio remains small enough for both horizon formation and a valid continuum Dirac description is invoked to support the LDOS result, but no quantitative value of this ratio, nor any check that the deformation remains stable at that ratio, is supplied.

    Authors: The referee is correct that a specific numerical value for the bond-length-to-radius ratio and an explicit stability check at that ratio are not supplied in the abstract. We will revise the manuscript to state the quantitative ratio achieved in the simulations and include supporting data or analysis confirming energetic stability at that ratio, thereby justifying horizon formation and the continuum Dirac description. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central claims rest on large-scale numerical simulations that demonstrate energetic stability of the pseudosphere deformation, a sufficiently small bond-length to radius ratio, and an LDOS near the horizon that matches an external thermal distribution at tens of Kelvin. No equation or step reduces a reported temperature or stability metric to a parameter fitted from the same data by construction, nor does any load-bearing premise rely on a self-citation chain or imported uniqueness theorem. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the continuum Dirac approximation remaining valid on a discrete lattice with negative curvature, on the pseudosphere geometry being realizable without prohibitive strain energy, and on the simulation faithfully reproducing the curved-spacetime metric; none of these are independently verified in the abstract.

axioms (1)
  • domain assumption Graphene low-energy excitations obey a Dirac equation that can be mapped onto a curved spacetime metric when the sheet is deformed into a pseudosphere.
    Invoked when the abstract states that the link between Dirac-like excitations and relativistic QFT extends to curved spacetime.

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