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arxiv: 2604.07915 · v1 · submitted 2026-04-09 · ✦ hep-th · gr-qc

Recognition: 2 theorem links

· Lean Theorem

Rindler Physics with a UV Cutoff on the Lattice

Seiken Chikazawa , Seiji Terashima
Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:43 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords Rindler spaceUnruh effectUV cutofflattice regularizationstretched horizonMinkowski vacuumretarded Green functionUnruh-DeWitt detector
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The pith

A lattice UV cutoff in Rindler coordinates makes the Minkowski vacuum non-thermal with respect to the local Rindler Hamiltonian, yet correlation functions and detector responses approach the expected thermal form far from the horizon in the

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

The paper places a free scalar field on a spatial lattice in Rindler coordinates to impose a UV cutoff. It shows that the global Minkowski vacuum is not an exact thermal state for the local lattice Rindler Hamiltonian. Nevertheless, the two-point Wightman function and the response of an Unruh-DeWitt detector recover the standard thermal expressions once the lattice spacing is taken to zero, provided the observation points lie at a fixed proper distance from the horizon. The vacuum energy density matches the usual continuum result away from the horizon, but the ultraviolet divergence is replaced by a finite contribution localized at a stretched horizon whose width is set by the cutoff. The retarded propagator acquires an additional reflected component, indicating that waves propagating toward the horizon are reflected at a distance of order the lattice spacing.

Core claim

Once a UV cutoff is introduced via lattice regularization in Rindler coordinates, the global Minkowski vacuum and the wedge description based on the local Rindler Hamiltonian cease to be equivalent at the level of operators; exact thermality is lost, but the Unruh effect remains intact for all operational probes whose support lies sufficiently far from the horizon in the continuum limit, with the horizon singularity regularized into a stretched-horizon contribution.

What carries the argument

Lattice discretization of a free scalar field in Rindler coordinates, which defines both the local Rindler Hamiltonian and the regulated correlation functions that are compared to the Minkowski vacuum.

If this is right

  • The global Minkowski description and the local Rindler wedge description become inequivalent at the operator level once a cutoff is present.
  • The vacuum energy density agrees with the standard continuum expression at distances much larger than the cutoff but is replaced by a finite stretched-horizon term near the horizon.
  • The retarded Green function develops a reflected component, so that an ingoing wave packet is reflected at a proper distance of order the cutoff.
  • Exact thermality of the Minkowski vacuum with respect to the Rindler Hamiltonian is lost, while operational thermality for distant probes is recovered in the continuum limit.

Where Pith is reading between the lines

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

  • The stretched-horizon reflection supplies a concrete, cutoff-scale mechanism that could be used to model black-hole horizon dynamics in other regulated theories.
  • Lattice simulations of this setup could be used to test whether similar operational thermality persists for interacting fields or in higher dimensions.
  • The loss of operator-level equivalence between global and wedge descriptions may constrain attempts to define local observables near a horizon in any UV-regulated quantum gravity model.

Load-bearing premise

The chosen lattice spacing and coordinate discretization capture the short-distance physics of the continuum theory without leaving behind cutoff-dependent artifacts that persist for observables at fixed proper distance from the horizon.

What would settle it

An explicit computation, at fixed proper distance from the horizon, of the lattice-regulated detector response or Wightman function that remains visibly non-thermal even after the continuum limit is taken would falsify the operational recovery of the Unruh effect.

Figures

Figures reproduced from arXiv: 2604.07915 by Seiji Terashima, Seiken Chikazawa.

Figure 1
Figure 1. Figure 1: Penrose diagram of Rindler spacetime. Let us consider a massless free scalar field ϕ on Rindler spacetime. The action is S = − 1 2 Z d 2x √ −ggµν∂µϕ ∂νϕ (2.4) = Z d 2x  1 2κx (∂tϕ) 2 − κx 2 (∂xϕ) 2  ≡ Z d 2xL, (2.5) and the canonical momentum π conjugate to ϕ, the Hamiltonian density H, and the Hamil￾tonian H are π = ∂L ∂(∂tϕ) = 1 κx ∂tϕ, (2.6) H = π(∂tϕ) − L = 1 2 κx π2 + 1 2 κx (∂xϕ) 2 , (2.7) H = Z dx… view at source ↗
Figure 2
Figure 2. Figure 2: n-dependence and N-dependence of λn. where x = 1 κ e κξ , (2.22) and then the theory is equivalent to the theory on ds 2 = − dt 2 + dξ 2 for the massless scalar field. The space-like size is ln(xN /x1)/κ ∼ ln N/κ and the spectrum is consistent with (2.20), even though the lattice is not equal spacing in ξ. Note that the light spectrum (2.20) for n ≪ ln N will correspond to the light modes of the brick wall… view at source ↗
Figure 3
Figure 3. Figure 3: Plots of a 2 ⟨T00⟩ (left) and a 2 (n − 1 2 ) 2 ⟨T00⟩ (right) for N = 10000. The yellow lines represent the continuum theory [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of a field reflected by the stretched horizon. [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Plot of −ia2 q (j1 − 1 2 )(j2 − 1 2 ) Gj1,j2 . We set N = 10000, j1 = 100, j2 = 1000, and normalize to κ = 1. In the following, we set κ = 1. The plot in [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Plots of Nn,n (left) and ln Nn,n (right) for N = 10000. The yellow line in the left figure is the Bose distribution, and the yellow line in the right figure is the Bose distribution for λn ≫ 1. 0 20 40 60 80 100 λn −0.3 −0.2 −0.1 0.0 0.1 0.2 0.3 0.4 Nn,n+1 [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Plot of Nn,n+1 calculated for N = 10000. The quantity Nn,n deviates significantly from the thermal distribution, and as an example of the case m ̸= n, Nn,n+1 takes a non-zero value. As n becomes larger, the magnitude of Nn,n+1 becomes relatively smaller, which indicates that entanglement between different energy levels in |0⟩M occurs predominantly among low-energy modes. The large deviation of Nn,n from th… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of the Wightman function for π between the lattice and continuum theories. We set N = 10000, j1 = 50, and κ = 1. Since the oscillation frequency changes with time t, we apply Gaussian smearing with a width of 0.05 for 0 < t < 1 and a width of 0.5 for t ≥ 1. The effect of introducing a UV cutoff in the Wightman function, namely the appearance of the brick wall, becomes visible for t ≫ 1. To obser… view at source ↗
Figure 9
Figure 9. Figure 9: Plot of a 2W(t − iε) for N = 10000, j1 = 50, κ = 1, and ε = 0.15. −0.4 −0.2 0.0 0.2 0.4 0.6 a 2 W(t) Raw Numerical Data Re [a 2W(t)] Re [a 2Wconti(t)] 0 5 10 15 20 25 t −0.4 −0.2 0.0 0.2 0.4 0.6 a 2 W(t) Raw Numerical Data Im [a 2W(t)] Im [a 2Wconti(t)] [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: A reduced version of Fig. 8 [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
read the original abstract

We investigate quantum field theory in Rindler space with a UV cutoff by considering a free scalar field on a lattice in Rindler coordinates. We find that the Minkowski vacuum is not exactly thermal with respect to the local lattice Rindler Hamiltonian. Nevertheless, for observables sufficiently far from the horizon, the Wightman function and the Unruh--DeWitt detector response reproduce the expected thermal behavior in the continuum limit. Thus, the Unruh effect survives operationally, even though exact thermality is lost at the state level. We also show that the Rindler vacuum energy density reproduces the standard continuum behavior away from the horizon, while the UV singularity at the horizon is replaced by a stretched-horizon contribution. Furthermore, the retarded Green function exhibits a component reflected at the stretched horizon, implying that an ingoing wave packet is reflected at a proper distance of order the cutoff. This provides an effective brick-wall picture in the UV-regulated theory. Our analysis suggests that, once a cutoff is introduced, the global Minkowski description and the wedge description based on a local Rindler Hamiltonian are no longer equivalent at the operator level.

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 / 2 minor

Summary. The manuscript studies a free scalar field quantized on a lattice in Rindler coordinates, thereby imposing a UV cutoff. It reports that the Minkowski vacuum is not exactly thermal with respect to the local lattice Rindler Hamiltonian. Nevertheless, the Wightman function and the response of an Unruh-DeWitt detector recover the standard thermal Unruh spectrum for points at fixed proper distance from the horizon once the continuum limit is taken. The Rindler vacuum energy density is shown to match the continuum result away from the horizon, with the UV divergence replaced by a finite stretched-horizon contribution; the retarded Green function acquires a reflected component, furnishing an explicit lattice realization of the brick-wall model. The authors conclude that the global Minkowski and local Rindler descriptions cease to be equivalent at the operator level once a cutoff is present.

Significance. If the continuum limit is under control, the work supplies a concrete, non-perturbative lattice realization of how a UV regulator modifies Rindler physics. It gives explicit evidence that operational thermality (Wightman functions and detector response) can survive even when exact thermality at the state level is lost, and it furnishes a microscopic picture of a stretched horizon together with brick-wall reflection. These results are directly relevant to ongoing discussions of black-hole thermodynamics in regulated theories and to the operational status of the Unruh effect.

major comments (2)
  1. [§3 (Wightman function and continuum limit)] The central claim that the Wightman function and Unruh-DeWitt response recover the exact thermal form for observables at fixed proper distance d ≫ a in the a → 0 limit rests on the assumption that the chosen Rindler-coordinate lattice discretization introduces no persistent artifacts. Because the proper spatial spacing is a/ρ (with ρ the Rindler radial coordinate), the local UV cutoff is position-dependent. The manuscript must demonstrate, either analytically or numerically, that the contribution of near-horizon lattice modes to the mode sum (or Bogoliubov coefficients) vanishes uniformly at fixed proper distance; without such a control, the operational recovery could be an artifact of the regulator.
  2. [§5 (Retarded Green function)] The statement that the retarded Green function exhibits reflection at a proper distance of order the cutoff (the brick-wall picture) is load-bearing for the claim of an effective stretched horizon. The precise location of the reflection point, its dependence on the lattice spacing a, and the coefficient of the reflected wave must be extracted explicitly from the lattice retarded propagator; a qualitative description is insufficient to establish that the reflection survives the continuum limit at fixed proper distance.
minor comments (2)
  1. The abstract and introduction introduce the term 'stretched horizon' without a brief definition or reference to the original brick-wall literature; a short clarifying sentence would aid readers.
  2. Notation for the lattice spacing, Rindler coordinate ρ, and proper distance should be introduced once and used consistently; occasional switches between coordinate and proper-distance language obscure the discussion of the position-dependent cutoff.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments. We address each major comment below and will revise the manuscript to incorporate the requested clarifications and explicit demonstrations.

read point-by-point responses

  1. Referee: [§3 (Wightman function and continuum limit)] The central claim that the Wightman function and Unruh-DeWitt response recover the exact thermal form for observables at fixed proper distance d ≫ a in the a → 0 limit rests on the assumption that the chosen Rindler-coordinate lattice discretization introduces no persistent artifacts. Because the proper spatial spacing is a/ρ (with ρ the Rindler radial coordinate), the local UV cutoff is position-dependent. The manuscript must demonstrate, either analytically or numerically, that the contribution of near-horizon lattice modes to the mode sum (or Bogoliubov coefficients) vanishes uniformly at fixed proper distance; without such a control, the operational recovery could be an artifact of the regulator.

    Authors: We agree that an explicit demonstration is required to rule out persistent artifacts from the position-dependent cutoff. The discretization is uniform in the Rindler coordinate, so the proper spacing a/ρ becomes fine at any fixed d > 0 as a → 0. In the revised manuscript we will add both an analytical bound showing that the contribution of modes with ρ ≲ a to the Bogoliubov coefficients (and hence to the Wightman function) at fixed d decays at least as a power of a, and numerical evaluations of the mode sum and detector response for several decreasing values of a at fixed d, confirming uniform approach to the thermal result. revision: yes

  2. Referee: [§5 (Retarded Green function)] The statement that the retarded Green function exhibits reflection at a proper distance of order the cutoff (the brick-wall picture) is load-bearing for the claim of an effective stretched horizon. The precise location of the reflection point, its dependence on the lattice spacing a, and the coefficient of the reflected wave must be extracted explicitly from the lattice retarded propagator; a qualitative description is insufficient to establish that the reflection survives the continuum limit at fixed proper distance.

    Authors: We accept that a qualitative statement is insufficient. In the revised version we will compute the lattice retarded propagator explicitly and report the extracted reflection point (found to lie at proper distance of order a), its scaling with a, and the amplitude of the reflected component. These quantities will be presented for a sequence of lattice spacings, demonstrating that the reflection persists at fixed proper distance in the continuum limit and thereby furnishing a quantitative lattice realization of the brick-wall model. revision: yes

Circularity Check

0 steps flagged

No circularity: direct lattice construction yields independent results

full rationale

The paper performs an explicit lattice discretization of a free scalar field in Rindler coordinates, computes the Minkowski vacuum with respect to the local Rindler Hamiltonian, and takes the continuum limit for observables at fixed proper distance from the horizon. All reported behaviors (loss of exact thermality, recovery of thermal Wightman functions and detector response, stretched-horizon energy density, and reflected retarded propagator) are obtained by direct summation over lattice modes and Bogoliubov transformations without any parameter fitting, self-referential definitions, or load-bearing self-citations. The central operational-versus-state distinction follows immediately from the lattice operator algebra and does not reduce to any input quantity by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claims rest on a lattice discretization of a free scalar field whose continuum limit is assumed to reproduce standard Rindler physics away from the horizon; the lattice spacing itself functions as the sole regulator.

free parameters (1)
  • lattice spacing a
    Implements the UV cutoff; taken to zero to recover continuum results for far observables.
axioms (1)
  • domain assumption Free massless scalar field on a lattice in Rindler coordinates
    The discretization is taken to preserve the essential causal structure and vacuum properties of the continuum theory.
invented entities (1)
  • stretched horizon no independent evidence
    purpose: Finite replacement for the UV singularity at the Rindler horizon
    Emerges automatically from the lattice cutoff and produces reflection of wave packets.

pith-pipeline@v0.9.0 · 5488 in / 1394 out tokens · 71075 ms · 2026-05-10T17:43:33.158741+00:00 · methodology

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Reference graph

Works this paper leans on

36 extracted references · 24 canonical work pages · 3 internal anchors

  1. [1]

    Kruskal Space and the Uniformly Accelerated Frame,

    W. Rindler, “Kruskal Space and the Uniformly Accelerated Frame,”Am. J. Phys.34 (1966) 1174

    1966

  2. [2]

    Notes on black hole evaporation,

    W. G. Unruh, “Notes on black hole evaporation,”Phys. Rev. D14(1976) 870

    1976

  3. [3]

    Particle Creation by Black Holes,

    S. W. Hawking, “Particle Creation by Black Holes,”Commun. Math. Phys.43(1975) 199–220. [Erratum: Commun.Math.Phys. 46, 206 (1976)]. 12If one discretizes the local BW ansatz [5]Kloc BW∝ ∫ x>0xT 00 dxusing the same midpoint prescription as in our paper, then one essentially reproduces our lattice Rindler Hamiltonian, with the kinetic term weighted byxn = (n...

    1975

  4. [4]

    Thermo field dynamics of black holes,

    W. Israel, “Thermo field dynamics of black holes,”Phys. Lett. A57(1976) 107–110

    1976

  5. [5]

    On the Duality Condition for Quantum Fields,

    J. J. Bisognano and E. H. Wichmann, “On the Duality Condition for Quantum Fields,”J. Math. Phys.17(1976) 303–321

    1976

  6. [6]

    Lattice Unruh effect and world-line entanglement for the XXZ chain,

    K. Okunishi and K. Seki, “Lattice Unruh effect and world-line entanglement for the XXZ chain,”J. Phys. Soc. Jap.88no. 11, (2019) 114002,arXiv:1906.10441 [cond-mat.quant-gas]

    work page arXiv 2019

  7. [7]

    Spin systems as quantum simulators of quantum field theories in curved spacetimes,

    S. Kinoshita, K. Murata, D. Yamamoto, and R. Yoshii, “Spin systems as quantum simulators of quantum field theories in curved spacetimes,”Phys. Rev. Res.7no. 2, (2025) 023197,arXiv:2410.07587 [hep-th]

    work page arXiv 2025

  8. [8]

    Simulating quantum field theory in curved spacetime with quantum many-body systems,

    R.-Q. Yang, H. Liu, S. Zhu, L. Luo, and R.-G. Cai, “Simulating quantum field theory in curved spacetime with quantum many-body systems,”Phys. Rev. Res.2no. 2, (2020) 023107,arXiv:1906.01927 [gr-qc]

    work page arXiv 2020

  9. [9]

    Quantum simulation of Hawking radiation and curved spacetime with a superconducting on-chip black hole,

    Y.-H. Shiet al., “Quantum simulation of Hawking radiation and curved spacetime with a superconducting on-chip black hole,”Nature Commun.14no. 1, (2023) 3263, arXiv:2111.11092 [quant-ph]

    work page arXiv 2023

  10. [10]

    Rindler bulk reconstruction and subregion duality in AdS/CFT,

    S. Sugishita and S. Terashima, “Rindler bulk reconstruction and subregion duality in AdS/CFT,”JHEP11(2022) 041,arXiv:2207.06455 [hep-th]

    work page arXiv 2022

  11. [11]

    Nonuniqueness of canonical field quantization in Riemannian space-time,

    S. A. Fulling, “Nonuniqueness of canonical field quantization in Riemannian space-time,”Phys. Rev. D7(1973) 2850–2862

    1973

  12. [12]

    Quantum Field Theory in Schwarzschild and Rindler Spaces,

    D. G. Boulware, “Quantum Field Theory in Schwarzschild and Rindler Spaces,”Phys. Rev. D11(1975) 1404

    1975

  13. [13]

    On the vacuum stress induced by uniform acceleration or supporting the ether,

    P. Candelas and D. Deutsch, “On the vacuum stress induced by uniform acceleration or supporting the ether,”Proc. Roy.Soc. Lond. A354(1977) 79–99

    1977

  14. [14]

    The Energy momentum tensor in Fulling-Rindler vacuum,

    R. Parentani, “The Energy momentum tensor in Fulling-Rindler vacuum,”Class. Quant. Grav.10(1993) 1409–1416,arXiv:hep-th/9303062

    work page arXiv 1993

  15. [15]

    Kawamoto and S

    T. Kawamoto and S. Terashima to appear

  16. [16]

    The Large N Limit of Superconformal Field Theories and Supergravity

    J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,”Adv. Theor. Math. Phys.2(1998) 231–252,arXiv:hep-th/9711200

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  17. [17]

    Eternal Black Holes in AdS

    J. M. Maldacena, “Eternal black holes in anti-de Sitter,”JHEP04(2003) 021, arXiv:hep-th/0106112

    work page Pith review arXiv 2003

  18. [18]

    On the Quantum Structure of a Black Hole,

    G. ’t Hooft, “On the Quantum Structure of a Black Hole,”Nucl. Phys. B256(1985) 727–745. 26

    1985

  19. [19]

    The Stretched Horizon and Black Hole Complementarity

    L. Susskind, L. Thorlacius, and J. Uglum, “The Stretched horizon and black hole complementarity,”Phys. Rev. D48(1993) 3743–3761,arXiv:hep-th/9306069

    work page Pith review arXiv 1993

  20. [20]

    The fuzzball proposal for black holes: an elementary review

    S. D. Mathur, “The Fuzzball proposal for black holes: An Elementary review,” Fortsch.Phys.53(2005) 793–827,arXiv:hep-th/0502050

    work page Pith review arXiv 2005

  21. [21]

    Black Holes: Complementarity or Firewalls?

    A. Almheiri, D. Marolf, J. Polchinski, and J. Sully, “Black Holes: Complementarity or Firewalls?,”JHEP02(2013) 062,arXiv:1207.3123 [hep-th]

    work page Pith review arXiv 2013

  22. [22]

    Iizuka and S

    N. Iizuka and S. Terashima, “Brick Walls for Black Holes in AdS/CFT,”Nucl. Phys. B895(2015) 1–32,arXiv:1307.5933 [hep-th]

    work page arXiv 2015

  23. [23]

    Simple bulk reconstruction in anti-de Sitter/conformal field theory correspondence,

    S. Terashima, “Simple bulk reconstruction in anti-de Sitter/conformal field theory correspondence,”PTEP2023no. 5, (2023) 053B02,arXiv:2104.11743 [hep-th]

    work page arXiv 2023

  24. [24]

    Subregion Complementarity in AdS/CFT

    S. Sugishita and S. Terashima, “Subregion Complementarity in AdS/CFT,” arXiv:2309.04231 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  25. [25]

    Bulk reconstruction and gauge invariance,

    S. Sugishita and S. Terashima, “Bulk reconstruction and gauge invariance,”Phys. Rev. D112no. 4, (2025) 046003,arXiv:2409.02534 [hep-th]

    work page arXiv 2025

  26. [26]

    Holography at Finite N: Breakdown of Bulk Reconstruction for Subregions,

    S. Terashima, “Holography at Finite N: Breakdown of Bulk Reconstruction for Subregions,”arXiv:2508.11592 [hep-th]

    work page arXiv

  27. [27]

    AdS/CFT Correspondence in Operator Formalism,

    S. Terashima, “AdS/CFT Correspondence in Operator Formalism,”JHEP02(2018) 019,arXiv:1710.07298 [hep-th]

    work page arXiv 2018

  28. [28]

    Classical Limit of Large N Gauge Theories with Conformal Symmetry,

    S. Terashima, “Classical Limit of Large N Gauge Theories with Conformal Symmetry,”JHEP02(2020) 021,arXiv:1907.05419 [hep-th]

    work page arXiv 2020

  29. [29]

    Bulk locality in the AdS/CFT correspondence,

    S. Terashima, “Bulk locality in the AdS/CFT correspondence,”Phys. Rev. D104 no. 8, (2021) 086014,arXiv:2005.05962 [hep-th]

    work page arXiv 2021

  30. [30]

    Rindler Quantum Gravity,

    B. Czech, J. L. Karczmarek, F. Nogueira, and M. Van Raamsdonk, “Rindler Quantum Gravity,”Class. Quant. Grav.29(2012) 235025,arXiv:1206.1323 [hep-th]

    work page arXiv 2012

  31. [31]

    Stretched horizon dissipation and the fate of echoes,

    S. Terashima, “Stretched horizon dissipation and the fate of echoes,”JHEP10(2025) 147,arXiv:2506.20462 [hep-th]

    work page arXiv 2025

  32. [32]

    Testing the nature of dark compact objects: a status report

    V. Cardoso and P. Pani, “Testing the nature of dark compact objects: a status report,”Living Rev. Rel.22no. 1, (2019) 4,arXiv:1904.05363 [gr-qc]

    work page internal anchor Pith review arXiv 2019

  33. [33]

    Quantum Black Holes in the Sky,

    J. Abedi, N. Afshordi, N. Oshita, and Q. Wang, “Quantum Black Holes in the Sky,” Universe6no. 3, (2020) 43,arXiv:2001.09553 [gr-qc]. 27

    work page arXiv 2020

  34. [34]

    Firewalls as artefacts of inconsistent truncations of quantum geometries,

    C. Germani and D. Sarkar, “Firewalls as artefacts of inconsistent truncations of quantum geometries,”Fortsch.Phys.64(2016) 131–143,arXiv:1502.03129 [hep-th]

    work page arXiv 2016

  35. [35]

    Scalar particle production in Schwarzschild and Rindler metrics,

    P. C. W. Davies, “Scalar particle production in Schwarzschild and Rindler metrics,” J. Phys. A8(1975) 609–616

    1975

  36. [36]

    Quantum Field Theory in Curved Space-Time,

    B. S. DeWitt, “Quantum Field Theory in Curved Space-Time,”Phys. Rept.19 (1975) 295–357. 28

    1975