pith. sign in

arxiv: 2606.06404 · v1 · pith:44622EKKnew · submitted 2026-06-04 · ✦ hep-th · gr-qc

Smooth horizons from topology change in canonical quantum gravity

Venkatesa Chandrasekaran This is my paper

Pith reviewed 2026-06-28 00:03 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords firewall paradoxJT gravitytopology changecanonical quantum gravityblack hole interiorboost edge modesPage timeDirac observables
0
0 comments X

The pith

Topology change under the gravitational Hamiltonian eliminates the firewall branch in black hole interiors, leaving a smooth horizon.

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

The paper claims that in JT gravity the gravitational Hamiltonian induces topology-changing transitions via a pair of pants interaction that maps a single interior sector to a connected two-interior sector. After evolution over a Page time the connected branch dominates, but gluing the interior back to the exterior by quotienting with the gravitational constraints removes the branch carrying a nontrivial one-sided boost. The surviving zero-mode branch makes the horizon vacuum measurement and the early radiation purity measurement the same Dirac observable. This identification arises because Page time dynamics induces a large diffeomorphism that equates the operator algebra of the interior Hawking partner with that of the decoded early radiation.

Core claim

The gravitational Hamiltonian acts on the black hole interior through a pair of pants interaction, mapping between a single interior sector and a connected two interior sector. Evolution over a Page time causes the connected two interior branch to dominate. One of these is the naive semiclassical interior, which carries a nontrivial one sided boost upon gluing the interior back to the exterior, and hence a firewall. The other interior is a zero mode of the one sided boost generator. Gluing the interior back to the exterior quotients by the gravitational constraints, which annihilates the firewall branch. On the surviving branch, the horizon vacuum measurement and the early radiation purity m

What carries the argument

The pair of pants interaction in the gravitational Hamiltonian on the split Hilbert space with boost edge modes at the horizon, whose covariance in the crossed product algebra realizes the firewall as a one-sided boost.

If this is right

  • The firewall branch is annihilated upon gluing the interior back to the exterior via the gravitational constraints.
  • The horizon vacuum measurement and the early radiation purity measurement become the same Dirac observable on the surviving branch.
  • Page time dynamics induces a large diffeomorphism under which the operator algebra of the interior Hawking partner is identified with that of the decoded early radiation.
  • Covariance of the crossed product algebra provides a gravitational realization of the firewall as a one sided boost of the interior edge mode.

Where Pith is reading between the lines

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

  • The mechanism may extend to other models of black hole evaporation where relational time evolution is used.
  • Similar topology-changing processes could affect other interior observables beyond the boost generator.
  • The dominance of the connected branch after Page time suggests a dynamical selection rule that could be checked in numerical simulations of JT gravity.
  • The identification of measurements as Dirac observables implies that certain interior and exterior operators commute after the transition.

Load-bearing premise

The pair of pants interaction is the relevant topology changing process under the gravitational Hamiltonian and evolution over Page time causes the connected two interior branch to dominate.

What would settle it

An explicit calculation in the JT gravity model of whether the one-sided boost generator annihilates the firewall-carrying branch after Page time evolution and constraint quotienting.

Figures

Figures reproduced from arXiv: 2606.06404 by Venkatesa Chandrasekaran.

Figure 1
Figure 1. Figure 1: Penrose diagram of the AMPS setup for a one sided black hole in JT gravity with a dynamical end of the world brane. The interval from T0 to T1 denotes the O(S0) evolution needed to reach the Page time. We model an already old black hole with early radiation E of size e S0 collected in an external reservoir. In our analysis the matter sector consists only of probe degrees of freedom, e.g. internal spin stat… view at source ↗
Figure 2
Figure 2. Figure 2: Penrose diagram of the one sided black hole in JT gravity with a dynamical end of the world brane. The red curve γ(T) is the infalling observer’s worldline. The label Πbeb marks the early radiation purity measurement while Π˜bb is the horizon vacuum measurement. The cyan curve is the observer dressed slice ΣT : it starts on the end of the world brane, intersects the future horizon H at the distinguished co… view at source ↗
Figure 3
Figure 3. Figure 3: Pair of pants topology changing vertex in the extended Hilbert space description of the black hole interior. The lower horizon slot yˆ is the parent interior leg and the upper slots xˆ1, xˆ2 are the two daughter interior legs. Here a hatted label denotes the complete one leg data: xˆi = (sC,i, xi), xi = (r˜i ,˜ii), and similarly for yˆ, so each slot carries the horizon corner boost frame together with the … view at source ↗
Figure 4
Figure 4. Figure 4: Cutting, topology change, and gluing. (a) shows the full observer dressed interval ΣT from the end of the world brane, shown by the magenta endpoint, to the observer event γ(T), shown by the red endpoint, with horizon corner CT . (b) applies the cutting map C ε H , producing an interior interval Σ − T and an exterior interval Σ + T separated by cutoff ε. (c) shows the interior topology changing process 1 →… view at source ↗
Figure 5
Figure 5. Figure 5: Schwinger Keldysh contour for the inclusive connected branch probability. The interval from T0 to T1 is of order the Page time ∼ S0 and is divided into timefolds Ij of size O(1). At leading order, a pair of pants vertex at T ∈ Ij on the forward branch is paired with its adjoint at T ′ ∈ Ij ′ on the backward branch. Group averaging produces the clock propagator ⟨T ′ |T⟩ when computing the correlator. The co… view at source ↗
Figure 6
Figure 6. Figure 6: Circuit representation of the connected branch purity measurement. The input pair is |Φ⟩ b˜b1 , with unobserved state |χ0⟩Ee. The map Vs(T1) acts only on ˜b1 ⊗ Ee, producing the recovered subsystem eb and an environment, while b is unchanged. The state immediately after the channel is |Ψs(T1)⟩. After tracing out the environment, the physical purity measurement is Πbeb on b ⊗ eb, and the output legs indicat… view at source ↗
Figure 7
Figure 7. Figure 7: Bra and ket representation of the connected branch inner product. The lower pair of pants is the ket preparation 1 → 2, while the upper inverted pair of pants is the bra partner in the inclusive correlator, so the probability is represented schematically by a doubled 1 → 2 → 1 geometry. The orange squiggle denotes the dressed interior mode ˜b(xˆ1), the orange contraction line is the dressed kernel BT , and… view at source ↗
read the original abstract

We propose a resolution of the firewall paradox in JT gravity by incorporating topology change into canonical quantization under relational time evolution. The gravitational Hamiltonian acts on the black hole interior through a pair of pants interaction, mapping between a single interior sector and a connected two interior sector. To describe dynamics in the interior while keeping track of the exterior, we pass to an extended phase space description obtained by splitting the bulk Hilbert space across the event horizon. The split introduces boost edge modes at the horizon, which the Hawking modes become gravitationally dressed to. Covariance of the resulting crossed product algebra provides a precise gravitational realization of the firewall: a one sided boost of the interior edge mode relative to the exterior holding the matter fixed, or equivalently, a relative phase between the interior and exterior Hawking partners holding the edge modes fixed. Although each topology changing transition is exponentially suppressed, evolution over a Page time causes the connected two interior branch to dominate. One of these is the naive semiclassical interior, which we show carries a nontrivial one sided boost upon gluing the interior back to the exterior, and hence a firewall. The other interior is shown to be a zero mode of the one sided boost generator. Gluing the interior back to the exterior quotients by the gravitational constraints, which annihilates the firewall branch. On the surviving branch, we show the horizon vacuum measurement and the early radiation purity measurement become the same Dirac observable. Equivalently, we show that Page time dynamics induces a large diffeomorphism on the connected branch under which the operator algebra of the interior Hawking partner and that of the decoded early radiation are identified.

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

3 major / 2 minor

Summary. The manuscript proposes a resolution of the firewall paradox in JT gravity by incorporating topology change into canonical quantization under relational time evolution. The gravitational Hamiltonian is argued to act on the black hole interior via a pair-of-pants interaction that maps the single-interior sector to a connected two-interior sector. An extended phase space with boost edge modes at the horizon is introduced, leading to a crossed-product algebra whose covariance realizes the firewall as a one-sided boost. After Page time the connected branch is claimed to dominate; one sub-branch carries a nontrivial boost (firewall) while the other is a zero mode of the boost generator. Gluing the interior back to the exterior quotients by the gravitational constraints, annihilating the firewall component and identifying the horizon vacuum measurement with the early-radiation purity measurement as the same Dirac observable.

Significance. If the central identifications hold, the work supplies a concrete mechanism by which topology change plus constraint quotienting can eliminate firewalls while preserving unitarity, offering a new angle on the black-hole information problem within canonical quantum gravity. The construction of boost edge modes and the crossed-product realization of gravitational dressing are technically novel and could be useful beyond the present application.

major comments (3)
  1. [Page-time dominance argument (abstract and § on dynamics)] The claim that 'evolution over a Page time causes the connected two interior branch to dominate' is load-bearing yet unsupported by any explicit matrix-element calculation or balance between the exponential suppression of each topology-changing transition and the growth in the dimension of the connected sector; without this step the subsequent dominance argument cannot be assessed.
  2. [Gluing and constraint quotient (abstract and § on extended phase space)] The statement that gluing the interior back to the exterior 'quotients by the gravitational constraints, which annihilates the firewall branch' while preserving the zero mode of the one-sided boost generator is presented without an explicit operator-level demonstration or check that the zero-mode state lies in the kernel of the constraints after gluing; this identification is central to the resolution.
  3. [Hamiltonian action on interior (abstract and § on topology change)] The assertion that the gravitational Hamiltonian induces a pair-of-pants interaction mapping single-interior to connected two-interior sectors is introduced as an axiom without derivation from the JT action or explicit form of the interaction term in the canonical theory; this assumption underpins the entire topology-change framework.
minor comments (2)
  1. [Extended phase space construction] The definition of the crossed-product algebra and the precise action of the boost edge modes on the Hawking partners should be written out explicitly rather than left at the level of covariance statements.
  2. [Throughout] Notation for the 'connected two interior sector' and 'naive semiclassical interior' is introduced without a clear diagram or Hilbert-space decomposition that would help the reader track the branches.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We respond to each major comment below, providing clarifications from the existing arguments while acknowledging where additional explicit details can strengthen the presentation. We plan revisions accordingly.

read point-by-point responses

  1. Referee: [Page-time dominance argument (abstract and § on dynamics)] The claim that 'evolution over a Page time causes the connected two interior branch to dominate' is load-bearing yet unsupported by any explicit matrix-element calculation or balance between the exponential suppression of each topology-changing transition and the growth in the dimension of the connected sector; without this step the subsequent dominance argument cannot be assessed.

    Authors: In the dynamics section we argue that the exponential growth of the dimension of the connected two-interior Hilbert space overcomes the per-transition suppression after Page time, based on the known scaling of JT gravity state spaces. We agree an explicit matrix-element estimate would make the balance more rigorous and will add a sketch of the relevant amplitudes (drawing on standard JT transition results) in the revised manuscript. revision: partial

  2. Referee: [Gluing and constraint quotient (abstract and § on extended phase space)] The statement that gluing the interior back to the exterior 'quotients by the gravitational constraints, which annihilates the firewall branch' while preserving the zero mode of the one-sided boost generator is presented without an explicit operator-level demonstration or check that the zero-mode state lies in the kernel of the constraints after gluing; this identification is central to the resolution.

    Authors: The extended phase space section shows that after gluing the constraints identify the horizon vacuum with the early-radiation purity observable, with the nontrivial boost component annihilated because it fails to be invariant. We acknowledge that a fully explicit operator-level verification of the zero-mode kernel membership is not written out and will include this calculation in the revision. revision: partial

  3. Referee: [Hamiltonian action on interior (abstract and § on topology change)] The assertion that the gravitational Hamiltonian induces a pair-of-pants interaction mapping single-interior to connected two-interior sectors is introduced as an axiom without derivation from the JT action or explicit form of the interaction term in the canonical theory; this assumption underpins the entire topology-change framework.

    Authors: The pair-of-pants term is motivated as the canonical generator of topology change allowed by diffeomorphism invariance in the JT model with an interior boundary. While the manuscript presents it as the natural implementation, we agree a more explicit derivation from the JT action and canonical constraints would be valuable and will supply this derivation in the revised version. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation relies on model assumptions without reducing claims to self-definition or fitted inputs by construction.

full rationale

The paper's central steps invoke the gravitational Hamiltonian inducing pair-of-pants topology change, Page-time dominance of the connected branch, and constraint quotienting that annihilates the firewall branch while identifying observables. These are presented as consequences of the extended phase space and crossed-product construction in JT gravity, but the provided text supplies no equations or self-citations that make any final observable (e.g., the Dirac equivalence of horizon vacuum and radiation purity) tautologically identical to the input assumptions by construction. No fitted parameters are renamed as predictions, no uniqueness theorems are imported from prior self-work, and no ansatz is smuggled via citation. The framework is therefore self-contained against external benchmarks within the scope of the given material, consistent with a normal non-circular outcome.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

The central claim rests on several domain assumptions about relational time and the form of the Hamiltonian interaction, plus ad hoc elements like the pair of pants process and boost edge modes introduced without external falsifiable evidence. No explicit free parameters are fitted to data in the abstract.

axioms (2)
  • domain assumption Relational time evolution governs the dynamics in the interior while keeping track of the exterior.
    Invoked to describe dynamics in the interior while tracking the exterior via the split Hilbert space.
  • ad hoc to paper The gravitational Hamiltonian acts on the black hole interior through a pair of pants interaction mapping between single interior and connected two interior sectors.
    Central modeling choice for incorporating topology change.
invented entities (2)
  • Boost edge modes at the horizon no independent evidence
    purpose: To describe the split across the event horizon and gravitational dressing of Hawking modes in the extended phase space.
    Introduced by splitting the bulk Hilbert space across the event horizon; no independent evidence provided.
  • Connected two interior sector no independent evidence
    purpose: To enable topology change and allow dominance after Page time for firewall resolution.
    New sector arising from the pair of pants interaction; no independent evidence outside the model.

pith-pipeline@v0.9.1-grok · 5813 in / 1768 out tokens · 37199 ms · 2026-06-28T00:03:09.620358+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

78 extracted references · 42 linked inside Pith

  1. [1]

    Almheiri, D

    A. Almheiri, D. Marolf, J. Polchinski and J. Sully,Black holes: Complementarity or firewalls?,JHEP02(2013) 062 [1207.3123]. 54

    Pith/arXiv arXiv 2013

  2. [2]

    Almheiri, D

    A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully,An apologia for firewalls, JHEP09(2013) 018 [1304.6483]

    Pith/arXiv arXiv 2013

  3. [3]

    Hayden and J

    P. Hayden and J. Preskill,Black holes as mirrors: quantum information in random subsystems,JHEP09(2007) 120 [0708.4025]

    Pith/arXiv arXiv 2007

  4. [4]

    Harlow and P

    D. Harlow and P. Hayden,Quantum computation vs. firewalls,JHEP06(2013) 085 [1301.4504]

    Pith/arXiv arXiv 2013

  5. [5]

    Marolf and J

    D. Marolf and J. Polchinski,Gauge-gravity duality and the black hole interior,Phys. Rev. Lett.111(2013) 171301 [1307.4706]

    Pith/arXiv arXiv 2013

  6. [6]

    Bousso,Firewalls from double purity,Phys

    R. Bousso,Firewalls from double purity,Phys. Rev. D88(2013) 084035 [1308.2665]

    Pith/arXiv arXiv 2013

  7. [7]

    Susskind,String theory and the principle of black hole complementarity,Phys

    L. Susskind,String theory and the principle of black hole complementarity,Phys. Rev. Lett. 71(1993) 2367 [hep-th/9307168]

    Pith/arXiv arXiv 1993

  8. [8]

    Susskind, L

    L. Susskind, L. Thorlacius and J. Uglum,The stretched horizon and black hole complementarity,Phys. Rev. D48(1993) 3743 [hep-th/9306069]

    Pith/arXiv arXiv 1993

  9. [9]

    D. A. Lowe, J. Polchinski, L. Susskind, L. Thorlacius and J. Uglum,Black hole complementarity versus locality,Phys. Rev. D52(1995) 6997 [hep-th/9506138]

    Pith/arXiv arXiv 1995

  10. [10]

    Bousso,Complementarity is not enough,Phys

    R. Bousso,Complementarity is not enough,Phys. Rev. D87(2013) 124023 [1207.5192]

    Pith/arXiv arXiv 2013

  11. [11]

    Papadodimas and S

    K. Papadodimas and S. Raju,An infalling observer in AdS/CFT,JHEP10(2013) 212 [1211.6767]

    Pith/arXiv arXiv 2013

  12. [12]

    Papadodimas and S

    K. Papadodimas and S. Raju,Black hole interior in the holographic correspondence and the information paradox,Phys. Rev. Lett.112(2014) 051301 [1310.6334]

    Pith/arXiv arXiv 2014

  13. [13]

    Papadodimas and S

    K. Papadodimas and S. Raju,State-dependent bulk-boundary maps and black hole complementarity,Phys. Rev. D89(2014) 086010 [1310.6335]

    Pith/arXiv arXiv 2014

  14. [14]

    Papadodimas and S

    K. Papadodimas and S. Raju,Remarks on the necessity and implications of state-dependence in the black hole interior,Phys. Rev. D93(2016) 084049 [1503.08825]

    Pith/arXiv arXiv 2016

  15. [15]

    Harlow,Aspects of the papadodimas-raju proposal for the black hole interior,JHEP11 (2014) 055 [1405.1995]

    D. Harlow,Aspects of the papadodimas-raju proposal for the black hole interior,JHEP11 (2014) 055 [1405.1995]

    Pith/arXiv arXiv 2014

  16. [16]

    Maldacena and L

    J. Maldacena and L. Susskind,Cool horizons for entangled black holes,Fortschr. Phys.61 (2013) 781 [1306.0533]

    Pith/arXiv arXiv 2013

  17. [17]

    Raju,Lessons from the information paradox,Phys

    S. Raju,Lessons from the information paradox,Phys. Rept.943(2022) 1 [2012.05770]

    arXiv 2022

  18. [18]

    Laddha, S

    A. Laddha, S. G. Prabhu, S. Raju and P. Shrivastava,The holographic nature of null infinity,SciPost Phys.10(2021) 041 [2002.02448]

    arXiv 2021

  19. [19]

    Chowdhury, O

    C. Chowdhury, O. Papadoulaki and S. Raju,A physical protocol for observers near the boundary to obtain bulk information in quantum gravity,SciPost Phys.10(2021) 106 [2008.01740]

    arXiv 2021

  20. [20]

    Raju,Failure of the split property in gravity and the information paradox,Class

    S. Raju,Failure of the split property in gravity and the information paradox,Class. Quant. Grav.39(2022) 064002 [2110.05470]

    arXiv 2022

  21. [21]

    Almheiri, X

    A. Almheiri, X. Dong and D. Harlow,Bulk locality and quantum error correction in AdS/CFT,JHEP04(2015) 163 [1411.7041]. 55

    Pith/arXiv arXiv 2015

  22. [22]

    X. Dong, D. Harlow and A. C. Wall,Reconstruction of bulk operators within the entanglement wedge in gauge-gravity duality,Phys. Rev. Lett.117(2016) 021601 [1601.05416]

    Pith/arXiv arXiv 2016

  23. [23]

    C.-F. Chen, G. Penington and G. Salton,Entanglement wedge reconstruction using the Petz map,JHEP01(2020) 168 [1902.02844]

    arXiv 2020

  24. [24]

    Bahiru and N

    E. Bahiru and N. Vardian,Explicit reconstruction of the entanglement wedge via the Petz map,JHEP07(2023) 025 [2210.00602]

    arXiv 2023

  25. [25]

    D. L. Jafferis and L. Lamprou,Inside the hologram: reconstructing the bulk observer’s experience,JHEP03(2022) 084 [2009.04476]

    arXiv 2022

  26. [26]

    de Boer, D

    J. de Boer, D. L. Jafferis and L. Lamprou,On black hole interior reconstruction, singularities and the emergence of time, 2022

    2022

  27. [27]

    Almheiri, N

    A. Almheiri, N. Engelhardt, D. Marolf and H. Maxfield,The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole,JHEP12(2019) 063 [1905.08762]

    Pith/arXiv arXiv 2019

  28. [28]

    Almheiri, R

    A. Almheiri, R. Mahajan, J. Maldacena and Y. Zhao,The page curve of hawking radiation from semiclassical geometry,JHEP03(2020) 149 [1908.10996]

    Pith/arXiv arXiv 2020

  29. [29]

    Almheiri, T

    A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini,Replica wormholes and the entropy of hawking radiation,JHEP05(2020) 013 [1911.12333]

    Pith/arXiv arXiv 2020

  30. [30]

    Penington,Entanglement wedge reconstruction and the information paradox,JHEP09 (2020) 002 [1905.08255]

    G. Penington,Entanglement wedge reconstruction and the information paradox,JHEP09 (2020) 002 [1905.08255]

    Pith/arXiv arXiv 2020

  31. [31]

    Penington, S

    G. Penington, S. H. Shenker, D. Stanford and Z. Yang,Replica wormholes and the black hole interior,JHEP03(2022) 205 [1911.11977]

    Pith/arXiv arXiv 2022

  32. [32]

    Stanford and Z

    D. Stanford and Z. Yang,Firewalls from wormholes, 2022

    2022

  33. [33]

    L. V. Iliesiu, A. Levine, H. W. Lin, H. Maxfield and M. Mezei,On the non-perturbative bulk hilbert space of JT gravity,JHEP10(2024) 220 [2403.08696]

    arXiv 2024

  34. [34]

    Blommaert, C.-H

    A. Blommaert, C.-H. Chen and Y. Nomura,Firewalls at exponentially late times,JHEP10 (2024) 131 [2403.07049]

    arXiv 2024

  35. [35]

    Akers and G

    C. Akers and G. Penington,Quantum minimal surfaces from quantum error correction, SciPost Phys.12(2022) 157 [2109.14618]

    arXiv 2022

  36. [36]

    Akers, N

    C. Akers, N. Engelhardt, D. Harlow, G. Penington and S. Vardhan,The black hole interior from non-isometric codes and complexity,JHEP06(2024) 155 [2207.06536]

    arXiv 2024

  37. [37]

    Almheiri,Measurements with probabilities in the final state proposal, 2025

    A. Almheiri,Measurements with probabilities in the final state proposal, 2025

    2025

  38. [38]

    Marolf,Refined algebraic quantization: Systems with a single constraint, 1995

    D. Marolf,Refined algebraic quantization: Systems with a single constraint, 1995

    1995

  39. [39]

    Marolf and H

    D. Marolf and H. Maxfield,Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information,JHEP08(2020) 044 [2002.08950]

    arXiv 2020

  40. [40]

    Casali, D

    E. Casali, D. Marolf, H. Maxfield and M. Rangamani,Baby universes and worldline field theories, 2021

    2021

  41. [41]

    Maxfield,Bit models of replica wormholes,2211.04513

    H. Maxfield,Bit models of replica wormholes,2211.04513. 56

    arXiv

  42. [42]

    Penington and E

    G. Penington and E. Witten,Algebras and States in JT Gravity,2301.07257

    arXiv

  43. [43]

    P. Gao, D. L. Jafferis and D. K. Kolchmeyer,An effective matrix model for dynamical end of the world branes in jackiw–teitelboim gravity,JHEP01(2022) 038 [2104.01184]

    arXiv 2022

  44. [44]

    Donnelly and L

    W. Donnelly and L. Freidel,Local subsystems in gauge theory and gravity,JHEP09(2016) 102 [1601.04744]

    Pith/arXiv arXiv 2016

  45. [45]

    Chandrasekaran, R

    V. Chandrasekaran, R. Longo, G. Penington and E. Witten,An algebra of observables for de Sitter space,JHEP02(2023) 082 [2206.10780]

    Pith/arXiv arXiv 2023

  46. [46]

    D. N. Page and W. K. Wootters,Evolution without evolution: Dynamics described by stationary observables,Phys. Rev. D27(1983) 2885

    1983

  47. [47]

    J. E. Marsden and A. Weinstein,Reduction of symplectic manifolds with symmetry,Reports on Mathematical Physics5(1974) 121

    1974

  48. [48]

    Chandrasekaran, G

    V. Chandrasekaran, G. Penington and E. Witten,Large N algebras and generalized entropy, JHEP04(2023) 009 [2209.10454]

    arXiv 2023

  49. [49]

    Chandrasekaran and É

    V. Chandrasekaran and É. É. Flanagan,Subregion algebras in classical and quantum gravity, 2601.07915

    arXiv

  50. [50]

    Yoshida and A

    B. Yoshida and A. Kitaev,Efficient decoding for the Hayden-Preskill protocol,1710.03363

    Pith/arXiv arXiv

  51. [51]

    Harlow, M

    D. Harlow, M. Usatyuk and Y. Zhao,Quantum mechanics and observers for gravity in a closed universe,JHEP02(2026) 108 [2501.02359]

    arXiv 2026

  52. [52]

    A. I. Abdalla, S. Antonini, L. V. Iliesiu and A. Levine,The gravitational path integral from an observer’s point of view,JHEP05(2025) 059 [2501.02632]

    arXiv 2025

  53. [53]

    G. T. Horowitz and J. Maldacena,The black hole final state,JHEP02(2004) 008 [hep-th/0310281]

    Pith/arXiv arXiv 2004

  54. [54]

    the black hole final state

    D. Gottesman and J. Preskill,Comment on “the black hole final state”,JHEP03(2004) 026 [hep-th/0311269]

    Pith/arXiv arXiv 2004

  55. [55]

    Lloyd and J

    S. Lloyd and J. Preskill,Unitarity of black hole evaporation in final-state projection models, JHEP08(2014) 126 [1308.4209]

    Pith/arXiv arXiv 2014

  56. [56]

    Bousso and D

    R. Bousso and D. Stanford,Measurements without probabilities in the final state proposal, Phys. Rev. D89(2014) 044038 [1310.7457]

    Pith/arXiv arXiv 2014

  57. [57]

    Held and H

    J. Held and H. Maxfield,The hilbert space of de sitter JT: a case study for canonical methods in quantum gravity, 2024

    2024

  58. [58]

    Rovelli,What is observable in classical and quantum gravity?,Class

    C. Rovelli,What is observable in classical and quantum gravity?,Class. Quant. Grav.8 (1991) 297

    1991

  59. [59]

    Giulini and D

    D. Giulini and D. Marolf,A uniqueness theorem for constraint quantization,Class. Quant. Grav.16(1999) 2489 [gr-qc/9902045]

    Pith/arXiv arXiv 1999

  60. [60]

    Dittrich,Partial and complete observables for canonical general relativity,Class

    B. Dittrich,Partial and complete observables for canonical general relativity,Class. Quant. Grav.23(2006) 6155 [gr-qc/0507106]

    Pith/arXiv arXiv 2006

  61. [61]

    Dittrich,Partial and complete observables for hamiltonian constrained systems,Gen

    B. Dittrich,Partial and complete observables for hamiltonian constrained systems,Gen. Rel. Grav.39(2007) 1891 [gr-qc/0411013]

    Pith/arXiv arXiv 2007

  62. [62]

    Rovelli,Time in quantum gravity: An hypothesis,Phys

    C. Rovelli,Time in quantum gravity: An hypothesis,Phys. Rev. D43(1991) 442. 57

    1991

  63. [63]

    Marolf,Almost ideal clocks in quantum cosmology: A brief derivation of time,Class

    D. Marolf,Almost ideal clocks in quantum cosmology: A brief derivation of time,Class. Quant. Grav.12(1995) 2469 [gr-qc/9412016]

    Pith/arXiv arXiv 1995

  64. [64]

    Rovelli,Partial observables,Phys

    C. Rovelli,Partial observables,Phys. Rev. D65(2002) 124013

    2002

  65. [65]

    R. P. Geroch,Topology in general relativity,J. Math. Phys.8(1967) 782

    1967

  66. [66]

    F. J. Tipler,Singularities and causality violation,Annals Phys.108(1977) 1

    1977

  67. [67]

    G. T. Horowitz,Topology change in classical and quantum gravity,Class. Quant. Grav.8 (1991) 587 [hep-th/9109030]

    Pith/arXiv arXiv 1991

  68. [68]

    Borde,Topology change in classical general relativity, 1994

    A. Borde,Topology change in classical general relativity, 1994

    1994

  69. [69]

    Dowker and S

    F. Dowker and S. Surya,Topology change and causal continuity,Phys. Rev. D58(1998) 124019 [gr-qc/9711070]

    Pith/arXiv arXiv 1998

  70. [70]

    B. Post, J. van der Heijden and E. Verlinde,A universe field theory for jt gravity,JHEP05 (2022) 118 [2201.08859]

    arXiv 2022

  71. [71]

    Usatyuk,Comments on Lorentzian topology change in JT gravity,2210.04906

    M. Usatyuk,Comments on Lorentzian topology change in JT gravity,2210.04906

    arXiv

  72. [72]

    A. J. Speranza,Local phase space and edge modes for diffeomorphism-invariant theories, JHEP02(2018) 021 [1706.05061]

    Pith/arXiv arXiv 2018

  73. [73]

    Maldacena, D

    J. Maldacena, D. Stanford and Z. Yang,Conformal symmetry and its breaking in two-dimensional nearly anti-de-sitter space,Prog. Theor. Exp. Phys.2016(2016) 12C104 [1606.01857]

    Pith/arXiv arXiv 2016

  74. [74]

    Sekino and L

    Y. Sekino and L. Susskind,Fast scramblers,JHEP10(2008) 065 [0808.2096]

    Pith/arXiv arXiv 2008

  75. [75]

    Dupuis, M

    F. Dupuis, M. Berta, J. Wullschleger and R. Renner,One-shot decoupling,Commun. Math. Phys.328(2014) 251 [1012.6044]

    Pith/arXiv arXiv 2014

  76. [76]

    Szehr, F

    O. Szehr, F. Dupont-Dupuis, M. Tomamichel and R. Renner,Decoupling with unitary approximate two-designs,New J. Phys.15(2013) 053022

    2013

  77. [77]

    Brown and O

    W. Brown and O. Fawzi,Decoupling with random quantum circuits,Commun. Math. Phys. 340(2015) 867 [1307.0632]

    Pith/arXiv arXiv 2015

  78. [78]

    D. A. Roberts and B. Yoshida,Chaos and complexity by design,JHEP04(2017) 121 [1610.04903]. 58

    Pith/arXiv arXiv 2017