Non-linear equation of motion for higher curvature semiclassical gravity

Naman Kumar

REVIEW 5 major objections 5 minor 14 references

Non-linear equation of motion for higher curvature semiclassical gravity

T0 review · 5 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper claims that the fully non-linear semiclassical equation of motion for a general diffeomorphism-invariant, higher-curvature theory of gravity follows from assigning generalized entropy to causal horizons and imposing the…

desk verdict A serious attempt at a real open gap, but the causal-diamond route assumes the field equation it claims to derive, and the stretched-light-cone route has gaps too. read the letter →

arxiv 2501.10527 v1 pith:WU6JZOXX submitted 2025-01-17 gr-qc hep-th

Naman Kumar This is my paper · ORCID

classification gr-qchep-th MSC 83C4783C57

keywords highercurvaturegravitysemiclassicalgeneralizedentropyWaldquantumfocusingcausaldiamondstretchedlightconeentanglementequilibrium

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper aims to derive the semiclassical gravitational field equations for a general diffeomorphism-invariant, higher-curvature theory, not just the linearized approximation. It claims that the full non-linear equation E_ab = P^cde_a R_bcde − 2∇^c∇^d P_acdb − (L/2)g_ab + Λg_ab = 8πG⟨T_ab⟩ follows when generalized entropy is assigned to causal horizons and either the Clausius relation or an equilibrium condition is imposed. If true, this closes a gap left by earlier entanglement-equilibrium derivations, which could only obtain linearized equations for higher-curvature gravity. It matters because it suggests that semiclassical gravitational dynamics is fixed by horizon thermodynamics even when curvature corrections are not small.

What carries the argument

The central object is the generalized entropy S_gen = S_Wald + S_out and its variation, tied to the quantum expansion Θ through (4G/A) dS_gen/dλ. The load-bearing mechanism is the 'higher-curvature Raychaudhuri equation,' Eq. (35), which replaces the Ricci null-null term R_ab k^a k^b in the standard Raychaudhuri equation with the equation-of-motion tensor E_ab k^a k^b. This equation is what lets the pointwise equilibrium condition Θ = 0, guaranteed by restricted quantum focusing, transmute focusing of the null congruence into the semiclassical field equations.

What would settle it

Check whether Eq. (35) can be derived independently from the action of Eq. (36) by directly computing dθ_HC/dλ from the Wald-entropy density for a specific higher-curvature theory such as f(R) or Gauss-Bonnet gravity. If the right-hand side does not reduce to −θ_HC²/2 − ξ² − E_ab k^a k^b with E_ab exactly the tensor appearing in the field equations, the derivation's central input fails. Alternatively, compare the resulting Eq. (26) with independently derived semiclassical equations for quadratic gravity in a concrete spacetime, such as Schwarzschild or a cosmological FLRW background, and look for a mismatch.

Watch

Extended reading notes

Core claim

The paper derives the full non-linear semiclassical equation of motion for higher-curvature gravity through two complementary routes. In the first, perturbative quantum gravity on a Rindler horizon is mapped to a stretched future light cone, where the physical-process relation ⟨Q⟩ = T δS_Wald yields the reversible Wald-entropy variation; combining that with the Clausius relation and imposing conservation gives Eq. (26). In the second, a causal diamond in a maximally symmetric spacetime is used, where the higher-curvature Raychaudhuri equation dθ_HC/dλ = −θ_HC²/2 − ξ² − E_ab k^a k^b is combined with the pointwise vanishing of the quantum expansion Θ, enforced by restricted quantum focusing, and with the CFT result S''_out = 2πA⟨T_kk⟩, to obtain δS_gen = 0 and hence the same non-linear equation. The paper concludes that the earlier limitation of the variational approach is a linearization artifact and that the physical-process formulation preserves the full non-linear structure.

Load-bearing premise

The load-bearing premise is that the higher-curvature Raychaudhuri equation, Eq. (35), which already contains the equation-of-motion tensor E_ab on its right-hand side, is a genuine dynamical relation rather than a restatement of the field equations.

Editorial extensions

If this is right

For Einstein-Hilbert gravity, E_ab reduces to the Einstein tensor, so both derivations reproduce the known semiclassical Einstein equation.
The same thermodynamic route yields the full non-linear semiclassical equations for any higher-curvature Lagrangian, including Lagrangians with derivatives of the Riemann tensor, which earlier entanglement-equilibrium derivations could only deliver in linearized form.
The field equations are to be read as expectation values, ⟨E_ab⟩ = 8πG⟨T_ab⟩, consistent with the semiclassical approximation and with the quantum-expectation-value origin of the area and entropy changes.
The causal-diamond derivation shows that the equilibrium condition is enforced by restricted quantum focusing, so the derivation does not rely on holography or on the maximum-vacuum-entanglement hypothesis used in earlier equilibrium derivations.
An undetermined cosmological constant Λ appears naturally and is fixed by conservation of the stress-energy tensor, following the standard pattern in thermodynamic derivations of gravity.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the higher-curvature Raychaudhuri equation is sound, then the generalized entropy production along a null surface is literally governed by the field equations themselves, suggesting that semiclassical gravity in this class of theories can be read as the coarse-grained equation of state of the quantum matter-gravity system.
A concrete check is to compute E_ab for f(R) gravity from Eq. (26) and verify that it reduces to the known fourth-order f(R) field equations; failure to match would pinpoint the step where the thermodynamic input is incorrect.
The same logic might extend to non-maximally-symmetric causal diamonds, where shear no longer vanishes; the derivation would then need explicit control of the ξ² term, possibly producing additional curvature constraints in generic spacetimes.
The pointwise condition Θ = 0 at the diamond boundary implies that the null boundary is a quantum extremal surface, linking this thermodynamic derivation to extremality conditions used in holographic entropy calculations, even though the paper does not develop that connection.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

First, what's genuinely new: the paper aims at the fully non-linear semiclassical equation for a general diffeo-invariant theory, where previous causal-diamond or light-cone derivations stopped at linearized order. That target is real, and the author's reading of Bueno et al. and Svesko is fair. The two-route structure—perturbative quantum gravity on a Rindler horizon mapped to a stretched light cone, and a causal diamond with quantum expansion—makes sense, and the paper gives a clear statement of what the final equation should be.

What's good: crisp identification of the gap, sensible citations, and transparent statements of where things are being asserted. The manuscript does not hide that some steps are assumptions, like the extension of Bianchi's area law to Wald entropy. But the soft spots are not minor.

The causal-diamond argument is the problem. Eq. (35) posits a 'higher curvature Raychaudhuri equation' whose curvature source is E_ab, and E_ab is defined in Eq. (37) as the metric variation of the action—exactly the equation-of-motion tensor. The subsequent manipulation drops θ^2 and ξ^2 and imposes δS_gen=0, outputting E_kk = 8πG⟨T_kk⟩. Unless Eq. (35) is derived from an independent principle, the field equation is an input. The paper cites Wall–Yan and Yan for generalized Raychaudhuri equations, but does not show that their results imply (35) with this E_ab. That is a load-bearing gap, not a detail.

The stretched-light-cone route has parallel gaps. Eq. (20) asserts that Bianchi's perturbative area law extends to Wald entropy; that is plausible but not shown. The leap from (25) to (26) is compressed: f is undetermined, the −L/2 term appears without explanation, and the 'imposing conservation' step is not demonstrated. The paper also waivers between Wald entropy and generalized entropy; the distinction matters for the equilibrium condition.

Overall, this is a serious attempt at a real open problem, but as written the central derivation is not established. The author's earlier paper (Kumar 2023) had a similar structure, and this extends it, but the extension inherits the same fragility.

Who should read it: people working on thermodynamics of spacetime and entropic gravity. A referee who knows the Raychaudhuri-generalization literature could tell whether (35) is a known theorem; if it is, the causal diamond argument goes through. Without that, the paper is an interesting sketch, not a derivation.

My call: send it to a competent referee rather than desk-reject. The flaws are specific and potentially fixable, and the target is important enough to justify referee time.

Referee Report

5 major / 5 minor

Summary. The paper claims to derive the fully non-linear semiclassical equation of motion for a general diffeomorphism-invariant higher-curvature theory of gravity, Eq. (26) and Eq. (44), from thermodynamic relations for causal horizons. Two complementary derivations are presented. The first uses perturbative quantum gravity on a Rindler horizon, maps the result to a stretched light cone, and invokes the Clausius relation <Q> = T δS_rev with Wald entropy. The second uses a causal diamond in a maximally symmetric spacetime, introduces a 'higher-curvature Raychaudhuri equation' for a redefined expansion scalar θ_HC, and imposes the vanishing of the quantum expansion Θ pointwise to obtain δS_gen = 0. The paper claims to resolve the previous limitation that only linearized semiclassical equations were known for higher-curvature gravity.

Significance. If the derivation were sound, this would be a significant advance: it would extend Jacobson's thermodynamic derivation of Einstein's equation to the full non-linear semiclassical field equations of arbitrary diffeomorphism-invariant theories without invoking holography, and it would directly connect generalized entropy, quantum focusing, and higher-curvature corrections. The paper also makes constructive use of prior results such as restricted quantum focusing and the entropy from second shape variations of von Neumann entropy. However, the significance is entirely conditional because the key technical steps are asserted rather than derived, and at least one central step appears to assume the field equation that the paper claims to obtain.

major comments (5)

[Section 3, Eq. (35)] The 'higher-curvature Raychaudhuri equation' dθ_HC/dλ = -θ_HC²/2 - ξ² - E_ab k^a k^b is stated without derivation, and E_ab is defined in Eq. (37) as the metric variation of the gravitational action, i.e., the equation-of-motion tensor. Since the final result Eq. (44) is exactly E_ab + Λg_ab = 8πG⟨T_ab⟩, the field equation is effectively inserted as the source term in the Raychaudhuri equation. This makes the derivation circular: E_ab cannot simultaneously be the object to be derived and the input to the entropy-evolution law. An independent derivation of Eq. (35) from the dynamics of θ_HC, with E_ab emerging rather than being posited, is required for the argument to be non-tautological.
[Section 3, Eqs. (38)-(42)] The step from the Taylor expansion of Θ to Eq. (40), where the θ_HC² and ξ² terms are dropped and the pointwise vanishing of Θ is imposed, is not logically clean. If Θ vanishes pointwise along the null generator as required by restricted quantum focusing, then δS_gen in Eq. (28) vanishes identically by definition, and the subsequent manipulation leading to Eq. (42) is redundant. If Θ is only taken to vanish at the surface p, then the argument that the integrand in Eq. (42) vanishes pointwise is not justified. The paper should clarify exactly which condition is being imposed and how Eqs. (39)-(42) follow from it.
[Section 2, Eq. (20)] The extension of Bianchi's perturbative result from the area law δS_EE = δA/4G to the Wald entropy law <Q>/T = δS_Wald is asserted, not derived. The schematic equation (19) for higher-curvature perturbations is never written out, and the claim that the resulting corrections to the area law are 'captured by the Wald entropy' is not demonstrated. Since the entire stretched-light-cone derivation relies on Eq. (20), this is a load-bearing gap.
[Section 2, Eqs. (23)-(26)] The transition from δS_rev in Eq. (23) and <Q> in Eq. (24) to Eq. (25) is not shown. In particular, the undetermined function f in Eq. (25) and the appearance of the term -L/2 g_ab + Λg_ab in Eq. (26) are not derived; the statement 'Imposing conservation on both sides, we finally obtain...' omits the actual calculation. Because the -L/2 term is essential to the final equation of motion, this step cannot be left as an unstated exercise.
[Section 2, paragraph after Eq. (20)] The mapping from the Rindler horizon to the stretched light cone is justified only by analogy: the modular Hamiltonian for a stretched light cone is 'proportional to the radial boost operator,' and the quantities K and δA differ in their expressions. The paper does not show that Bianchi's derivation, which uses specific Rindler coordinates and null coordinates v and y, survives these replacements. Without explicit verification that the perturbative area calculation goes through on the stretched light cone, the first derivation is incomplete.

minor comments (5)

[Eq. (6)] The index conventions in P^{cde}_a R_{bcde} are not fully defined; the symmetries of P^{abcd} should be stated explicitly to avoid confusion.
[Eq. (39)] The term (S''_out - S'_out θ) appears without derivation or explanation of the sign; its origin from differentiating S'_out with respect to λ should be shown.
[Eq. (42)] The integral over H is written without limits or a definition of the measure dλdA; the integration domain and the range of λ should be specified.
[Section 3, Eqs. (33)-(34)] The terminology 'higher-curvature expansion' for θ_HC is misleading, since θ_HC is not the standard expansion scalar of the null congruence but a derivative of Wald entropy; a distinct name such as 'entropy expansion' would be clearer.
[Section 3, Eq. (41)] The CFT result S''_out = 2πA⟨T_kk⟩ is cited, but the extension to arbitrary QFTs with a UV fixed point is only stated in one sentence; a more careful discussion of the limit l_p << l << l_QFT and its validity for the pointwise equation (44) is needed.

Circularity Check

1 steps flagged · score 6.0 of 10

The causal-diamond derivation postulates the field-equation tensor E_ab as the source in the higher-curvature Raychaudhuri equation, then recovers the same tensor as its output.

self definitional [Section 3, Eqs. (35), (37), (42)-(44)]
"The evolution of higher curvature expansion (θHC) shall be governed by a higher curvature Raychaudhuri equation ... dθHC/dλ = −θ2HC/2 − ξ2 − Eabkakb. (35) where Eab is given by (37). ... In particular, the Ricci curvature term Rabkakb is replaced by Eabkakb, where Eab incorporates contributions from the higher curvature corrections. ... Varying the action with respect to metric gives the equation of motion as Eab = 2√−g δL δgab = −2√−g δLm δgab ≡ Tab. (37) ... we obtain the full non-linear semiclassical equation of motion valid at all points in spacetime as Eab + Λgab = 8πG⟨Tab⟩. (44)"

In Eq. (35), the source term of the unproved 'higher curvature' Raychaudhuri equation is E_ab, and Eq. (37) defines E_ab as the equation-of-motion tensor obtained by varying the gravitational action. The equilibrium computation then sets δS_gen = 0, drops the θ_HC^2 and S'_out θ terms, substitutes S''_out = 2πA⟨T_kk⟩, and outputs E_ab + Λgab = 8πG⟨T_ab⟩. This is the very field equation already contained in the input E_ab. The paragraph after (35) states explicitly that the GR Ricci term R_ab k^a k^b has been replaced by E_ab k^a k^b; without a derivation of this replacement from an independent entropy/area law, the causal-diamond derivation is a tautology: the field equation is assumed in the Raychaudhuri source and recovered as the conclusion.

full rationale

The stretched-light-cone route in Section 2 is primarily an application of established Wald-entropy thermodynamics; the step 'imposing conservation on both sides' after Eq. (25) is terse but follows the standard diffeomorphism-invariance argument that fixes f as −L/2 + Λ, so it is not circular in the same way. The serious circularity is confined to Section 3: the higher-curvature Raychaudhuri equation (35) is not derived from an independent entropy variation, and its curvature source is simply the equation-of-motion tensor E_ab of Eq. (37). Imposing δS_gen = 0 then returns E_ab + Λgab = 8πG⟨T_ab⟩, making the field equation an input rather than an output. If Wall and Yan (2024) or Yan (2024) contain an independent proof of exactly this generalized Raychaudhuri equation for θ_HC, that would break the circularity, but the manuscript does not provide or state such a proof, and as written Eq. (35) simply names the EOM tensor as the source. Self-citations such as Kumar (2023) for the physical-process relation ⟨Q⟩ = TδS_gen are premises rather than reductions and do not themselves force the conclusion, so they do not raise the score beyond the Eq. (35) issue. Overall, one of the two claimed derivations reduces by construction, giving a partial but significant circularity.

Assumptions & free parameters 2 free parameters · 9 assumptions · 2 invented entities

The derivation rests on several unproven or weakly supported inputs: the physical-process relation from the author's own prior work, the unproven extension of Bianchi's area law to Wald entropy, the assumed higher-curvature Raychaudhuri equation that already contains the field-equation tensor, and the mapping of CFT entropy results to arbitrary QFTs. These are the main sources of the circularity and soundness problems.

free parameters (2)

Cosmological constant Λ = undetermined
Introduced by hand in Eqs. (26) and (44). The null-null condition (42) cannot fix Λ because g_kk = 0 for null vectors, and the conservation step that would fix it is not shown in the paper.
Function f in Eq. (25) = unspecified
Appears in the intermediate equation P^cde_a R_bcde - 2∇^c∇^d P_acdb + f g_ab = 8πG⟨T_ab⟩. The text claims conservation fixes f, but the computation is omitted, and the jump to -L/2 + Λ is unexplained.

assumptions (9)

domain assumption The semiclassical physical process relation ⟨Q⟩ = T δS_gen (Eq. 7)
Stated as the foundational relation for both approaches; taken from the author's prior work (Kumar 2023) and not derived in this paper.
domain assumption Extension of Bianchi's perturbative area law to Wald entropy: ⟨Q⟩/T = δS_Wald
Section 2, Eq. (20). The paper asserts that higher-curvature corrections to the area law are captured by Wald entropy, but does not derive this from the perturbative quantum gravity calculation.
domain assumption Mapping of Rindler-horizon results to a stretched light cone
Section 2, paragraph after Eq. (20). The paper states the results directly map and hold with minor technical modifications, relying on Parikh and Svesko (2018).
ad hoc to paper Higher-curvature Raychaudhuri equation (Eq. 35): dθHC/dλ = -θHC²/2 - ξ² - E_ab k^a k^b
Stated without derivation in Section 3. E_ab is already the equation-of-motion tensor, so this equation encodes the field equation it is used to derive.
domain assumption Restricted quantum focusing allows pointwise Θ = 0
Section 3, after Eq. (39). The paper uses the result of Shahbazi-Moghaddam (2024), noting it is proven only in a Braneworld scenario, to impose the equilibrium condition δS_gen = 0.
domain assumption S''_out = 2πA⟨T_kk⟩ for CFTs extends to any QFT with a UV fixed point
Section 3, Eq. (41) and following. The CFT result from Leichenauer et al. (2018) and Balakrishnan et al. (2022) is mapped to arbitrary QFTs under the stated scale assumptions.
domain assumption Matter is a QFT with UV fixed point and l_p << l << l_QFT
Section 3, stated before Eq. (42); same assumption as Jacobson's entanglement equilibrium approach.
domain assumption Entanglement entropy is identified with generalized entropy S_EE = S_gen (Eq. 3)
Introduction, Eq. (3). The paper notes the identification is tempting but admits UV-cutoff challenges, yet relies on it throughout.
standard math Stokes theorem, classical Raychaudhuri equation, and shear-free property of conformal Killing horizons
Used in Eqs. (22), (30)-(35); standard results cited to Dyer and Honig (1979).

invented entities (2)

Higher-curvature expansion scalar θHC
purpose: Defined in Eq. (34) as (4G/A) dS_Wald/dλ to generalize the classical expansion for higher-curvature gravity; its evolution is assumed to follow the new Raychaudhuri equation.
No independent derivation or observable prediction is provided; its definition and evolution equation are introduced ad hoc for this derivation.
Higher-curvature Raychaudhuri equation
purpose: Replaces the classical Raychaudhuri equation in the causal-diamond argument; the Ricci term is replaced by E_ab, which is the field-equation tensor.
Postulated in Eq. (35) without derivation; it is the key circular step because it embeds the field equation.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Non-linear equation of motion for higher curvature semiclassical gravity." pith.science (2026). https://pith.science/paper/WU6JZOXX

@misc{pith2026250110527,
  author       = {Pith},
  title        = {Pith review of: Non-linear equation of motion for higher curvature semiclassical gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WU6JZOXX}},
  note         = {Machine review of arXiv:2501.10527}
}

abstract

We derive the non-linear semiclassical equation of motion for a general diffeomorphism-invariant theory of gravity by leveraging the thermodynamic properties of closed causal horizons. Our work employs two complementary approaches. The first approach utilizes perturbative quantum gravity applied to a Rindler horizon. The result is then mapped to a stretched light cone, which can be understood as a union of Rindler planes. Here, we adopt the semiclassical physical process formulation, encapsulated by $\langle Q\rangle = T \delta S_{gen}$ where the heat-flux $\langle Q\rangle$ is related to the expectation value of stress-energy tensor $T_{ab}$ and $S_{gen}$ is the generalized entropy. The second approach introduces a "higher curvature" Raychaudhuri equation, where the vanishing of the quantum expansion $\Theta$ pointwise as required by restricted quantum focusing establishes an equilibrium condition, $\delta S_{\text{gen}} = 0$, at the null boundary of a causal diamond. While previous studies have only derived the linearized semiclassical equation of motion for higher curvature gravity, our work resolves this limitation by providing a fully non-linear formulation without invoking holography.

Figures

Figures reproduced from arXiv: 2501.10527 by the authors.

**Figure 1.** A Rindler horizon H. B is a codimension-2 surface spanned by light rays. When a matter flux Q crosses the beam, it gets perturbed. The difference in the asymptotic area of the unperturbed and perturbed beam gives the change in the area of the Rindler horizon δA. since these null rays span a Rindler horizon. Then using the equation of motion (11) and the expression δS vN = −Tr(δρ log ρ0) = 2πTr(Kδρ) = 2π Z d 2 y Z ∞ … view at source ↗

**Figure 2.** A stretched future light cone at a point p is generated by a congruence of radially accelerating worldlines with the same proper acceleration 1/α. It describes a timelike hypersurface Σ. The boundary is given by two constant time slices of Σ at time t = 0 and t = ϵ. mit a true Killing vector but an approximate Killing vector and therefore, the Killing identity will fail in some order. Third, a Rindler horizon has b… view at source ↗

**Figure 3.** A causal diamond in MSS for a ball-shaped spacelike surface Σ with ∂Σ as its boundary. p and p ′ are the future and past vertices of the diamond. The solid curves are the flow lines of the conformal Killing vector ζ. The null boundary H is the conformal Killing horizon. A key quantity for our analysis is the Quantum expansion Bousso et al. (2016). Suppose a spatial surface σ of area A splits a Cauchy surface Σ into… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

14 extracted references · 9 canonical work pages

[5]

Journal of High Energy Physics 2020, 1–53

The python’s lunch: geometric obstructions to decoding hawking radiation. Journal of High Energy Physics 2020, 1–53. Bueno, P., Min, V .S., Speranza, A.J., Visser, M.R.,

work page 2020
[10]

thermodynamics

Gravitational dynamics from entanglement “thermodynamics”. Journal of High Energy Physics 2014, 1–16. Leichenauer, S., Levine, A., Shahbazi-Moghaddam, A.,

work page 2014
[11]

Journal of High Energy Physics 2022, 1–123

Sewing space- time with lorentzian threads: complexity and the emergence of time in quan- tum gravity. Journal of High Energy Physics 2022, 1–123. Ryu, S., Takayanagi, T., 2006a. Aspects of holographic entanglement entropy. Journal of High Energy Physics 2006,

work page 2022
[13]

arXiv preprint arXiv:1405.2933

Universality of gravity from entangle- ment. arXiv preprint arXiv:1405.2933 . Wall, A.C., Yan, Z.,

arXiv
[1972]

Black holes and the second law. Lett. Nuovo Cim. 4, 737–740. doi: 10.1007/BF02757029. Bekenstein, J.D.,

doi:10.1007/bf02757029
[1997]

URL: https://arxiv.org/abs/gr-qc/9705006, arXiv:gr-qc/9705006

The statistical mechanics of black hole ther- modynamics. URL: https://arxiv.org/abs/gr-qc/9705006, arXiv:gr-qc/9705006. Susskind, L., Uglum, J.,

arXiv
[2013]

URL: https://arxiv.org/abs/1211.0522, arXiv:1211.0522

Black hole entropy from graviton entanglement. URL: https://arxiv.org/abs/1211.0522, arXiv:1211.0522. Bianchi, E., Satz, A.,

arXiv
[2014]

Journal of High Energy Physics 2014, 1–41

Gravitation from entanglement in holographic cfts. Journal of High Energy Physics 2014, 1–41. Guedens, R., Jacobson, T., Sarkar, S.,

work page 2014

Show all 14 references

[2015]

Journal of High Energy Physics 2015, 1–27

Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime. Journal of High Energy Physics 2015, 1–27. Faulkner, T., Guica, M., Hartman, T., Myers, R.C., Van Raamsdonk, M.,

2015
[2018]

Journal of High Energy Physics 2018, 1–33

Entropy, extremality, euclidean variations, and the equations of motion. Journal of High Energy Physics 2018, 1–33. Dyer, C., Honig, E.,

2018
[2020]

Journal of High Energy Physics 2020, 1–43

Quantum max- imin surfaces. Journal of High Energy Physics 2020, 1–43. Balakrishnan, S., Chandrasekaran, V ., Faulkner, T., Levine, A., Shahbazi- Moghaddam, A.,

2020
[2022]

Journal of High Energy Physics 2022, 1–42

Entropy variations and light ray operators from replica defects. Journal of High Energy Physics 2022, 1–42. Bekenstein, J.D.,

2022
[2023]

Journal of High Energy Physics 2023, 1–48

Gravitation from optimized computation: Einstein and beyond. Journal of High Energy Physics 2023, 1–48. Dong, X., Lewkowycz, A.,

2023
[2024]

URL: https://arxiv.org/abs/2412.07107, arXiv:2412.07107

Gravitational focusing and horizon entropy for higher-spin fields. URL: https://arxiv.org/abs/2412.07107, arXiv:2412.07107. 7

arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [5]

Journal of High Energy Physics 2020, 1–53

The python’s lunch: geometric obstructions to decoding hawking radiation. Journal of High Energy Physics 2020, 1–53. Bueno, P., Min, V .S., Speranza, A.J., Visser, M.R.,

work page 2020

[2] [10]

thermodynamics

Gravitational dynamics from entanglement “thermodynamics”. Journal of High Energy Physics 2014, 1–16. Leichenauer, S., Levine, A., Shahbazi-Moghaddam, A.,

work page 2014

[3] [11]

Journal of High Energy Physics 2022, 1–123

Sewing space- time with lorentzian threads: complexity and the emergence of time in quan- tum gravity. Journal of High Energy Physics 2022, 1–123. Ryu, S., Takayanagi, T., 2006a. Aspects of holographic entanglement entropy. Journal of High Energy Physics 2006,

work page 2022

[4] [13]

arXiv preprint arXiv:1405.2933

Universality of gravity from entangle- ment. arXiv preprint arXiv:1405.2933 . Wall, A.C., Yan, Z.,

arXiv

[5] [1972]

Black holes and the second law. Lett. Nuovo Cim. 4, 737–740. doi: 10.1007/BF02757029. Bekenstein, J.D.,

doi:10.1007/bf02757029

[6] [1997]

URL: https://arxiv.org/abs/gr-qc/9705006, arXiv:gr-qc/9705006

The statistical mechanics of black hole ther- modynamics. URL: https://arxiv.org/abs/gr-qc/9705006, arXiv:gr-qc/9705006. Susskind, L., Uglum, J.,

arXiv

[7] [2013]

URL: https://arxiv.org/abs/1211.0522, arXiv:1211.0522

Black hole entropy from graviton entanglement. URL: https://arxiv.org/abs/1211.0522, arXiv:1211.0522. Bianchi, E., Satz, A.,

arXiv

[8] [2014]

Journal of High Energy Physics 2014, 1–41

Gravitation from entanglement in holographic cfts. Journal of High Energy Physics 2014, 1–41. Guedens, R., Jacobson, T., Sarkar, S.,

work page 2014