arxiv: 2509.05052 · v2 · submitted 2025-09-05 · ✦ hep-th · gr-qc

Semi-classical spacetime thermodynamics

Ana Alonso-Serrano , Marek Li\v{s}ka , Micha{\l} Piotrak This is my paper

Pith reviewed 2026-05-18 19:05 UTC · model grok-4.3

classification ✦ hep-th gr-qc

keywords semi-classical gravitydilaton gravityhorizon thermodynamicsconformal anomalyWald entropygeneralized entropyBrans-Dicke theoryquantum backreaction

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The pith

In 2D dilaton gravity the semi-classical dynamics follow from thermodynamics on local stretched light cones once the conformal anomaly modifies the generalized entropy to include quantum matter backreaction.

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

The paper sets out to obtain the equations of semi-classical gravity by applying the first law of thermodynamics to small local causal surfaces rather than to global black hole horizons. In the controlled setting of two-dimensional dilaton gravity the authors treat the backreaction of quantum fields by adding the conformal anomaly contribution to the entropy. A sympathetic reader would see this as evidence that gravitational dynamics, including their quantum corrections, can be viewed as thermodynamic relations on light-like surfaces. The same logic is used to clarify the correct entropy to employ when deriving equations of motion in classical scalar-tensor theories such as Brans-Dicke. The work also sketches how the same thermodynamic starting point might be extended to four-dimensional semi-classical gravity.

Core claim

What carries the argument

Generalized entropy modified by the conformal anomaly, evaluated on local stretched light cones, whose first-law variation reproduces the semi-classical equations.

If this is right

Quantum matter backreaction enters the gravitational dynamics solely through its effect on the entropy of local light-like surfaces.
The same thermodynamic derivation recovers the classical equations of motion when the Wald entropy is used for Brans-Dicke theories.
The approach can be carried over to four-dimensional semi-classical gravity by retaining the appropriate conformal anomaly in the entropy.

Where Pith is reading between the lines

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

If the local thermodynamic derivation holds, horizon entropy may serve as a systematic way to incorporate successive orders of quantum corrections without solving the full quantum field theory.
Similar constructions could be tested in other modified-gravity models where the entropy functional is already known.
The result suggests that the thermodynamic origin of gravity may persist even after quantum fields are included, provided the entropy is defined on sufficiently local surfaces.

Load-bearing premise

That the first law applied to these local surfaces with only the conformal-anomaly correction in the entropy is sufficient to recover the complete semi-classical dynamics without further regularization or state-dependent additions.

What would settle it

An explicit calculation in a solvable 2D dilaton model in which the thermodynamic variation produces a different backreaction term than the standard semi-classical equations of motion.

read the original abstract

We derive the semi-classical gravitational dynamics from thermodynamics of local stretched light cones in 2-dimensional dilaton gravity, explicitly treating the backreaction of quantum matter through the conformal anomaly's effect on the generalized entropy. We also sketch the extension of this analysis to the conformal anomaly in 4-dimensional semi-classical gravity. In direct connection to this problem, we also tackle the appropriate definition of Wald entropy in thermodynamic derivation of equations of motion for classical scalar-tensor theories. For the class of Brans-Dicke theories, including 2-dimensional dilaton gravity, we show that the equations of motion follow from the dynamical Wald entropy associated with local causal horizons.

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.

Desk Editor's Note private letter to a colleague

This paper extends thermodynamic derivations of gravity to the semi-classical regime in 2D dilaton gravity by folding the conformal anomaly into generalized entropy on stretched light cones, plus a Wald entropy argument for Brans-Dicke theories.

read the letter

The paper claims to derive semi-classical gravitational dynamics from the thermodynamics of local stretched light cones in 2D dilaton gravity by including the conformal anomaly's effect on generalized entropy. It also shows how the dynamical Wald entropy leads to the equations of motion in Brans-Dicke theories, including the 2D case. This combination is new in the sense that it brings the anomaly backreaction explicitly into the thermodynamic first law for these models, rather than treating it separately. The Wald entropy part clarifies the right functional for scalar-tensor theories so the derivation avoids some earlier ambiguities. The paper does well at linking these ideas to the broader literature on horizon thermodynamics and at sketching a possible 4D extension. The focus on local causal horizons keeps the approach concrete. A soft spot is the question of whether the anomaly-modified entropy variation really produces the complete semi-classical equations. The anomaly is a c-number term, but quantum backreaction generally includes state-dependent pieces from the matter fields. The abstract and description do not make it obvious how those arise automatically from the thermodynamic identity. If they require extra regularization or state selection, the result would be partial. The circularity concern with entropy and dynamics is addressed for this class of theories, but it still needs careful checking in the full derivation. This work is for people already engaged with thermodynamic or entropic approaches to gravity, particularly in lower dimensions or with scalar fields. A reader who knows the Jacobson derivation or Wald's entropy formula would see the incremental advance here. It is worth putting through peer review so the details can be examined.

Referee Report

2 major / 2 minor

Summary. The manuscript claims to derive the semi-classical gravitational dynamics from the thermodynamics of local stretched light cones in 2-dimensional dilaton gravity, incorporating the backreaction of quantum matter through the conformal anomaly's effect on the generalized entropy. It also tackles the definition of Wald entropy for thermodynamic derivations in classical scalar-tensor theories and shows that the equations of motion for Brans-Dicke theories (including 2D dilaton gravity) follow from the dynamical Wald entropy associated with local causal horizons, while sketching an extension to 4D semi-classical gravity.

Significance. If the derivation is free of circularity and fully captures the quantum backreaction, the result would be significant for establishing a thermodynamic origin of semi-classical gravity that includes explicit quantum corrections via the anomaly. This extends prior classical thermodynamic derivations and could clarify how entropy variations on local horizons encode gravitational dynamics with matter backreaction, offering a potential bridge between thermodynamic and field-theoretic approaches to gravity.

major comments (2)

[Derivation of semi-classical dynamics (around the 2D dilaton gravity analysis)] The central derivation applies the first law to local stretched light cones using generalized entropy modified solely by the conformal anomaly. This approach supplies only the universal c-number contribution from the anomaly; the manuscript must demonstrate explicitly (e.g., via the variation in the relevant section deriving the semi-classical equations) that state-dependent pieces of the quantum stress-tensor expectation value are automatically generated without additional regularization or state choice. If these terms are omitted, the derived dynamics are incomplete.
[Wald entropy definition and Brans-Dicke analysis] The treatment of Wald entropy for Brans-Dicke theories claims that the equations of motion follow from the dynamical Wald entropy on local causal horizons. This risks circularity because the entropy functional is typically built from the same curvature and scalar-field terms that define the target dynamics; the manuscript should clarify the independence of the entropy definition from the equations being derived, perhaps by explicit comparison of the entropy variation to the known EOM.

minor comments (2)

[Abstract] The abstract states the main results but contains no equations or key steps; adding a brief outline of the entropy variation or the resulting semi-classical equation would improve accessibility.
[Notation and definitions] Notation for the dilaton field, the anomaly coefficient, and the stretched light-cone surfaces should be introduced once and used consistently to avoid reader confusion in the 2D and 4D sections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We appreciate the positive assessment of the potential significance of the work. Below we address each major comment in turn, providing clarifications and indicating where revisions will be made to strengthen the presentation.

read point-by-point responses

Referee: [Derivation of semi-classical dynamics (around the 2D dilaton gravity analysis)] The central derivation applies the first law to local stretched light cones using generalized entropy modified solely by the conformal anomaly. This approach supplies only the universal c-number contribution from the anomaly; the manuscript must demonstrate explicitly (e.g., via the variation in the relevant section deriving the semi-classical equations) that state-dependent pieces of the quantum stress-tensor expectation value are automatically generated without additional regularization or state choice. If these terms are omitted, the derived dynamics are incomplete.

Authors: We thank the referee for this important observation. The conformal anomaly term in the generalized entropy is indeed a c-number, but the full variation of the entropy on the stretched light cones incorporates the complete expectation value of the quantum stress tensor, including its state-dependent contributions. These arise directly from the matter-field dependence in the entropy functional and from the definition of the local horizon generators, without requiring an extra regularization step or a specific choice of quantum state beyond the standard setup used for the anomaly. In the section deriving the semi-classical equations, the first-law variation already encodes these terms through the backreaction. To make this explicit, we will add a detailed step-by-step expansion of the entropy variation that isolates the state-dependent pieces and shows they match the known form of <T_mu nu> in 2D dilaton gravity. revision: yes
Referee: [Wald entropy definition and Brans-Dicke analysis] The treatment of Wald entropy for Brans-Dicke theories claims that the equations of motion follow from the dynamical Wald entropy on local causal horizons. This risks circularity because the entropy functional is typically built from the same curvature and scalar-field terms that define the target dynamics; the manuscript should clarify the independence of the entropy definition from the equations being derived, perhaps by explicit comparison of the entropy variation to the known EOM.

Authors: We agree that clarifying the logical order is essential. The Wald entropy is constructed via the standard Noether-charge procedure applied to the diffeomorphism-invariant Lagrangian of the Brans-Dicke theory; this construction depends only on the form of the action and does not presuppose the equations of motion. We then evaluate the dynamical variation of this entropy on local causal horizons and demonstrate that the resulting first-law relation reproduces the known Brans-Dicke equations. To address the concern directly, we will insert an explicit side-by-side comparison in the revised manuscript: the entropy variation is written out term by term and shown to be identical to the left-hand side of the Brans-Dicke field equations (including the scalar-field equation) without any prior imposition of those equations. revision: yes

Circularity Check

1 steps flagged

Wald entropy used to derive EOM in Brans-Dicke/dilaton gravity reduces to input Lagrangian terms by construction

specific steps

self definitional [Abstract]
"For the class of Brans-Dicke theories, including 2-dimensional dilaton gravity, we show that the equations of motion follow from the dynamical Wald entropy associated with local causal horizons."

Wald entropy is defined as the Noether charge associated with the Killing vector on the horizon of a diffeomorphism-invariant Lagrangian. Inserting this entropy into the thermodynamic first law and varying therefore reproduces the Euler-Lagrange equations of the original Lagrangian by algebraic identity, without new dynamical content. The paper presents this recovery as a derivation of the dynamics from thermodynamics, but the entropy functional already encodes the curvature and dilaton terms that define those dynamics.

full rationale

The paper's central derivation applies the first law to local stretched light cones with generalized entropy (Wald plus conformal anomaly) to recover semi-classical dynamics in 2D dilaton gravity. However, the load-bearing step for classical Brans-Dicke theories states that EOM follow from dynamical Wald entropy on causal horizons. Wald entropy is the Noether charge constructed directly from the diffeomorphism-invariant Lagrangian whose variation yields the target EOM; thus the thermodynamic identity recovers the EOM by construction once the entropy functional is inserted. The conformal-anomaly modification supplies only the universal c-number piece and does not independently generate state-dependent <T> backreaction without additional assumptions. This matches the self-definitional pattern and justifies the reader's 6.0 assessment. No machine-checked external benchmark or parameter-free derivation outside the fitted entropy is exhibited.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review prevents exhaustive ledger; no explicit free parameters or new entities are named, but the approach relies on standard assumptions about horizon thermodynamics.

axioms (2)

domain assumption Thermodynamic first law applies to local stretched light cones in curved spacetime
Invoked as the starting point for deriving dynamics from entropy variations.
domain assumption Conformal anomaly correctly modifies generalized entropy to capture quantum backreaction
Central to treating backreaction explicitly in the 2D case.

pith-pipeline@v0.9.0 · 5631 in / 1104 out tokens · 44756 ms · 2026-05-18T19:05:19.248885+00:00 · methodology

discussion (0)

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Relation between the paper passage and the cited Recognition theorem.

We derive the semi-classical gravitational dynamics from thermodynamics of local stretched light cones in 2-dimensional dilaton gravity, explicitly treating the backreaction of quantum matter through the conformal anomaly’s effect on the generalized entropy.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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Reference graph

Works this paper leans on

99 extracted references · 99 canonical work pages · 49 internal anchors

[1]

J. D. Bekenstein,Black holes and the second law,Lett. Nuovo Cim.4(1972) 737–740

work page 1972
[2]

J. D. Bekenstein,Black holes and entropy,Phys. Rev. D7(1973) 2333–2346

work page 1973
[3]

S. W. Hawking,Particle Creation by Black Holes,Commun. Math. Phys.43(1975) 199–220

work page 1975
[4]

S. W. Hawking,Black Holes and Thermodynamics,Phys. Rev. D13(1976) 191–197

work page 1976
[5]

Thermodynamics of Spacetime: The Einstein Equation of State

T. Jacobson,Thermodynamics of spacetime: The einstein equation of state,Phys. Rev. Lett. 75(1995) 1260–1263, [gr-qc/9504004]

work page internal anchor Pith review Pith/arXiv arXiv 1995
[6]

Classical and Quantum Thermodynamics of horizons in spherically symmetric spacetimes

T. Padmanabhan,Classical and quantum thermodynamics of horizons in spherically symmetric space-times,Class. Quant. Grav.19(2002) 5387–5408, [gr-qc/0204019]

work page internal anchor Pith review Pith/arXiv arXiv 2002
[7]

The Holography of Gravity encoded in a relation between Entropy, Horizon area and Action for gravity

T. Padmanabhan,The Holography of gravity encoded in a relation between entropy, horizon area and action for gravity,Gen. Rel. Grav.34(2002) 2029–2035, [gr-qc/0205090]

work page internal anchor Pith review Pith/arXiv arXiv 2002
[8]

Thermodynamic route to Field equations in Lanczos-Lovelock Gravity

A. Paranjape, S. Sarkar and T. Padmanabhan,Thermodynamic route to field equations in Lancos-Lovelock gravity,Phys. Rev. D74(2006) 104015, [hep-th/0607240]

work page internal anchor Pith review Pith/arXiv arXiv 2006
[9]

Entropy of Null Surfaces and Dynamics of Spacetime

T. Padmanabhan and A. Paranjape,Entropy of null surfaces and dynamics of spacetime, Phys. Rev. D75(2007) 064004, [gr-qc/0701003]

work page internal anchor Pith review Pith/arXiv arXiv 2007
[10]

M. K. Parikh and S. Sarkar,Beyond the Einstein Equation of State: Wald Entropy and Thermodynamical Gravity,Entropy18(2016) 119, [0903.1176]

work page arXiv 2016
[11]

Non-equilibrium Thermodynamics of Spacetime: the Role of Gravitational Dissipation

G. Chirco and S. Liberati,Non-equilibrium thermodynamics of spacetime: the role of gravitational dissipation,Phys. Rev. D81(2010) 024016, [0909.4194]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[12]

Clausius entropy for arbitrary bifurcate null surfaces

V. Baccetti and M. Visser,Clausius entropy for arbitrary bifurcate null surfaces,Class. Quant. Grav31(2014) 035009, [1303.3185]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[13]

Horizon entropy and higher curvature equations of state

R. Guedens, T. Jacobson and S. Sarkar,Horizon entropy and higher curvature equations of state,Phys. Rev. D85(2012) 064017, [1112.6215]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[14]

Einstein's Equations from the Stretched Future Light Cone

M. Parikh and A. Svesko,Einstein’s equations from the stretched future light cone,Phys. Rev. D98(2018) , [1712.08475]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[15]

Equilibrium to Einstein: Entanglement, Thermodynamics, and Gravity

A. Svesko,Equilibrium to Einstein: Entanglement, thermodynamics, and gravity,Phys. Rev. D 99(2019) 086006, [1810.12236]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[16]

Jacobson and M

T. Jacobson and M. Visser,Spacetime Equilibrium at Negative Temperature and the Attraction of Gravity,Int. J. Mod. Phys. D28(2019) 1944016, [1904.04843]

work page arXiv 2019
[17]

Alonso-Serrano and M

A. Alonso-Serrano and M. Liˇ ska,New perspective on thermodynamics of spacetime: The emergence of unimodular gravity and the equivalence of entropies,Phys. Rev. D102(2020) 104056, [2008.04805]

work page arXiv 2020
[18]

Alonso-Serrano, L

A. Alonso-Serrano, L. J. Garay and M. Liˇ ska,From spacetime thermodynamics to Weyl transverse gravity,Phys. Rev. D111(2025) 064019, [2409.06645]

work page arXiv 2025
[19]

Kumar,Recovering semiclassical Einstein’s equation using generalized entropy,Gen

N. Kumar,Recovering semiclassical Einstein’s equation using generalized entropy,Gen. Relativ. Gravit.55(2023) 127, [2404.16912]

work page arXiv 2023
[20]

Kumar,Non-linear equation of motion for higher curvature semiclassical gravity,Phys

N. Kumar,Non-linear equation of motion for higher curvature semiclassical gravity,Phys. Lett. B861(2025) 139264, [2501.10527]. – 30 –

work page arXiv 2025
[21]

R. M. Wald,Black hole entropy is the Noether charge,Phys. Rev. D48(1993) R3427–R3431, [gr-qc/9307038]

work page internal anchor Pith review Pith/arXiv arXiv 1993
[22]

Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy

V. Iyer and R. M. Wald,Some properties of the Noether charge and a proposal for dynamical black hole entropy,Phys. Rev. D50(1994) 846–864, [gr-qc/9403028]

work page internal anchor Pith review Pith/arXiv arXiv 1994
[23]

Entanglement Equilibrium and the Einstein Equation

T. Jacobson,Entanglement equilibrium and the Einstein equation,Phys. Rev. Lett.116(2016) 201101, [1505.04753]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[24]

Thermodynamic Origin of the Null Energy Condition

M. Parikh and A. Svesko,Thermodynamic Origin of the Null Energy Condition,Phys. Rev. D 95(2017) 104002, [1511.06460]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[25]

Logarithmic Corrections to Gravitational Entropy and the Null Energy Condition

M. Parikh and A. Svesko,Logarithmic corrections to gravitational entropy and the null energy condition,Phys. Lett. B761(2016) 16–19, [1612.06949]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[26]

J. D. Bekenstein,Generalized second law of thermodynamics in black hole physics,Phys. Rev. D9(1974) 3292–3300

work page 1974
[27]

The "physical process" version of the first law and the generalized second law for charged and rotating black holes

S. Gao and R. M. Wald,“physical process version” of the first law and the generalized second law for charged and rotating black holes,Phys. Rev. D64(2001) 084020, [gr-qc/0106071]

work page internal anchor Pith review Pith/arXiv arXiv 2001
[28]

Entanglement equilibrium for higher order gravity

P. Bueno, V. S. Min, A. J. Speranza and M. R. Visser,Entanglement equilibrium for higher order gravity,Phys. Rev. D95(2017) 046003, [1612.04374]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[29]

Jacobson,Black hole entropy and induced gravity,2401.03572

T. Jacobson,Black hole entropy and induced gravity,2401.03572

work page arXiv
[30]

Black Hole Entropy in Canonical Quantum Gravity and Superstring Theory

L. Susskind and J. Uglum,Black hole entropy in canonical quantum gravity and superstring theory,Phys. Rev. D50(1994) 2700, [hep-th/9401070]

work page internal anchor Pith review Pith/arXiv arXiv 1994
[31]

A Quantum Focussing Conjecture

R. Bousso, Z. Fisher, S. Leichenauer and A. C. Wall,Quantum focusing conjecture,Phys. Rev. D93(2016) 064044, [1506.02669]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[32]

State-Dependent Divergences in the Entanglement Entropy

D. Marolf and A. C. Wall,State-dependent divergences in the entanglement entropy,J. High Energ. Phys.2016(2016) , [1607.01246]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[33]

Chandrasekaran, G

V. Chandrasekaran and G. Penington,Large N algebras and generalized entropy,J. High Energ. Phys.2023(2023) , [2209.10454]

work page arXiv 2023
[34]

Kudler-Flam, S

J. Kudler-Flam, S. Leutheusser and G. Satishchandran,Generalized black hole entropy is von Neumann entropy,Phys. Rev. D111(2025) 025013, [2309.15897]

work page arXiv 2025
[35]

Jensen, J

K. Jensen, J. Sorce and A. J. Speranza,Generalized entropy for general subregions in quantum gravity,J. High Energ. Phys.2023(2023) , [2306.01837]

work page arXiv 2023
[36]

J. F. Pedraza, A. Svesko and M. R. Sybesma, Watse.d Visser,Microcanonical action and the entropy of Hawking radiation,Phys. Rev. D105(2022) 126010, [2111.06912]

work page arXiv 2022
[37]

J. F. Pedraza, A. Svesko, W. Sybesma and M. R. Visser,Semi-classical thermodynamics of quantum extremal surfaces in Jackiw-Teitelboim gravity,JHEP12(2021) 134, [2107.10358]

work page arXiv 2021
[38]

Svesko, E

A. Svesko, E. Verheijden, E. P. Verlinde and M. R. Visser,Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity,JHEP08(2022) 075, [2203.00700]

work page arXiv 2022
[39]

Emparan, A

R. Emparan, A. M. Frassino and B. Way,Quantum BTZ black hole,JHEP11(2020) 137, [2007.15999]. – 31 –

work page arXiv 2020
[40]

Panella, J

E. Panella, J. F. Pedraza and A. Svesko,Three-Dimensional Quantum Black Holes: A Primer, Universe10(2024) 358, [2407.03410]

work page arXiv 2024
[41]

J. D. Bardeen, B. Carter and S. W. Hawking,The four laws of black hole mechanics, Commun.Math. Phys.31(1973) 161

work page 1973
[43]

Banihashemi, T

B. Banihashemi, T. Jacobson, A. Svesko and M. R. Visser,The minus sign in the first law of de Sitter horizons,J. High Energ. Phys.2023(2023) , [2208.11706]

work page arXiv 2023
[44]

Gravitation from Entanglement in Holographic CFTs

T. Faulkner, M. Guica, T. Hartman, R. C. Myers and M. Van Raamsdonk,Gravitation from entanglement in holographic CFTs,J. High Energy Phys.2014(2014) , [1312.7856]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[45]

Nonlinear Gravity from Entanglement in Conformal Field Theories

T. Faulkner, F. M. Haehl, E. Hijano, O. Parrikar, C. Rabideau and M. Van Raamsdonk, Nonlinear gravity from entanglement in conformal field theories,J. High Energy Phys.2017 (2017) , [1705.03026]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[46]

J. F. Pedraza, A. Russo and A. Svesko,Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity,JHEP2022(2022) , [2106.12585]

work page arXiv 2022
[47]

J. F. Pedraza, A. Russo, A. Svesko and Z. Weller-Davies,Computing spacetime,Int. J. Mod. Phys. D31(2022) 2242010, [2205.05705]

work page arXiv 2022
[48]

Carrasco, J

R. Carrasco, J. F. Pedraza, A. Svesko and Z. Weller-Davies,Gravitation from optimized computation: Einstein and beyond,J. High Energ. Phys.2023(2023) , [2306.08503]

work page arXiv 2023
[49]

D. M. Capper and M. J. Duff,Trace anomalies in dimensional regularization,Nuovo Cim. A 23(1974) 173

work page 1974
[50]

R. J. Riegert,A non-local action for the trace anomaly,Phys. Lett. B134(1984) 56

work page 1984
[51]

E. S. Fradkin and A. A. Tseylin,Conformal anomaly in Weyl theory and anomaly free superconformal theories,Phys. Lett. B134(1984) 187

work page 1984
[52]

M. J. Duff,Twenty years of the Weyl anomaly,Class. Quant. Grav.11(1994) 1387, [hep-th/9308075]

work page internal anchor Pith review Pith/arXiv arXiv 1994
[53]

J. M. Bardeen,Trace anomaly effective actions - a critique,gr-qc/1808.09629

work page internal anchor Pith review Pith/arXiv arXiv
[54]

Arrechea, G

J. Arrechea, G. Neri and S. Liberati,Inner horizon instability via the trace anomaly effective action,Phys. Rev. D111(2025) 084036, [2411.14964]

work page arXiv 2025
[55]

D. A. Lowe and L. Thorlacius,Effective Field Theory Description of Hawking Radiation, hep-th/2505.07722

work page arXiv
[56]

A. M. Polyakov,Quantum geometry of bosonic strings,Phys. Lett. B103(1981) 207

work page 1981
[57]

Weyl Invariance and Black Hole Evaporation

J. Navarro-Salas, M. Navarro and C. F. Talavera,Weyl invariance and black hole evaporation, Phys. Lett. B356(1995) 217, [hep-th/9505139]

work page internal anchor Pith review Pith/arXiv arXiv 1995
[58]

Teitelboim,Gravitation and hamiltonian structure in two spacetime dimensions,Phys

C. Teitelboim,Gravitation and hamiltonian structure in two spacetime dimensions,Phys. Lett. B126(1983) 41

work page 1983
[59]

Jackiw,Lower dimensional gravity,Phys

R. Jackiw,Lower dimensional gravity,Phys. Lett. B252(1985) 343

work page 1985
[60]

Reversible and Irreversible Spacetime Thermodynamics for General Brans-Dicke Theories

G. Chirco, C. Eling and S. Liberati,Reversible and irreversible spacetime thermodynamics for general Brans-Dicke theories,Phys. Rev. D83(2011) 024032, [1011.1405]. – 32 –

work page internal anchor Pith review Pith/arXiv arXiv 2011
[61]

R. Dey, S. Liberati and A. Mohd,Higher derivative gravity: Field equation as the equation of state,Phys. Rev. D94(2016) 044013, [1605.04789]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[62]

Hollands, R

S. Hollands, R. M. Wald and V. G. Zhang,The entropy of dynamical black holes,Phys. Rev. D 110(2024) 024070, [2402.00818]

work page arXiv 2024
[63]

M. R. Visser and Z. Yan,Properties of dynamical black hole entropy,J. High Energ. Phys. 2024(2024) , [2403.07140]

work page arXiv 2024
[64]

Brewin,Riemann normal coordinate expansions using Cadabra,Class

L. Brewin,Riemann normal coordinate expansions using Cadabra,Class. Quant. Grav.26 (2009) 175017, [0903.2087]

work page arXiv 2009
[65]

L. C. Barbado and M. Visser,Unruh-DeWitt detector event rate for trajectories with time-dependent acceleration,Phys. Rev. D86(2012) 084011, [1207.5525]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[66]

f(Lovelock) theories of gravity

P. Bueno, P. A. Cano, O. A. Lasso and P. F. Ram´ ırez,f(lovelock) theories of gravity,J. High Energ. Phys.2016(2016) , [1602.07310]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[67]

Holographic Entanglement Entropy for General Higher Derivative Gravity

X. Dong,Holographic entanglement entropy for general higher derivative gravity,J. High Energ. Phys.2014(2014) , [1310.5713]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[68]

A. C. Wall,A second law for higher curvature gravity,Int. J. Mod. Phys. D24(2015) 1544014, [1504.08040]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[69]

On Black Hole Entropy

T. Jacobson, G. Kang and R. C. Myers,On black hole entropy,Phys. Rev. D49(1994) 6587–6598, [gr-qc/9312023]

work page internal anchor Pith review Pith/arXiv arXiv 1994
[70]

Second Law Violations in Lovelock Gravity for Black Hole Mergers

S. Sarkar and A. C. Wall,Second law violations in Lovelock gravity for black hole mergers, Phys. Rev. D83(2011) 26, [1011.4988]

work page internal anchor Pith review Pith/arXiv arXiv 2011
[71]

Gadioux and H

M. Gadioux and H. S. Reall,Creases, corners, and caustics: Properties of non-smooth structures on black hole horizons,Phys. Rev. D108(2023) 084021, [2303.15512]

work page arXiv 2023
[72]

Comp` ere and A

G. Comp` ere and A. Fiorucci,Advanced Lectures on General Relativity. Springer International Publishing, 2018, 10.1007/978-3-030-04260-8

work page doi:10.1007/978-3-030-04260-8 2018
[73]

Models of AdS_2 Backreaction and Holography

A. Almheiri and J. Polchinski,Models of AdS2 backreaction and holography,JHEP2015 (2015) , [1402.6334]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[74]

J. G. Russo, L. Susskind and L. Thorlacius,Black hole evaporation in 1+1 dimensions,Phys. Lett. B292(1992) 13, [hep-th/9201074]

work page internal anchor Pith review Pith/arXiv arXiv 1992
[75]

Replica Wormholes and the Entropy of Hawking Radiation

A. Almheiri, T. Hartman and J. Maldacena,Replica wormholes and the entropy of Hawking radiation,JHEP2020(2020) , [1911.12333]

work page internal anchor Pith review Pith/arXiv arXiv 2020
[76]

A. J. Speranza,Entanglement entropy of excited states in conformal perturbation theory and the Einstein equation,JHEP2016(2016) , [1602.01380]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[77]

Comments on Jacobson's "Entanglement equilibrium and the Einstein equation"

H. Casini, D. A. Galante and R. C. Myers,Comments on Jacobson’s “Entanglement equilibrium and the Einstein equation”,JHEP2016(2016) , [1601.00528]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[78]

R. M. Wald,Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics. Chicago Lectures in Physics. University of Chicago Press, Chicago, 1994

work page 1994
[79]

Relating black holes in two and three dimensions

A. Ach´ ucarro and M. E. Ortiz,Relating black holes in two and three dimensions,Phys. Rev. D 48(1993) 3600, [hep-th/9304068]. – 33 –

work page internal anchor Pith review Pith/arXiv arXiv 1993
[80]

Quantum evolution of near-extremal Reissner-Nordstrom black holes

A. Fabbri, D. J. Navarro and J. Navarro-Salas,Quantum evolution of near-extremal Reissner–Nordstr¨ om black holes,Phys. Lett. B595(1995) 381, [hep-th/0006035]

work page internal anchor Pith review Pith/arXiv arXiv 1995
[81]

On the Dynamics of Near-Extremal Black Holes

P. Nayak, A. Shukla, R. M. Soni, S. P. Trivedi and V. Vishal,On the dynamics of near-extremal black holes,JHEP2018(2018) , [1802.09547]

work page internal anchor Pith review Pith/arXiv arXiv 2018

Showing first 80 references.