Anti-de Sitter Black Holes, Thermal Phase Transition and Holography in Higher Curvature Gravity

Ishwaree P. Neupane; Y. M. Cho

REVIEW

Anti-de Sitter Black Holes, Thermal Phase Transition and Holography in Higher Curvature Gravity

Y. M. Cho, Ishwaree P. Neupane

High Energy Physics - Theory · Submitted 21 Feb 2002 · 55 references

Pith's verdict: The Gauss-Bonnet half is solid and the Wald/first-law entropy check is genuinely useful; the (Riemann)² k=-1 transition is an extrapolation of a first-order expansion at coupling O(1), and the abstract misstates two of its own results.

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arXiv IDhep-th/0202140 (version 3)

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CitationIshwaree P. Neupane, Y. M. Cho. "Anti-de Sitter Black Holes, Thermal Phase Transition and Holography in Higher Curvature Gravity." arXiv:hep-th/0202140 (2002). https://pith.science/paper/EEA7EIRT

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Two things here are worth your time, and one isn't earned yet. Start with the good part, because it's real: the Gauss-Bonnet thermodynamics is done carefully, and the entropy cross-check is the result I'd actually use. The first-law entropy (Eq. 27) and the Wald/Noether-charge entropy (Eq. 70) agree exactly, for arbitrary cosmological term and all three horizon geometries. That's clean and checkable. The k=-1 Hawking-Page window they find in GB gravity (0.48 < α̂/ℓ² < 0.52, Figs. 8–9) is exact, but look at how narrow it is — that's a fine-tuning, not a robust phenomenon, and the paper doesn't dwell on it. The (Riemann)² half is where I'd push back, and the stress-test note lands. The k=-1 transition there needs γ̂/L² > 1/2 by their own Fig. 13 numbers, while the solution (Eq. 50) and free energy (Eq. 56) are truncated at first order in γ̂. At γ̂/L² ≈ 0.5 the dropped O(γ̂²) terms are not small, and F is a difference whose zero crossing defines the transition, so a correction of that size can move or erase the window. Compounding it, their dictionary γ̂/L² = 1/(8N) puts that window at N < 1/4, outside any regime where the 1/N expansion means anything. The paper says only that k=-1 'does not give a physical bound for N' and moves on. That's the load-bearing gap, and the abstract doesn't carry it. Two abstract errors worth flagging to the authors: s7 says S_BH ≤ S_H for k=0 and k=-1, but the body (Eq. 99 and the paragraph after) says S_H ≤ S_BH for k=0 and k=1, and the conclusions side with the body. And s3's N>5 is a k=+1 statement, not k=-1, despite the juxtaposition in s2–s3. Footnote 2 also flags a sign disagreement with Ref. [43] on the free energy and a contradiction on the entropy comparison, left unresolved. Recommendation: send it out. The GB results will hold up and the entropy check is worth having in the literature. Tell the referee to check the abstract against the body and to treat the (Riemann)² k=-1 claim as a conjecture until someone does the second-order calculation.

Referee report

Major objections (3)

[Abstract s2/s3; Section V, Fig. 13] The abstract juxtaposes the k=-1 transition (s2) with the N>5 statement (s3) in a way that suggests N>5 is the condition for the k=-1 transition. In the text, however, N>5 is derived for k=+1 (Section V: 'For k = +1, existence of a thermal AdS phase (F > 0) requires γ̂/L² < 1/42, which implies that N > 5'), while the k=-1 case requires γ̂/L² > 1/2, i.e., N < 1/4. The authors acknowledge that this 'does not give a physical bound for N' but do not state the consequence: the k=-1 (Riemann)² transition lies outside the N ≥ 1 regime in which the duality-motivated expansion is controlled. The abstract should be revised to make clear which horizon geometry each statement refers to, and the physical status of the k=-1 (Riemann)² window should be stated explicitly.
[Section V, Eqs. (50), (52), (56)] The k=-1 (Riemann)² free-energy window is read off a first-order expansion in γ̂ at γ̂/L² ≈ 0.5. At this value the neglected O(γ̂²) terms are parametrically of the same order as the retained O(γ̂) terms, and since the transition is defined by a zero crossing of F, a correction of that size can move or remove the window. The manuscript does not estimate the size of the neglected terms or provide a second-order check. The k=-1 (Riemann)² claim should either be supported by an estimate of the O(γ̂²) correction or explicitly downgraded to a heuristic observation.
[Section VI.B, Eq. (99); Abstract s7] There is a sign inconsistency. Eq. (99) gives S_H - S_BH = -48πV3γ r_H(k + r_H²/(3L²)). For k=0 this is negative, so S_H < S_BH; the body text correctly states 'In the k = 0 and k = 1 cases, one finds S_H ≤ S_BH.' But the abstract (s7) states 'for k=0 and k=-1, would imply S_BH ≤ S_H,' which is the opposite inequality for k=0 and also names k=-1 rather than k=+1. For k=-1, Eq. (99) gives S_H - S_BH = 48πV3γ r_H(1 - r_H²/(3L²)), which is negative for r_H² > 3L², so S_H < S_BH; the body text states the opposite ('S_H > S_BH if r_H² > 3L²'). The abstract, the body text, and Eq. (99) cannot all be correct; the authors should reconcile them.

Minor objections (5)

[Eq. (87)] The expression κ4 = 2Lκ5/(1+λε) appears to have a dimensional mismatch; Eq. (88) uses κ4 = 2κ5/L(1 - 2γ̂/L²), which suggests the correct form is κ4 = 2κ5/(L(1+λε)). Please check.
[Section III.C, Fig. 9] The text says 'under the limit 0.48 < α̂/ℓ² < 0.52, free energy is always positive,' but Fig. 9 shows F > 0 only for small r_H and F < 0 for large r_H. The phrase 'always positive' should be corrected to 'positive for small r_H.'
[Section III.C] The k=-1 Gauss-Bonnet transition window 0.48 < α̂/ℓ² < 0.52 is narrow; it would be useful to state explicitly how robust this window is and whether it survives at d+1 > 5.
[Footnote 2; Section V] The manuscript notes a sign discrepancy with Ref. [43] in the last term of the free energy and states that its entropy result 'clearly contradict[s] with the observations made in Ref. [43].' It would strengthen the paper to identify the source of the discrepancy (e.g., a different convention for the boundary term or a different definition of the horizon curvature) rather than simply recording the disagreement.
[Abstract s3; Section V] 'N>5' should be stated as N ≥ 6 (since γ̂/L² = 1/(8N) < 1/42 gives N > 5.25).

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The paper

The paper claims

The paper argues that higher-curvature terms can allow a Hawking-Page thermal phase transition for anti-de Sitter black holes with hyperbolic horizons, a case forbidden in Einstein gravity.

The reading

The paper asks whether the Hawking-Page thermal transition—normally a black-hole-to-thermal-AdS change seen only for positively curved horizons in Einstein gravity—can survive when the bulk action includes a Gauss-Bonnet term or a generic $(Riemann)^2$ term. Its central claim is yes: for a hyperbolic horizon ($k=-1$), the free energy can turn positive at small horizon radius and negative at large radius, so a thermal AdS phase can be preferred in a window even though Einstein gravity forbids such a transition. The payoff would be a thermal AdS/CFT setting with a non-spherical boundary, and a way to see finite-coupling ($1/N$) corrections in black-hole thermodynamics. The paper also checks entropy: for Gauss-Bonnet the first-law entropy matches the Wald Noether-charge formula exactly, while for $(Riemann)^2$ the two agree only approximately, becoming identical when $r_H$ is much larger than $L$. One internal caveat should be recorded: the abstract states $S_{BH} < S_H$ for $k=0$ and $k=-1$, whereas Section VI derives the opposite inequality $S_H < S_{BH}$ for $k=0$ and $k=1$.

What carries the argument

The argument is carried by the sign of the regularized Euclidean free energy, $F=I_E/beta$, measured relative to thermal AdS with $F=0$. The Hawking temperature comes from the periodicity of imaginary time, $T=(e^{2varphi})'|_{r_H}/4pi$, and a phase transition occurs when $F$ changes sign as $r_H$ varies: $F>0$ favors thermal AdS, $F<0$ favors the black hole. For Gauss-Bonnet the authors use the exact solution $e^{2varphi}=k+r^2/(2hatalpha)+epsilon r^2/(2hatalpha)[1-4hatalpha/ell^2(1-hatalpha/ell^2)+4hatalpha m/r^d]^{1/2}$ and derive $F$, $T$, and $S$; for $(Riemann)^2$ they use a first-order perturbative metric and free energy. Entropy is cross-checked with the Noether-charge formula $tilde S=(4pi/kappa_{d+1})int d^{d-1}xsqrt{h}[1+2alphakappa_{d+1}R(h)]$ for Gauss-Bonnet and its higher-curvature generalization for $(Riemann)^2$.

Extended reading notes

Core claim

The paper's central result is that higher-curvature interactions change the phase structure of anti-de Sitter black holes. In Einstein gravity only $k=1$ horizons show a Hawking-Page transition; with the Gauss-Bonnet combination the authors find an exact branch where the $k=-1$ free energy can be positive for a range of horizon radii and negative for large radii, opening a first-order transition between a small topological black hole and thermal AdS. In the $(Riemann)^2$ theory, treated perturbatively to first order in $hatgamma$, a spherical horizon can show the transition only when $hatgamma/L^2 < 1/42$, which the authors translate as $N>5$, while a hyperbolic horizon requires $hatgamma/L^2>1/2$, a large-coupling regime that does not give a physical bound on $N$. The paper also shows that the Gauss-Bonnet entropy from the first law coincides with the Wald entropy for an arbitrary cosmological term, and that the $(Riemann)^2$ entropy agrees with Wald's formula in the large-horizon limit.

Load-bearing premise

For the $(Riemann)^2$ half of the claim, the load-bearing premise is that the first-order perturbative free energy remains reliable in the regime where the hyperbolic free energy turns positive, even though that regime requires $hatgamma/L^2>1/2$, an $O(1)$ coupling outside the perturbative expansion.

Editorial extensions

If this is right

A $k=-1$ Hawking-Page transition would let thermal AdS/CFT be studied on a hyperbolic boundary, not only on $S^{d-1}times S^1$.
The $N>5$ threshold in $(Riemann)^2$ gravity makes the transition a finite-$N$ effect, so the free-energy density should carry subleading $1/N$ terms beyond the Einstein result.
If the Gauss-Bonnet entropy identity holds for arbitrary $Lambda$, the area law is replaced by a horizon-curvature correction fixed by the first law and Noether charge, not by the horizon area alone.
The brane-world translation gives FRW equations in which the induced matter is not radiation-like when $gammatilde=0$ is violated, so the holographic entropy comparison can be phrased as a bound on brane matter.

Reading between the lines

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

If the hyperbolic transition survives at second order in $hatgamma$, it would be a clean finite-coupling test for a dual CFT on a hyperbolic boundary; a thermal CFT on $H^3times S^1$ should show a corresponding confinement-like jump.
The paper's $N>5$ condition is a statement about the sign of a coefficient in a $1/N$ expansion; comparing it with the known $N=2$ $Sp(N)$ free energy at weak coupling could turn the threshold into a quantitative check rather than a sign test.
The abstract/text entropy-inequality mismatch suggests recalculating $S_H-S_{BH}$ for all $k$; the sign may depend on whether one uses the horizon radius or the brane radius in the Hubble formula.
Because the $k=-1$ $(Riemann)^2$ window needs $hatgamma/L^2>1/2$, a natural extension is to solve the full theory numerically and see whether the window is an artifact of first-order truncation or a real strong-coupling phase.

Original abstract

We study anti-de Sitter black holes in the Einstein-Gauss-Bonnet and the generic R^2 gravity theories, evaluate different thermodynamic quantities, and also examine the possibilities of Hawking-Page type thermal phase transitions in these theories. In the Einstein theory, with a possible cosmological term, one observes a Hawking-Page phase transition only if the event horizon is a hypersurface of positive constant curvature (k=1). But, with the Gauss-Bonnet or/and the (Riemann)^2 interaction terms, there may occur a similar phase transition for a horizon of negative constant curvature (k=-1). We examine the finite coupling effects, and find that N>5 could trigger a Hawking-Page phase transition in the latter theory. For the Gauss-Bonnet black holes, one relates the entropy of the black hole to a variation of the geometric property of the horizon based on first law and Noether charge. With (Riemann)^2 term, however, we can do this only approximately, and the two results agree when, r_H>>L, the size of the horizon is much bigger than the AdS curvature scale. We establish some relations between bulk data associated with the AdS black hole and boundary data defined on the horizon of the AdS geometry. Following a heuristic approach, we estimate the difference between Hubble entropy {\cal S}_H and Bekenstein-Hawking entropy {\cal S}_{BH} with (Riemann)^2 term, which, for k=0 and k=-1, would imply {\cal S}_{BH}\leq {\cal S}_H.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,550 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.89 · human participants 0.01 · controlled comparison 0.25 · randomized assignment 0.01 · states quantitative result 0.84 · compares with prior results 0.82 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We study anti-de Sitter black holes in the Einstein-Gauss-Bonnet and the generic R^2 gravity theories, evaluate different thermodynamic quantities, and also examine the possibilities of Hawking-Page type thermal phase transitions in these theories. In the Einstein theory, with a possible cosmological term, one observes a Hawking-Page phase transition only if the event horizon is a hypersurface of positive constant curvature (k=1). But, with the Gauss-Bonnet or/and the (Riemann)^2 interaction terms, there may occur a similar phase transition for a horizon of negative constant curvature (k=-1). We examine the finite coupling effects, and find that N>5 could trigger a Hawking-Page phase transition in the latter theory. For the Gauss-Bonnet black holes, one relates the entropy of the black hole to a variation of the geometric property of the horizon based on first law and Noether charge. With (Riemann)^2 term, however, we can do this only approximately, and the two results agree when, r_H>>L, the size of the horizon is much bigger than the AdS curvature scale. We establish some relations between bulk data associated with the AdS black hole and boundary data defined on the horizon of the AdS geometry. Following a heuristic approach, we estimate the difference between Hubble entropy {\cal S}_H and Bekenstein-Hawking entropy {\cal S}_{BH} with (Riemann)^2 term, which, for k=0 and k=-1, would imply {\cal S}_{BH}\leq {\cal S}_H.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study anti-de Sitter black holes in the Einstein-Gauss-Bonnet and the generic R^2 gravity theories, evaluate different thermodynamic quantities, and also examine the possibilities of Hawking-Page type thermal phase transitions in these theories.	contribution 1.00	0.95	0.10	asserted 0.91
s1	In the Einstein theory, with a possible cosmological term, one observes a Hawking-Page phase transition only if the event horizon is a hypersurface of positive constant curvature (k=1).	background 0.95	0.15	0.08	asserted 0.88
s2	But, with the Gauss-Bonnet or/and the (Riemann)^2 interaction terms, there may occur a similar phase transition for a horizon of negative constant curvature (k=-1).	result 0.96	0.38	0.30	hedged possibility 1.00
s3	We examine the finite coupling effects, and find that N>5 could trigger a Hawking-Page phase transition in the latter theory.	result 0.99	0.94	0.19	asserted 0.73
s4	For the Gauss-Bonnet black holes, one relates the entropy of the black hole to a variation of the geometric property of the horizon based on first law and Noether charge.	contribution 0.48	0.76	0.06	asserted 1.00
s5	With (Riemann)^2 term, however, we can do this only approximately, and the two results agree when, r_H>>L, the size of the horizon is much bigger than the AdS curvature scale.	limitation 0.76	0.92	0.07	asserted 0.80
s6	We establish some relations between bulk data associated with the AdS black hole and boundary data defined on the horizon of the AdS geometry.	contribution 0.84	0.92	0.08	asserted 1.00
s7	Following a heuristic approach, we estimate the difference between Hubble entropy {\cal S}_H and Bekenstein-Hawking entropy {\cal S}_{BH} with (Riemann)^2 term, which, for k=0 and k=-1, would imply {\cal S}_{BH}\leq {\cal S}_H.	result 0.72	0.91	0.14	hedged possibility 0.78

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

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Forward citations

Cited by 19 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Holographic studies of Einsteinian cubic gravity
hep-th 2018-01 conditional novelty 7.0 of 10

In the holographic model defined by Einsteinian cubic gravity in four bulk dimensions, the shear viscosity to entropy density ratio never falls below the KSS bound, because the parameter region that would allow a viol...
Viscosity Bound Violation in Higher Derivative Gravity
hep-th 2007-12 accept novelty 7.0 of 10

In Gauss-Bonnet gravity duals the shear viscosity to entropy density ratio is (1/4π)(1-4λ_GB), which drops below the conjectured 1/4π bound for positive coupling.
Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid
hep-th 2016-11 conditional novelty 6.0 of 10

The Haack-Yarom relation among second-order transport coefficients is violated at second order in the Gauss-Bonnet coupling, and the zero-viscosity limit does not yield a dissipationless fluid.
Complexity of Formation in Holography
hep-th 2016-10 conditional novelty 6.0 of 10

For holographic theories in three or more boundary dimensions, the extra circuit complexity needed to prepare the thermofield double state grows linearly with its thermal entropy, with coefficient ((d-2)/(d*pi))*cot(p...
From strong to weak coupling in holographic models of thermalization
hep-th 2016-05 conditional novelty 6.0 of 10

Curvature-squared and curvature-fourth corrections to holographic black branes create new poles that collide with hydrodynamic poles, and the viscosity-to-relaxation-time ratio flattens as the coupling weakens.

Show 14 more citing papers

Smarr Formula and an Extended First Law for Lovelock Gravity
hep-th 2010-05 conditional novelty 6.0 of 10

A Smarr formula and an extended first law are derived for static asymptotically AdS Lovelock black holes, with new geometric potentials conjugate to the Lovelock couplings.
Black objects in the Einstein-Gauss-Bonnet theory with negative cosmological constant and the boundary counterterm method
gr-qc 2008-06 conditional novelty 6.0 of 10

Boundary counterterms regularize the action and charges of Einstein-Gauss-Bonnet anti-de Sitter black objects up to nine dimensions, with explicit results for black holes and new numerical black string solutions.
Five-dimensional rotating black holes in Einstein-Gauss-Bonnet theory
hep-th 2008-01 conditional novelty 6.0 of 10

Numerical solutions for five-dimensional rotating black holes with two equal spins are constructed in Einstein-Gauss-Bonnet gravity with a negative cosmological constant, and their thermodynamic charges are computed.
Universal regularization prescription for Lovelock AdS gravity
hep-th 2007-08 conditional novelty 6.0 of 10

A boundary term built from intrinsic and extrinsic boundary curvature, with a dimension-dependent form and a theory-dependent coefficient, regularizes both the Noether charges and the Euclidean action of any Lovelock-...
Higher derivative corrections to near-extremal black holes in type IIB supergravity
hep-th 2006-04 conditional novelty 6.0 of 10

Leading alpha' corrections shift the Hawking-Page temperature by a factor of (1 - 40γ) and add a ln(T/ε) term to the free energy of charged black 3-branes with a chemical potential.
A Lovelock black hole bestiary
hep-th 2011-03 accept novelty 5.0 of 10

By reading black hole solutions off the shape of one Lovelock polynomial, the authors classify every branch by asymptotics, horizon topology, and thermodynamic stability.
Thermodynamics of the Maxwell-Gauss-Bonnet anti-de Sitter Black Hole with Higher Derivative Gauge Corrections
hep-th 2008-07 conditional novelty 5.0 of 10

Charged anti-de Sitter black holes with Gauss-Bonnet and quartic field-strength corrections have a richer thermal phase structure than their uncorrected counterparts, including new metastable states and a secondary Ha...
Born-Infeld Corrections to the Entropy Function of Heterotic Black Holes
hep-th 2006-04 conditional novelty 5.0 of 10

Born-Infeld terms change the near-horizon geometry and entropy of two-charge heterotic black holes, but only yield a consistent attractor when Gauss-Bonnet terms are present.
A Note on Thermodynamics of Black Holes in Lovelock Gravity
hep-th 2003-11 accept novelty 5.0 of 10

For Lovelock-gravity black holes with general horizon topology, mass, Hawking temperature and entropy reduce to simple functions of horizon radius, and flat horizons preserve the area law for entropy.
Vector mesons from a holographic QCD model in $f(R)$-dilaton gravity
hep-th 2025-02 unverdicted novelty 4.0 of 10

In Starobinsky-dilaton holographic QCD, rho meson masses match experiment for α = 10^{-8} and recover prior results at α = 0.
Black holes in Einstein-Gauss-Bonnet gravity with a background of modified Chaplygin gas
gr-qc 2019-08 conditional novelty 4.0 of 10

The authors obtain a static 5D Einstein-Gauss-Bonnet black hole solution surrounded by modified Chaplygin gas and analyze its thermodynamics, scalar tunneling, and perturbative stability.
Hamilton-Jacobi Counterterms for Einstein-Gauss-Bonnet Gravity
hep-th 2008-07 accept novelty 4.0 of 10

A Hamilton-Jacobi derivation gives the boundary counterterms that renormalize Einstein-Gauss-Bonnet gravity to first order in the Gauss-Bonnet coupling, and the resulting black hole free energy matches earlier backgro...
On Gauss-Bonnet black hole entropy
gr-qc 2004-02 accept novelty 4.0 of 10

The Noether charge entropy of Lovelock black holes reduces to an integral of Euler densities over the horizon, and the negative entropies seen for small Gauss-Bonnet black holes can be removed by an additive constant ...
The Lovelock Black Holes
gr-qc 2008-05 accept novelty 2.0 of 10

Lovelock gravity's black holes, especially the five-dimensional Boulware-Deser solution, show non-area-law entropy, thermodynamic stability, vacuum wormholes, and quantum-regular naked singularities.

How the literature uses it

35 arXiv papers cite this in 49 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 28 sentences without a confident label

Builds on it 1 paper

We will build our results from the well studied cases of Reissner-Nördstrom anti-de Sitter black holes [ref] and Gauss-Bonnet black holes [ref] , and generalize to the Gauss-Bonnet-$F^4$ black hole.

Thermodynamics of the Maxwell-Gauss-Bonnet anti-de Sitter Black Hole with Higher Derivative Gauge Corrections · Introduction · 0.96

Uses its method or tool 1 paper

Following the perturbative metric solution found in [ref] and the methods discussed in refs.

Entropy Bound and Causality Violation in Higher Curvature Gravity · Entropy Bound for (Riemann)$^2$ Gravity · 0.87

Compares with it 2 papers

The expressions of mass (without the Casimir term) and entropy agree with previous results in the literature found by using a different approach [ref] , [ref] , [ref] , [ref] .

Black objects in the Einstein-Gauss-Bonnet theory with negative cosmological constant and the boundary counterterm method · Static solutions · 1.00
Let us finally mention that the thermodynamic behavior of our black holes is qualitatively similar to the one observed for $D=5$ Gauss-Bonnet black holes [ref] [See also [ref] for the case of general quadratic gravity — the analysis becomes perturbative in that case though.].

Holographic studies of Einsteinian cubic gravity · Spherical boundary: Hawking-Page transitions · 0.99

Cites it as background 17 papers

Exact solutions and thermodynamic properties of black objects in Gauss-Bonnet gravity ([ref]) were discussed in [ref] (see also [ref] ).

Viscosity Bound Violation in Higher Derivative Gravity · Black brane geometry and thermodynamics · 0.96
Static AdS black hole solutions in EGB gravity denote GBAdS in this work, presenting a number of interesting features (see $e.g.$ [ref] , [ref] , [ref] and the references therein).

Thermodynamics of Gauss-Bonnet black holes revisited · Introduction · 0.83
The EGB black holes in anti de Sitter and de Sitter spaces have been discussed separately in [ref] and [ref] .

Black holes in Einstein-Gauss-Bonnet gravity with a background of modified Chaplygin gas · Introduction · 0.97

Discussion

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