The holographic principle

Raphael Bousso

REVIEW

The holographic principle

Raphael Bousso

High Energy Physics - Theory · Submitted 12 Mar 2002 · 128 references

Pith's verdict: The standard reference for the covariant entropy bound and light-sheet construction, honest about what it cannot prove, though the abstract claims more than the body delivers.

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arXiv IDhep-th/0203101 (version 2)

Pith IDUKOTJIYL, Pith's permanent record of this paper and its review

CitationRaphael Bousso. "The holographic principle." arXiv:hep-th/0203101 (2002). https://pith.science/paper/UKOTJIYL

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Editor's note

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Bousso's review is the canonical statement of the covariant entropy bound, and it earns that status. If you want the light-sheet construction — the four orthogonal null families, the θ ≤ 0 selection rule, termination at caustics, the five-step recipe in Sec. V.E — this is where to get it, and the FRW worked examples in Sec. VII.A are checkable line by line. The counterexamples to the spacelike bound in Sec. IV are the cleanest part of the paper: four ordinary systems, each of which kills the naive volume-law formulation, correctly attributed to Fischler-Susskind, Easther-Lowe, and Jacobson. The collapse-shell calculation in Sec. VII.B.3 is a nice piece of work and not something you see done often enough to be confident about it otherwise. What is new here is synthesis, not result. The bound itself is Bousso 1999a; the FMW sufficient conditions are cited; the AdS/CFT degree-of-freedom counting is Susskind-Witten. That is fine for a review, but it means the paper's authority is partly borrowed from work the author also wrote. Worth knowing when you cite it. Soft spots, in order. First, the abstract's 'a universal relation between geometry and information is thus uncovered' (s4) runs ahead of the body. Sec. V.C.2 says plainly that with only B fixed and no embedding geometry, 'one can at best hold the surface B fixed, but not the light-sheet of B', and that this 'leaves too much freedom for Eq. (5.1) to be checked explicitly.' So the general statement is a conjecture supported by a proper subset of cases. The paper says so; the abstract does not. Minor, but it is the sentence people will quote. Second, the FMW conditions are the main general support, and Bousso says himself they are not fundamental and do not cover all realistic systems. That is honest, and it also means the evidence base is narrower than 'a wide range of examples' suggests. Third, the Lowe objection in Sec. V.D.2 is dispatched largely by citing Bousso 2000a; the fluctuation argument is plausible but thin as stated. None of this is fatal. The geometry is right, the concessions sit where a reader will find them, and framing the bound as a pattern awaiting explanation is the correct move. Hand this to a student starting on holography, and cite it for the light-sheet definition. Send it out; referees will mostly ask for the abstract to be softened.

Referee report

Significance

If the covariant bound holds, it is a universal relation between geometry and information that survives precisely the regimes where the older bounds fail: cosmology, gravitational collapse, and black hole interiors. The review's main contributions are expository but substantial. First, the light-sheet construction (Sec. V.B) is stated as an explicit, checkable algorithm (restated operationally in Sec. V.E), which converts a slogan into a falsifiable statement in any approximately classical geometry with a specifiable entropy content. Second, the FRW analysis of Sec. VII.A is worked through in enough detail to be reproduced, and I checked the entropy-to-area ratios of Eqs. (7.24), (7.26), and (7.28) against the integrals of Eq. (7.15); they are mutually consistent and reduce to Eq. (7.31) with the stated q-dependence. Third, the paper is candid about what it cannot show, naming the failure of the spacelike bound, the non-fundamental status of the FMW conditions, and the classical-geometry restriction. Fourth, the connection drawn to AdS/CFT (Sec. IX.B), where the CFT count N ~ n^2/delta^3 saturates the boundary area, gives the principle at least one concrete realization. The paper's

Major objections (4)

[Abstract, sentence s4; Sec. V.C.2] The abstract states that 'a universal relation between geometry and information is thus uncovered' (abstract:s4), but Sec. V.C.2 concedes that when only the surface B is fixed and the embedding geometry is not, 'one can at best hold the surface B fixed, but not the light-sheet of B', and that 'this leaves too much freedom for Eq. (5.1) to be checked explicitly'. In that limit the paper says the bound 'essentially becomes the full statement of the holographic principle'. The evidence for the bound therefore comes from the restricted class of geometries in which a background metric and either an entropy fluid or a set of fully captured modes can be specified. I do not regard this as an error, and the body of the paper is honest about it, but the abstract's unqualified 'universal' overstates what Sec. V.C.2 supports. I recommend that the abstract and the concluding assessment in Sec. VIII.A carry the same qualification the body does, for instance by describing the relation as holding in every case in which it has been possible to test it, rather than as established universally.
[Sec. VI.C.2, Eq. (6.11)] The strengthened form of the bound, S <= (A - A')/4, is used in Sec. VI.C.2 to argue that the covariant bound implies the generalized second law for absorption processes (the Geroch process) and, under suitable assumptions, a version of the Bekenstein bound. The paper then shows that the same inequality, applied to a very flat rectangular system, yields Eq. (2.21), which is violated in the limit of vanishing height, and cites Guedens (2000) as an earlier counterexample. So the derivation of the GSL for absorption rests on a bound whose domain of validity is not delimited anywhere in the manuscript. The text acknowledges the tension in a parenthesis, but the logical structure of Sec. VI.C.2 still reads as though the GSL result follows. I recommend that the section state explicitly the class of systems for which Eq. (6.11) is established, or downgrade the absorption-process claim from an implication to a strong suggestion, so that the reader can see which of the results in Sec. VI.C depend on the unqualified bound and which depend on the strengthened one.
[Sec. VII.A.5, Eq. (7.32)] The cosmological verification of the bound in flat FRW universes is conditional on the assumption s <~ 1, that a Planck volume at the Planck time contains no more than one bit. This is stated plainly at Eq. (7.32) and is physically reasonable, but it is an assumption and not a derived input, and the subsequent conclusion that all light-sheets in any flat FRW universe with -1 <= w <= 1 satisfy the bound inherits that conditionality. Since Sec. VII is offered in the abstract (s3) as the demonstration of validity 'in a wide range of examples', the conditionality should be visible where the result is summarized, not only at the point of use. I suggest a sentence in Sec. VII.A.5 or in the Sec. VIII.A assessment recording that the cosmological checks presuppose a Planck-time entropy density of order unity, and noting what would follow if that assumption failed.
[Sec. V.C.1] The entropy on a light-sheet is defined by the convention that only modes fully captured on the light-sheet contribute, following Flanagan, Marolf, and Wald. This convention is doing real work: it is what makes the bound well-defined when a light-sheet intersects a thermodynamic system only partially, and it is what makes the FMW first theorem (Sec. VI.B.1) statable at all. But it is a choice, and a reader can reasonably ask whether the bound's content is convention-independent. The paper does not say whether a different, equally natural convention, for instance one that assigns partial weight to modes straddling the light-sheet boundary, could change the verdict in any of the examples of Sec. VII. A short paragraph in Sec. V.C.1 addressing the sensitivity of the bound to this convention would strengthen the section considerably.

Minor objections (13)

[Sec. VII.A.2] The text refers to 'any spherical surface A', which conflicts with the convention announced in the footnote to Sec. IV.A that B denotes a surface and A its area. The same slippage recurs in a few places in Sec. VII. A consistent pass would help, since the area-versus-surface distinction is exactly what the light-sheet construction turns on.
[Sec. IX.A.1] Two typographical errors in this section: 'stardard model' should read 'standard model', and 'Polchinksi' should read 'Polchinski'.
[Footnote 17] 'light-shees' should read 'light-sheets'.
[Footnote 25] 'practally testable' should read 'practically testable'.
[Sec. VII.B.3] 'arbitary total mass' should read 'arbitrary total mass'.
[Sec. I.A] 'superceded' should read 'superseded'.
[Sec. III.G] 'corresponding to an infalling and and an outside observer' contains a duplicated 'and'.
[Sec. VI.B.2] In the sentence introducing Eq. (6.13), 'hold at everywhere in the spacetime' should read 'hold everywhere in the spacetime'.
[Sec. VI.A] 'the expansion can only decrease..' carries a doubled full stop.
[Fig. 3 caption] The caption states without qualification that the two cones F1 and F3 have negative expansion and hence correspond to light-sheets. That is correct for the spherical room in flat space depicted, but the general selection rule of Sec. V.B.2 depends on the surface and on the cosmological evolution, as Sec. VII.A.2 makes clear. A clause noting that the figure illustrates the normal case would prevent the caption from being read as a general rule.
[Sec. IX.B] The notation is potentially confusing: N is reserved throughout for the number of degrees of freedom, while n denotes the rank of the gauge group and the five-form flux. Footnote 37 flags the conflict with the literature, which is helpful, but a short table of notation near Sec. I.B would save the reader from repeatedly checking back.
[Sec. IV.B.4, footnote 12] The boosted-slicing construction is the subtlest of the four counterexamples and is compressed into a single footnote. A sentence in the main text pointing to Fig. 2b and stating the conclusion, that the boundary area can be made arbitrarily small while the enclosed entropy is unchanged, would make the argument easier to follow on a first reading.
[General] The copy of the manuscript I received ends mid-sentence in Sec. IX.B and does not include the reference list, so I was unable to check the bibliography for completeness or for the accuracy of the citations to the primary literature discussed in Secs. II and IX.

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The paper

The paper claims

The paper argues that one inequality, $S[L(B)] ≤ A(B)/4$, ties the entropy any light-sheet can carry to the area of the surface that generates it, and that this bound holds in cosmology, in gravitational collapse, and inside black holes, so

The reading

This review makes the case that a single inequality governs how much information can sit in a region of spacetime: the entropy on any light-sheet of a surface $B$ never exceeds a quarter of the area of $B$, in Planck units. The author's aim is not to prove this but to show that it survives every test he can construct, including the cases that killed earlier proposals. The older spherical bound needed weak gravity, spherical symmetry and an asymptotically flat background; the older spacelike bound, which compares the entropy in a spatial volume to the area of its boundary, is shown to fail outright in a closed universe, in an expanding flat universe, in a collapsing star, and even for an ordinary ball of gas viewed in a boosted time-slicing. The covariant version replaces the spatial volume with a null hypersurface generated by surface-orthogonal light rays that are not expanding and that stop at caustics, and with that replacement the violations disappear. What follows, if the author is right, is that the number of fundamental degrees of freedom in nature scales with area rather than volume, that local quantum field theory drastically overcounts them, and that the bound must be built into whatever theory unifies matter, gravity and quantum mechanics.

What carries the argument

The light-sheet is the device that carries the whole argument. Given a surface $B$, one takes the four null directions orthogonal to it, keeps only those whose cross-sectional area is initially shrinking or constant ($θ ≤ 0$, the local stand-in for 'inside'), and follows the light rays until they self-intersect, since past a caustic the expansion turns positive and the sheet would begin sweeping up unbounded entropy. Raychaudhuri's equation, $dθ/dλ = -θ^2/(D-2) - σ_{ab}σ^{ab} + ω_{ab}ω^{ab} - 8πT_{ab}k^ak^b$, guarantees that expansion can only decrease when the null energy condition holds, so the termination condition is not an extra assumption but a consequence of gravity plus ordinary matter. This is what lets the bound escape the counterexamples: in a flat expanding universe, a sphere larger than the apparent horizon has no future-directed light-sheet at all, only past-directed ones that are cut off by the big bang and therefore sweep a shell of fixed width rather than an arbitrarily large comoving ball. The same mechanism, entropy costing energy, energy focussing light, focussing producing caustics, is offered as the qualitative reason the bound is true, though the author is explicit that present theory supplies no independent lower bound on the energy price of entropy to make the argument quantitative.

Extended reading notes

Core claim

The central claim is the covariant entropy bound (Sec. V.E, Eq. 5.6): pick any $(D-2)$-dimensional spatial surface $B$, of any shape, topology or location; four families of light rays leave $B$ orthogonally; at least two of them have non-positive expansion $θ ≤ 0$; follow one such family until it reaches a caustic, where neighbouring rays cross; the resulting null hypersurface $L(B)$ is a light-sheet, and the entropy on it satisfies $S[L(B)] ≤ A(B)/4$. The author's further claim is that this is not a corollary of black hole thermodynamics or of any other known law. It holds where the generalized second law cannot be derived, in strongly gravitating and cosmological regions, and conversely the generalized second law for black hole formation, the spherical entropy bound and the Bekenstein bound can be recovered from it under stated conditions (Sec. VI.C). From the bound's generality the review draws its interpretive conclusion (Sec. VIII): the area of a surface measures the number of independent quantum states of an underlying theory describing all physics on its light-sheets, $N[L(B)] ≤ e^{A(B)/4}$, and any candidate quantum gravity must make this manifest.

Load-bearing premise

The bound can only be checked where the entropy on a light-sheet is unambiguous, and the review concedes that once only the surface is fixed and the surrounding geometry is not, one can hold the surface fixed but not its light-sheet, which leaves too much freedom to test the inequality directly.

Editorial extensions

If this is right

The number of fundamental degrees of freedom in a region is set by the area of surfaces, not by volume, so a local field theory with a short-distance cutoff is a redundant description of nature rather than a fundamental one.
The generalized second law of thermodynamics for black hole formation, the spherical entropy bound, and the Bekenstein bound all follow from the covariant bound in the regimes where those older statements are valid, which reverses the usual logical order.
The bound constrains any cosmological model: for a flat Friedmann-Robertson-Walker universe with equation of state $p = wρ$, the bound holds on all light-sheets of all spheres provided $-1 ≤ w ≤ 1$, a range that follows from the causal energy condition.
The area of any sphere within the apparent horizon exceeds the entropy enclosed in it, provided the future light-sheet of that sphere is complete, which gives a precise and checkable criterion for when a spacelike holographic statement is legitimate.
A successful quantum gravity must exhibit the bound as a manifest property, and in the one worked example where it can be checked, the dual conformal field theory's degree count $N ≈ n^2/δ^3$ matches the boundary area $A ≈ R^8/δ^3$, saturating the bound up to factors of order unity.

Reading between the lines

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

If the bound is a genuine law, the natural next step is to look for its violations rather than its confirmations, in the one regime the review cannot test: light-sheets whose entropy is not well approximated as a fluid and whose geometry is not fixed, such as superposed geometries near the Planck scale.
The review's own recovery of the Bekenstein bound from the strengthened form of the bound (Eq. 6.11) produces a version that is demonstrably too strong for very flat systems, which suggests the strengthened form, not the original, is the statement that will need revision in a full quantum treatment.
Because the bound is time-reversal invariant while thermodynamic entropy is not, one might expect the underlying theory to treat entropy as a property of null hypersurfaces rather than of instants, which would put light cones rather than spatial slices at the centre of the formalism.
The construction of global holographic screens for arbitrary spacetimes, mentioned in the review's later sections, suggests a concrete programme: for any spacetime, find the preferred surface family on which all information can be stored at one bit per Planck area, and ask whether that family is unique.

Original abstract

There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 10^(69) bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light-sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. We explain how the bound is tested and demonstrate its validity in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. We survey some successes and challenges in implementing the holographic principle.

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, 6,618 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.42 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.93 · compares with prior results 0.15 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 10^(69) bits per square meter. We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes. The construction of light-sheets, which associate relevant spacetime regions to any given surface, is discussed in detail. We explain how the bound is tested and demonstrate its validity in a wide range of examples. A universal relation between geometry and information is thus uncovered. It has yet to be explained. The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter. It must be manifest in an underlying quantum theory of gravity. We survey some successes and challenges in implementing the holographic principle.

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	There is strong evidence that the area of any surface limits the information content of adjacent spacetime regions, at 10^(69) bits per square meter.	background 0.91	0.13	0.34	asserted 0.73
s1	We review the developments that have led to the recognition of this entropy bound, placing special emphasis on the quantum properties of black holes.	contribution 0.80	0.24	0.06	asserted 0.73
s2	The construction of light-sheets, which associate relevant spacetime regions to any given surface, is discussed in detail.	method 0.69	0.43	0.04	asserted 0.73
s3	We explain how the bound is tested and demonstrate its validity in a wide range of examples.	contribution 0.55	0.80	0.11	asserted 1.00
s4	A universal relation between geometry and information is thus uncovered.	result 0.50	0.66	0.68	asserted 1.00
s5	It has yet to be explained.	gap 0.93	0.09	0.04	asserted 0.78
s6	The holographic principle asserts that its origin must lie in the number of fundamental degrees of freedom involved in a unified description of spacetime and matter.	interpretation 0.77	0.11	0.34	asserted 0.78
s7	It must be manifest in an underlying quantum theory of gravity.	interpretation 0.85	0.06	0.10	asserted 0.83
s8	We survey some successes and challenges in implementing the holographic principle.	contribution 0.93	0.51	0.05	unclear 0.59

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 0.80.

What was examined, and what was not

sources read

arXiv listing abstract v2

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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Holographic dark matter arises from the Ricci cutoff in a baryon-plus-radiation universe, matching observed densities and reversing the sign of pre-existing negative vacuum energy to match observations.
Entropy Bounds and the Species Scale Distance Conjecture
hep-th 2023-06 conditional novelty 6.0 of 10

The Covariant Entropy Bound applied to dynamical-cobordism running solutions yields a bottom-up derivation of the Swampland Distance Conjecture and a convex-hull bound on the species scale decay rate, verified in M-th...
Causality, Unitarity, and the Weak Gravity Conjecture
hep-th 2021-09 conditional novelty 6.0 of 10

Unitarity and causality make the leading threshold corrections to extremal black holes positive, so black holes themselves satisfy the Weak Gravity Conjecture in weakly coupled effective field theories.
Tenfold Way for Holography : AdS/CFT and Beyond
hep-th 2020-09 conditional novelty 6.0 of 10

Real semisimple Lie groups are organized into bulk and boundary spaces using Iwasawa, Bruhat, and Sekiguchi-like decompositions, with the key intertwiners left to a sequel.
Spacetime structure near generic horizons and soft hair
hep-th 2019-08 conditional novelty 6.0 of 10

A family of horizon boundary conditions labeled by s yields BMS-like algebras with spin-s supertranslations, while another choice gives a non-linear Heisenberg-like algebra whose generators build the BMS-like ones.
Entanglement entropy and superselection sectors I. Global symmetries
hep-th 2019-05 conditional novelty 6.0 of 10

For a QFT realized as the invariant subalgebra of a theory with global symmetry G, the mutual-information deficit relative to the full theory saturates at log|G| for finite groups and grows logarithmically with the cu...
Gravitational Thermodynamics of Causal Diamonds in (A)dS
hep-th 2018-12 conditional novelty 6.0 of 10

Every spherical causal diamond in a maximally symmetric spacetime obeys a Smarr formula and a first law, and the diamond's gravitational temperature comes out negative.
Proof of the Weak Gravity Conjecture from Black Hole Entropy
hep-th 2018-01 conditional novelty 6.0 of 10

Positivity of higher-derivative corrections to black hole entropy implies that extremal black holes are unstable to decay, which satisfies the weak gravity conjecture within theories whose ultraviolet completion is tr...
A New Area Law in General Relativity
hep-th 2015-04 conditional novelty 6.0 of 10

The area of a hypersurface foliated by marginally trapped surfaces increases monotonically along the foliation, even across changes of signature, yielding an area law that applies in cosmology.
Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation
hep-th 2015-03 conditional novelty 6.0 of 10

Using T-duality to translate the weak gravity conjecture into a bound on instanton actions versus axion decay constants, the authors show that trans-Planckian axion decay constants require losing perturbative control.
Entropy on a null surface for interacting quantum field theories and the Bousso bound
hep-th 2014-06 conditional novelty 6.0 of 10

For interacting quantum field theories in more than two dimensions, the vacuum-subtracted entropy of a null slab equals the expectation value of a g-weighted integral of the null stress tensor, which extends the Bouss...
Holographic entanglement plateaux
hep-th 2013-06 accept novelty 6.0 of 10

For holographic field theories in finite volume, the entanglement entropy of a sufficiently large region saturates the Araki-Lieb inequality, so region plus complement recovers the thermal entropy.
Strong subadditivity and the covariant holographic entanglement entropy formula
hep-th 2012-04 conditional novelty 6.0 of 10

In three-dimensional AdS-Vaidya spacetimes, the covariant holographic entanglement entropy formula obeys strong subadditivity for positive-energy infalling matter and violates it for negative-energy matter.
Causal Holographic Information
hep-th 2012-04 conditional novelty 6.0 of 10

A causal-wedge surface area divided by four Newton constants is proposed as a holographic information measure that bounds entanglement entropy and coincides with it in all independently computable cases.
Central charge and black hole entropy for regular extremal black-bounce spacetimes
hep-th 2026-09 accept novelty 5.0 of 10

The Kerr/CFT approach successfully reproduces the Bekenstein-Hawking entropy for extremal black-bounce Kerr, Kerr-Newman, and Reissner-Nordström spacetimes.
Static Dark Fluid Thin Shells in Schwarzschild-de Sitter Spacetimes: Stability and Black Hole Shadows
gr-qc 2026-02 conditional novelty 5.0 of 10

Stable static dark-fluid shells separating two Schwarzschild–de Sitter spacetimes exist only for m_+/m_->1 and arise at three scales, imprinting observable black-hole shadow deviations.
Hubble Tension as an Effect of Horizon Entanglement Nonequilibrium
astro-ph.CO 2026-01 reject novelty 5.0 of 10

A phenomenological 'horizon entanglement deficit' with the form ρ ∝ H² is fit to low-z data under a forced H0=73 prior; the nonzero amplitude is a restatement of that prior.
Superluminal Transformations and Indeterminism
quant-ph 2026-01 reject novelty 5.0 of 10

A new no-go theorem claims superluminal order-reversing transformations are incompatible with finite information combined with a memory-bearing past and a causal time, suggesting any such theory needs infinite information.
Gravitational Entropy
hep-th 2025-09 conditional novelty 5.0 of 10

Gravitational entropy of horizons is reformulated as a Noether charge from a specially normalized null generator, reproducing the area law for black hole and cosmological horizons without invoking temperature.
Deriving the Cosmological Constant and Nature's Constants from SU(3) Confinement Volume
gr-qc 2025-07 reject novelty 5.0 of 10

The paper claims that the dark energy density equals the Planck-scale gluon zero-point energy divided by N = (R_u/R_p)^3 ≈ 10^123, with each QCD domain mapping to a Planck-area patch on the cosmic horizon.
Isentropic process of Reissner-Nordstr\"om black holes: a possible excess of the entropy bound via a non-perturbative channel
gr-qc 2025-05 conditional novelty 5.0 of 10

A quantum tunneling channel for isentropic charged-particle absorption into a Reissner-Nordström black hole could allow the internal Boltzmann entropy to exceed the Bekenstein-Hawking entropy.
Topological dark energy from black-hole formations and mergers through the gravity-thermodynamics approach
gr-qc 2024-12 reject novelty 5.0 of 10

Black hole formation and merger, through topology changes of the cosmic apparent horizon, generate an effective dark energy whose equation of state is phantom-like or quintessence-like depending on the sign of the Gau...
Non-Locality induces Isometry and Factorisation in Holography
hep-th 2024-11 conditional novelty 5.0 of 10

State-averaged wormhole corrections make the Gram matrix of time-shifted thermofield double microstates low-rank, giving a finite black hole Hilbert space of dimension e^{S_BH} and a type I von Neumann algebra.
An Embedding Space Approach to Carrollian CFT Correlators for Flat Space Holography
hep-th 2023-04 conditional novelty 5.0 of 10

A six-dimensional embedding-space construction reproduces the known two- and three-point Carrollian correlators, which equal flat-space scattering amplitudes written in a position basis.
Kaniadakis holographic dark energy and cosmology
gr-qc 2021-09 conditional novelty 5.0 of 10

A one-parameter extension of holographic dark energy based on Kaniadakis entropy reproduces the standard cosmic thermal history and yields an equation of state that can be quintessence-like or phantom-like depending o...
Edge modes and corner ambiguities in 3d Chern-Simons theory and gravity
gr-qc 2017-03 conditional novelty 5.0 of 10

Promoting finite gauge parameters to new boundary fields makes the covariant symplectic potential gauge-invariant and yields dressed boundary observables that satisfy the known affine Kac-Moody algebra in Abelian Cher...
Lower-Dimensional Black Hole Chemistry
gr-qc 2015-09 accept novelty 5.0 of 10

Charged BTZ black holes in 2+1 dimensions violate the reverse isoperimetric inequality and are superentropic, and the Smarr relation can be derived in 1+1 dimensions with a sign-reversed cosmological constant.
New insights on the matter-gravity coupling paradigm
gr-qc 2012-01 conditional novelty 5.0 of 10

Eddington-inspired Born-Infeld gravity with a perfect fluid is exactly General Relativity with a nonlinearly rescaled fluid, so modified coupling and modified equation of state are indistinguishable from outside the matter.
Barrow holographic dark energy interacting model in the presence of radiation and matter
gr-qc 2025-07 unverdicted novelty 4.0 of 10

Numerical study of interacting Barrow holographic dark energy in non-flat universes with radiation, showing EoS transitions and higher fitted H0 values that may address Hubble tension.
A Stringy Correspondence Principle in Cosmology
hep-th 2006-03 conditional novelty 4.0 of 10

A FRW universe with fluid equation of state p = w rho transitions to a highly excited string state when its temperature reaches the string scale, where horizon entropies and energies match to O(1).
Physical limits on information metrics and quantum gravity as gravitized quantum theory
gr-qc 2025-04 reject novelty 3.0 of 10

The authors argue that quantum gravity and general covariance force the information geometry of quantum theory to become dynamical, requiring a modified Born rule testable via triple-slit matter-wave interference.
Lectures on the Bondi--Metzner--Sachs group and related topics in infrared physics
gr-qc 2025-04 unverdicted novelty 3.0 of 10

Lecture notes that build the BMS group from prerequisites to applications in soft theorems, memory effects, and new material on asymptotic conformal Killing horizons.
The Weak Gravity Conjecture: A Review
hep-th 2022-01 accept novelty 3.0 of 10

The Weak Gravity Conjecture and its stronger tower and sublattice forms hold in every consistent quantum gravity theory examined so far, but none of them has been derived from first principles.
Lessons from the Information Paradox
hep-th 2020-12 conditional novelty 3.0 of 10

A review arguing that quantum gravity duplicates all information near the boundary of any region, so black holes never lose information and the interior is always reconstructible from outside.
Observational constraints on Barrow holographic dark energy
gr-qc 2020-05 conditional novelty 3.0 of 10

Barrow holographic dark energy with one extra parameter fits supernova and cosmic-chronometer data about as well as LambdaCDM, with the deformation parameter consistent with zero at one sigma.
Emergent Gravity in a Holographic Universe
hep-th 2019-08 conditional novelty 3.0 of 10

Causal diamonds in symmetric spacetimes obey a thermodynamic first law with negative temperature, and the Einstein equations can be recast as an entropy equilibrium condition, with a long-string CFT picture for non-Ad...
Challenges about entropy
nucl-th 2006-03 conditional novelty 3.0 of 10

The author claims that the microcanonical Boltzmann entropy is the only correct basis for thermodynamics and that canonical statistics fails in phase separation and cosmology.
A short overview on the Black Hole-Tower Correspondence and Species Thermodynamics
hep-th 2025-06 conditional novelty 2.0 of 10

A review of the black hole-tower correspondence and species thermodynamics, which aim to explain black hole entropy via towers of light states and to show only certain towers are allowed.

See all 70 Pith citations

How later papers used it

329 later papers cite it

Evidence: substantial. 311 of the citing papers share no author with it, and 22 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 450 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

8 later papers by other authors are listed below: 4 used its method or tool, 2 compared their own results with it and 2 cited it as support.

Uses its method or tool 4 of 8 papers with this label

Used its construction to define a pair of light-sheets from a co-dimension two spacelike surface.

On the reconstruction of Lifshitz spacetimes (2015) · 0.99 · paraphrased: the licence does not allow quoting
Followed its covariant formalism for general spacetimes to study the holographic properties of a presented spacetime.

K-essential covariant holography (2014) · 0.98 · paraphrased: the licence does not allow quoting
Imposed the CEB in its spacelike projected version on the extensive EFT entropy.

Entropy Bounds and the Species Scale Distance Conjecture (2023) · 0.87 · paraphrased: the licence does not allow quoting
Derived the holographic principle following its arguments.

Gravity as a thermodynamic phenomenon (2017) · 0.83 · paraphrased: the licence does not allow quoting

Compares with it 2 of 7 papers with this label

Said that based on its holographic bound it would have expected S(r) ≤ πr^2, though its own inequality is sub-optimal.

Tolman mass, generalized surface gravity, and entropy bounds (2010) · 0.98 · paraphrased: the licence does not allow quoting
Said that its own definition also resembles this paper's light-sheet construction.

Geometry of small causal diamonds (2019) · 0.83 · paraphrased: the licence does not allow quoting

Cites it as support 2 of 8 papers with this label

Used its bound on stored information as evidence, saying exceeding the Bekenstein bound must cause black hole formation, contradicting what is seen.

Truth, or Mere Beauty? (2022) · 0.99 · paraphrased: the licence does not allow quoting
Said that the black hole respects this paper's covariant entropy bound on the horizon because the collision entropy never passes through the horizon.

Large entropy production inside black holes: a simple model (2010) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

260 arXiv papers cite this in 351 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 · 183 sentences without a confident label

Uses its method or tool 6 papers

Using the holographic principle [ref] , we show that the classical universe we know begins at a significantly large scale factor compared to the Planck length due to the existence of finite vacuum energy, to begin with (Sec. 3).

A quantum cosmology approach to cosmic coincidence and inflation · Introduction · 0.91
The basic idea behind our proposal is to exploit the light-sheet construction of the covariant entropy bounds of Bousso [ref] .

A Covariant Holographic Entanglement Entropy Proposal · Introduction · 0.90
Upon imposing the CEB — in its spacelike projected version [ref] — on the extensive EFT entropy given in [ref] one arrives at the following QG requirement

Entropy Bounds and the Species Scale Distance Conjecture · A Bottom-up Argument for the ADC · 0.87

Compares with it 5 papers

Specifically, it resembles the holographic bound [ref] , which corresponds to $S(Ω)≤1/4𝒜(∂Ω)$.

Entropy bounds for uncollapsed matter · Discussion · 0.98
Although this formulation of entropy shares mathematical similarities with the constructions of Wald, Jacobson–Kang–Myers, and Bousso [ref] , its physical interpretation is distinctly different.

Who Writes the Gravitational Second Law of Thermodynamics? · Introduction · 0.99
The inequality is again sub-optimal, (based on the holographic bound [ref] we would have expected $S(r) ≤πr^2$), but on the other hand the inequality is extremely robust and easy to derive.

Tolman mass, generalized surface gravity, and entropy bounds · Introduction · 0.98

Cites it as support 7 papers

Gravity implies that the amount of information that can be stored in any finite amount of space must be bounded; exceeding this Bekenstein bound must result in a black hole formation, contradicting what we see [ref] .

Truth, or Mere Beauty? · Finitism is true · 0.99
The static patch holography conjecture is motivated by the covariant entropy bound and the holographic principle of Bousso [ref] .

de Sitter Connectivity from Holographic Entanglement · The Holographic Principle and de Sitter Space · 0.98
In the expanding phase of the cosmologies, the covariant entropy conjecture [ref] motivates us to place a holographic screen on each of the two apparent horizons, respectively – see also, [ref] .

Closed FRW holography: A time-dependent ER=EPR realization · Introduction · 0.98

Cites it as background 141 papers

The Covariant Entropy Bound (CEB) is a well tested conjecture in many gravitational scenarios including cosmology [ref] .

Inflationary implications of the Covariant Entropy Bound and the Swampland de Sitter Conjectures · Covariant Entropy Bound and Inflation · 0.95
The HRT conjecture for the covariant holographic entanglement entropy of a subsystem in a $CFT_d$ dual to a non-static $AdS_d+1$ space time [ref] , was inspired by the light sheet construction for the covariant Bousso bound [ref] .

Covariant holographic entanglement negativity · Review of the covariant holographic entanglement entropy · 0.90
Covariant entropy bound The covariant entropy bound [ref] (see Ref. [ref] for a review) establishes a general relation between quantum information and classical geometry: The entropy of matter on a light-sheet $L$ (a non-expanding null hypersurface) orthogonal to a spatial surface $B$ cannot exceed the surface area $A$, measured in Planck units: [equation] This holds for arbitrary spacelike surfaces $B$ of codimension two, open or closed, in any spacetime satisfying Einstein's equation with physically reasonable matter.

Saturating the holographic entropy bound · Introduction · 1.00

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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