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REVIEW 3 major objections 5 minor 44 references

Quasi-local energy and ADM mass in pure Lovelock gravity

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read In pure Lovelock gravity (m ≥ 2) the background-subtracted quasi-local energy vanishes at spatial infinity, so only its variation is well defined; the variation's large-surface limit equals the ADM mass variation.

desk verdict Useful perturbative ADM mass formula in pure Lovelock gravity, but the paper's claim that the absolute quasi-local energy vanishes at infinity is not proven and is likely wrong. read the letter →

arxiv 1908.05522 v2 pith:Q6F42PH2 submitted 2019-08-15 gr-qc hep-th

Jani Kastikainen This is my paper · ORCID
classification gr-qchep-th
keywords pureLovelockgravityquasi-localenergyADMmassBrown-YorkbackgroundsubtractionasymptoticallyflatspacetimeAdShigher-curvature
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper asks how the standard energy notions of general relativity—the ADM mass (total mass measured at spatial infinity) and the Brown-York quasi-local energy (the boundary-integral energy defined from the gravitational action)—extend to pure Lovelock gravity, a higher-curvature theory whose field equations stay second order in the metric. For pure Lovelock order $m \ge 2$ in asymptotically flat spacetimes, it argues that the absolute quasi-local energy defined by background subtraction has a large-surface limit of exactly zero, so only variations of the energy survive as well-defined quantities. The main discovery is that the variation of the quasi-local energy approaches the variation of the ADM mass as the boundary surface recedes to infinity, yielding a new boundary formula for the ADM mass. This matters because it supplies the mass-type charge needed for pure Lovelock black holes and the first law, and it clarifies why earlier approaches produced only proportional or non-integrable expressions.

What carries the argument

The workhorse is the generalized Gibbons-Hawking surface term (the boundary counterterm that makes the variational principle well-posed) for the codimension-two surface, together with the projected equation-of-motion tensor $\hat E^i{}_{j(m)}$ built from generalized Kronecker-delta contractions with surface Riemann tensors. The key identity, obtained by varying the surface term with the induced surface metric held fixed, is $2\bar P^{ab}{}_{cd(m)} n_a D_c \delta\gamma^d{}_b = -4m\,\hat E^i{}_{j(m-1)}\,\delta\hat K^j{}_i$; this converts the Hamiltonian boundary term into an integral over the variation of the extrinsic curvature $\delta\hat K^j{}_i$. What keeps the perturbation finite while the absolute background-subtracted energy collapses to zero is that $\hat E^i{}_{j(m-1)}$ in the limiting integral is not evaluated on the flat background. The asymptotic fall-off exponent $\beta = (D - 2m - 1)/m$ is engineered so that the decay of $\bar P^{ab}{}_{cd(m)}$ cancels the volume factor $r^{D-2}$ and the derivative $D_c\delta\gamma \sim r^{-\beta-1}$, making the boundary integral finite.

What would settle it

Take a non-spherically-symmetric asymptotically flat static solution of pure Lovelock gravity of order $m \ge 2$ in $D \ge 2m+3$ dimensions and compute the large-surface limit of the background-subtracted Brown-York energy (3.15); the paper's central claim predicts this limit is exactly zero for any solution satisfying the fall-off (2.19), so a nonzero result would falsify it. Independently, compute $\delta M^{(m)}_{\mathrm{ADM}}$ from the Hamiltonian formula (2.16) and from the surface formula (3.27) for a metric whose non-integrable term is nonzero; the two must agree for the central identity to hold.

Watch

Extended reading notes

Core claim

Working in dimensions $D > 2m+1$, the paper generalizes the Hamiltonian-surface derivation of the ADM mass to pure Lovelock gravity and finds that for asymptotically flat spacetimes the ADM mass is non-integrable: its variation $\delta M^{(m)}_{\mathrm{ADM}}$ is finite under the pure-Lovelock fall-off $\tilde\gamma_{ab} = O(r^{-\beta})$ with $\beta = (D - (2m+1))/m$, but it cannot be integrated to a function of the metric parameters because $\bar P^{ab}{}_{cd(m)}$ itself varies. The background-subtracted Brown-York energy is then shown to vanish in the large-surface limit for every $m \ge 2$, so the paper turns to the perturbative quantity $\delta M^{(m)}_B = \frac{m}{4\pi}\int_B \sqrt{\sigma}\,\hat E^i{}_{j(m-1)}\,\delta\hat K^j{}_i$ and proves its large-surface limit equals $\delta M^{(m)}_{\mathrm{ADM}}$. For spherical symmetry this integrates to $M^{(m)}_{\mathrm{ADM}} = \frac{1}{16\pi}\Omega_{D-2}\,a(m)\lim_{r\to\infty} r^{m\beta} F(r)^m$, which for pure Lovelock black holes gives $M \propto \alpha^m$, matching earlier integral-charge calculations. In asymptotically AdS spacetimes the obstruction disappears: the mass is integrable and proportional to the Einstein mass for all $m$, and the background-subtracted quasi-local energy has the correct ADM limit.

Load-bearing premise

The background-subtraction prescription assumes the boundary surface can be embedded in the reference flat (or AdS) spacetime with the same lapse and induced metric as in the physical spacetime, and the paper itself notes that this embedding is not possible in general.

Editorial extensions

If this is right

  • For $m \ge 2$ in asymptotically flat spacetimes, the background-subtracted quasi-local energy has a zero large-surface limit, so only the perturbative variation $\delta M^{(m)}_B$ is well defined as a charge.
  • The limit identity $\delta M^{(m)}_{\mathrm{ADM}} = \lim_{B\to\infty} \frac{m}{4\pi}\int_B \sqrt{\sigma}\,\hat E^i{}_{j(m-1)}\,\delta\hat K^j{}_i$ provides a practical boundary formula for the ADM mass, demonstrated on spherically symmetric static black holes and matching earlier integral-charge results.
  • For static spherically symmetric metrics the perturbative mass integrates to $M^{(m)}_{\mathrm{ADM}} = \frac{1}{16\pi}\Omega_{D-2}\,a(m)\lim_{r\to\infty} r^{m\beta}F(r)^m$, and for the pure Lovelock black hole $F(r)=\alpha r^{-\beta}$ this yields $M^{(m)}_{\mathrm{ADM}}\propto \alpha^m$.
  • In asymptotically AdS spacetimes the ADM mass is integrable and proportional to the Einstein value for every $m$, and the background-subtracted quasi-local energy has the correct ADM limit.
  • The alternative quasi-local energy built from vacuum-subtracted extrinsic curvatures agrees with the ADM mass in AdS, but in flat space its large-surface limit equals $m$ times the ADM mass for spherically symmetric metrics and differs from the ADM variation for generic metrics.

Reading between the lines

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

  • A testable consequence of the vanishing limit is that black hole thermodynamics in asymptotically flat pure Lovelock gravity must be formulated through variational quantities: the mass appearing in the first law is an integration parameter, not an absolute charge.
  • The surface formula has the structure of a symplectic charge pairing a background equation-of-motion tensor with the variation of extrinsic curvature; the same pairing should yield angular momentum and other charges when the extrinsic-curvature variation is replaced by a rotational perturbation, and checking a first law would test the construction beyond the mass.
  • Counterterm renormalization, already developed for AdS Lovelock, could be applied to the same spherically symmetric black holes in flat space; comparing the counterterm energy with the integrated mass formula would show whether the failure of absolute charges is specific to background subtraction or intrinsic to pure Lovelock.
  • The obstruction to absolute charges is similar in spirit to the degeneracy seen in special Lovelock vacua, suggesting that only perturbations may be well defined quite generally in higher-curvature gravity; testing conformal-mass type definitions on these flat solutions would separate the two mechanisms.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper studies how the standard ADM mass and Brown-York quasi-local energy generalize to pure Lovelock gravity. It derives a non-integrable perturbative ADM mass formula (2.16), proposes a background-subtracted Brown-York type quasi-local energy (3.15), and argues that its large-surface limit vanishes for asymptotically flat pure Lovelock gravity with m ≥ 2. The main positive result is the perturbative formula (3.26)-(3.27), which expresses the variation of the quasi-local energy as an integral over the codimension-two surface and whose large-surface limit coincides with the variation of the ADM mass. The author applies this formula to static spherically symmetric solutions, recovering known black hole masses, and also treats asymptotically AdS spacetimes, where the mass becomes integrable and proportional to the Einstein value for all m.

Significance. If the central claims hold, the paper provides a practical new formula for computing ADM masses in pure Lovelock gravity and sharpens the statement that only perturbative energy variations are well defined for asymptotically flat m ≥ 2. The paper is explicit and cross-checks its formulas against the Einstein gravity limit m = 1, the known spherically symmetric black hole masses, and the Chakraborty-Dadhich quasi-local energy. These checks are genuine strengths. However, the paper's main conceptual conclusion about the vanishing of the non-perturbative quasi-local energy rests on an asymptotic expansion whose higher-order terms are not controlled; this weakens the stated significance until the gap is closed. The perturbative ADM formula (3.27) may survive independently of that conclusion, and the spherical application is an useful demonstration.

major comments (3)
  1. [Section 3.3, Eqs. (3.19)-(3.22)] The vanishing large-surface limit of the background-subtracted quasi-local energy is not established by the given argument. Equation (3.21) expands \hat B_(m) only to first order in the metric perturbation and concludes in (3.22) that the integral vanishes because \bar P_(m)|_(0) is zero on flat space. A first-order expansion is insufficient here: after multiplication by \sqrt{\sigma} ~ r^{D-2}, the next-order contribution can be finite or divergent under the pure Lovelock falloff (2.19). For the static spherically symmetric metric (4.1) with m = 2, the quadratic term in \hat B - \hat B_0 is of order F^2/r^3, so the integral scales as r^{D-5}F^2; with F ~ r^{-\beta}, \beta = (D-5)/2, this is a non-zero constant as r \to \infty, and for m > 2 the analogous contribution grows. Thus Eq. (3.22) does not follow from the stated expansion, and the paper's central claim that the non-perturbative quasi-local energy vanishes for m ≥ 2 is not proven. The perturbative formula (3.27) may still be correct, but the motivation for restricting to variations needs either a second-order computation showing the offending terms cancel, or a non-perturbative proof of the limit.
  2. [Section 3.2, Eq. (3.10)] The Hamiltonian decomposition of the total action with a timelike boundary is introduced as a proposal rather than derived. The quasi-local energy (3.15) and hence the perturbative formula (3.23) are built on this decomposition, so the status of the assumption is load-bearing. If (3.10) is meant as a definition of the physical Hamiltonian, the paper should state this explicitly and verify that the resulting charge is independent of the choices made; if it is meant to be derived from the action variation (3.3), the derivation should be supplied. As it stands, the central ADM-mass formula inherits the uncertainty of this proposed decomposition.
  3. [Section 3.3, after Eq. (3.14)] The background subtraction prescription assumes that the codimension-two surface B can be embedded in the flat reference spacetime with the same lapse and induced metric as in the physical spacetime. The paper itself notes in the Summary that this embedding is not possible in general. Since the quasi-local energy (3.15) is the central object of the paper, the precise class of surfaces for which the definition is valid should be stated. In particular, for surfaces that are not approximately round and large, the subtraction is not well defined by this prescription, and the error introduced by an approximate embedding should be controlled or at least discussed.
minor comments (5)
  1. [Section 2.2, text after Eq. (2.16)] The sentence 'Obtaining a non-perturbative expression for M_ADM_(m) in pure Lovelock gravity of order m ≤ 2 cannot be done in general' appears to contain a typo: the non-integrable case is m ≥ 2, not m ≤ 2, because \bar P_(1) is metric-independent. Please correct this.
  2. [Section 1.2, Eq. (1.4)] The definition of the projection ~\delta reads '~δa b = ~δa b − nanb', which is circular as typeset. It should presumably be ~\delta^a_b = \delta^a_b - n^a n_b. Please fix the notation.
  3. [Section 3.2, Eq. (3.10)] The term K_(m) appearing in the proposed Hamiltonian decomposition is not defined. Since it is said to contain terms proportional to the extrinsic curvature of the Cauchy slice, a brief definition or reference would help the reader.
  4. [Section 2.3, Eq. (2.19)] The exponent is written as β = D − (2m + 1)/m, which is ambiguous. The intended expression is β = (D − 2m − 1)/m, as used in Eq. (4.4). Please add parentheses.
  5. [Abstract and Introduction] The phrase that the perturbative quasi-local energy 'correctly approaches' the ADM mass is stronger than what is proven: by Eqs. (2.16) and (3.23), both sides are the same boundary integrand by construction, so the equality is a consistency relation rather than an independent check. The wording should be softened accordingly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the perturbative quasi-local energy/ADM limit is a consistency relation, and the spherical-symmetric masses are verified against independent literature.

full rationale

The paper's main derivation chain is self-contained. Section 2 obtains the ADM mass variation (2.16) from the Hamiltonian boundary term of the pure Lovelock action; Section 3 obtains the Brown-York-like quasi-local energy (3.15) from the generalized Gibbons-Hawking term. The equality between the large-B limit of the perturbative quasi-local energy and the ADM mass variation (3.23 vs 2.16) uses the same boundary integrand by construction, so it is a consistency relation rather than an independently fitted prediction; it is not a circular dependency because neither quantity is defined in terms of the other, and the paper does not use this relation as an external benchmark. The genuinely new formula (3.27) is reached through the additional identity (3.24), which rewrites the boundary integrand in terms of the projected equation-of-motion tensor and the extrinsic-curvature variation; that step is nontrivial and is subsequently tested on static spherically symmetric metrics, where the resulting mass (4.5) and the black-hole value (4.7) agree with earlier independent calculations [13,17-20]. No self-citation is load-bearing; the surface-term and quasi-local-energy references [25,28] are prior independent work. The explicitly disclosed embedding assumption in the background-subtraction regularization is a limitation, not a circular step, and the possible higher-order terms in the large-surface expansion of \hat{B} are a correctness concern outside the circularity pass. Overall, no claim reduces to its own input by definition or by fit.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No free parameters are fitted to data; all constants are fixed by the action normalization or by the black hole solution parameter α. No new entities are postulated. The non-trivial inputs are the background-subtraction embedding assumption and the proposed Hamiltonian split (3.10).

assumptions (5)
  • standard math The pure Lovelock action and its boundary variation (2.4)-(2.7) are the starting point, with c(m)/GN set to 1.
    This is standard background from Lovelock gravity; no free parameters are fitted.
  • ad hoc to paper The Hamiltonian decomposition of the total action with timelike boundary takes the proposed form (3.10) with boundary term B-hat(m)+K(m).
    Introduced as a proposal in Section 3.2 rather than derived from the full action; the quasi-local energy definition (3.15) and its variation rest on it.
  • domain assumption Spacetimes are static (shift vector zero) and asymptotically flat with fall-off gamma-tilde_{ab}=O(r^{-β}), β=(D-2m-1)/m, or asymptotically AdS.
    The ADM mass and quasi-local energy formulas are derived under these fall-off conditions and staticity; Section 2.3 and Section 5.
  • domain assumption For background subtraction, the surface B can be embedded in the reference spacetime with matching lapse and induced metric.
    Stated after eq (3.14) and acknowledged as not generally possible in Section 6; needed for the quasi-local energy to be defined.
  • standard math Generalized Kronecker delta identities in Appendix A are used for tensor contractions.
    These are algebraic identities; they are standard and not content-bearing.

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Cite this review

Pith. "Pith review of Quasi-local energy and ADM mass in pure Lovelock gravity." pith.science (2026). https://pith.science/paper/Q6F42PH2

@misc{pith2026190805522,
  author       = {Pith},
  title        = {Pith review of: Quasi-local energy and ADM mass in pure Lovelock gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q6F42PH2}},
  note         = {Machine review of arXiv:1908.05522}
}
read the original abstract

We study how the standard definitions of ADM mass and Brown-York quasi-local energy generalize to pure Lovelock gravity. The quasi-local energy is renormalized using the background subtraction prescription and we consider its limit for large surfaces. We find that the large surface limit vanishes for asymptotically flat fall-off conditions except in Einstein gravity. This problem is avoided by focusing on the variation of the quasi-local energy which correctly approaches the variation of the ADM mass for large surfaces. As a result, we obtain a new simple formula for the ADM mass in pure Lovelock gravity. We apply the formula to spherically symmetric geometries verifying previous calculations in the literature. We also revisit asymptotically AdS geometries.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

44 extracted references · 24 canonical work pages

  1. [1]

    Komar, Covariant Conservation Laws in General Relativity , Physical Review 113 (1959) 934

    A. Komar, Covariant Conservation Laws in General Relativity , Physical Review 113 (1959) 934

    work page 1959

  2. [2]

    Arnowitt, S

    R. Arnowitt, S. Deser and C. W. Misner, The Dynamics of General Relativity , General Relativity and Gravitation 40 (2008) 1997 [ gr-qc/0405109]

    arXiv 2008

  3. [3]

    Regge and C

    T. Regge and C. Teitelboim, Role of surface integrals in the Hamiltonian formulation of general relativity, Annals of Physics 88 (1974) 286

    work page 1974

  4. [4]

    C. W. Misner, Gravitational Field Energy and ${g} {00}$, Physical Review 130 (1963) 1590. – 21 –

    work page 1963

  5. [5]

    R. M. Wald, Black Hole Entropy is Noether Charge , Physical Review D 48 (1993) R3427 [gr-qc/9307038]

    arXiv 1993

  6. [6]

    Iyer and R

    V. Iyer and R. M. Wald, Some Properties of Noether Charge and a Proposal for Dynamic al Black Hole Entropy , Physical Review D 50 (1994) 846 [ gr-qc/9403028]

    arXiv 1994

  7. [7]

    J. D. Brown and J. W. York, Quasilocal energy and conserved charges derived from the gravitational action , Physical Review D 47 (1993) 1407

    work page 1993

  8. [8]

    S. W. Hawking and G. T. Horowitz, The Gravitational Hamiltonian, Action, Entropy, and Surface Terms, Classical and Quantum Gravity 13 (1996) 1487 [ gr-qc/9501014]

    arXiv 1996

Show all 44 references
  1. [9]

    Brewin, A simple expression for the ADM mass , General Relativity and Gravitation 39 (2007) 521 [ gr-qc/0609079]

    L. Brewin, A simple expression for the ADM mass , General Relativity and Gravitation 39 (2007) 521 [ gr-qc/0609079]

    2007 arXiv

  2. [10]

    Padmanabhan and D

    T. Padmanabhan and D. Kothawala, Lanczos-Lovelock models of gravity , Physics Reports 531 (2013) 115 [ 1302.2151]

    2013 arXiv

  3. [11]

    Yale and T

    A. Yale and T. Padmanabhan, Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions, General Relativity and Gravitation 43 (2011) 1549 [ 1008.5154]

    2011 arXiv

  4. [12]

    Kastor and R

    D. Kastor and R. Mann, On black strings & branes in Lovelock gravity , Journal of High Energy Physics 2006 (2006) 048 [ hep-th/0603168]

    2006 arXiv

  5. [13]

    Kastor, Komar Integrals in Higher (and Lower) Derivative Gravity , Classical and Quantum Gravity 25 (2008) 175007 [ 0804.1832]

    D. Kastor, Komar Integrals in Higher (and Lower) Derivative Gravity , Classical and Quantum Gravity 25 (2008) 175007 [ 0804.1832]

    2008 arXiv

  6. [14]

    Dadhich, A discerning gravitational property for gravitational equ ation in higher dimensions, The European Physical Journal C 76 (2016) 104 [ 1506.08764]

    N. Dadhich, A discerning gravitational property for gravitational equ ation in higher dimensions, The European Physical Journal C 76 (2016) 104 [ 1506.08764]

    2016 arXiv

  7. [15]

    Kastor, S

    D. Kastor, S. Ray and J. Traschen, Mass and Free Energy of Lovelock Black Holes , Classical and Quantum Gravity 28 (2011) 195022 [ 1106.2764]

    2011 arXiv

  8. [16]

    Chakraborty and N

    S. Chakraborty and N. Dadhich, 1/r potential in higher dimensions , The European Physical Journal C 78 (2018) [ 1605.01961]

    2018 arXiv

  9. [17]

    Banados, C

    M. Banados, C. Teitelboim and J. Zanelli, Dimensionally Continued Black Holes , Physical Review D 49 (1994) 975 [ gr-qc/9307033]

    1994 arXiv

  10. [18]

    Cai and K.-S

    R.-G. Cai and K.-S. Soh, Topological black holes in the dimensionally continued gra vity, Physical Review D 59 (1999) [ gr-qc/9808067]

    1999 arXiv

  11. [19]

    Crisostomo, R

    J. Crisostomo, R. Troncoso and J. Zanelli, Black Hole Scan , Physical Review D 62 (2000) [hep-th/0003271]

    2000 arXiv

  12. [20]

    Cai and N

    R.-G. Cai and N. Ohta, Black Holes in Pure Lovelock Gravities , Physical Review D 74 (2006) [ hep-th/0604088]

    2006 arXiv

  13. [21]

    G. W. Gibbons and S. W. Hawking, Action integrals and partition functions in quantum gravity, Physical Review D 15 (1977) 2752

    1977

  14. [22]

    J. W. York, Role of Conformal Three-Geometry in the Dynamics of Gravita tion, Physical Review Letters 28 (1972) 1082

    1972

  15. [23]

    R. C. Myers, Higher-derivative gravity, surface terms, and string theo ry, Physical Review D 36 (1987) 392

    1987

  16. [24]

    Teitelboim and J

    C. Teitelboim and J. Zanelli, Dimensionally continued topological gravitation theory i n Hamiltonian form , Classical and Quantum Gravity 4 (1987) L125. – 22 –

    1987

  17. [25]

    Chakraborty, K

    S. Chakraborty, K. Parattu and T. Padmanabhan, A Novel Derivation of the Boundary Term for the Action in Lanczos-Lovelock Gravity , General Relativity and Gravitation 49 (2017) [ 1703.00624]

    2017 arXiv

  18. [26]

    Kraus, F

    P. Kraus, F. Larsen and R. Siebelink, The Gravitational Action in Asymptotically AdS and Flat Spacetimes, Nuclear Physics B 563 (1999) 259 [ hep-th/9906127]

    1999 arXiv

  19. [27]

    Miskovic and R

    O. Miskovic and R. Olea, Counterterms in Dimensionally Continued AdS Gravity , Journal of High Energy Physics 2007 (2007) 028 [ 0706.4460]

    2007 arXiv

  20. [28]

    Chakraborty and N

    S. Chakraborty and N. Dadhich, Brown-York quasilocal energy in Lanczos-Lovelock gravity and black hole horizons , Journal of High Energy Physics 2015 (2015) 1 [ 1509.02156]

    2015 arXiv

  21. [29]

    Deser and B

    S. Deser and B. Tekin, Gravitational Energy in Quadratic Curvature Gravities , Physical Review Letters 89 (2002) 101101 [ hep-th/0205318]

    2002 arXiv

  22. [30]

    Deser and B

    S. Deser and B. Tekin, Energy in Generic Higher Curvature Gravity Theories , Physical Review D 67 (2003) 084009 [ hep-th/0212292]

    2003 arXiv

  23. [31]

    Senturk, T

    C. Senturk, T. C. Sisman and B. Tekin, Energy and Angular Momentum in Generic F(Riemann) Theories, Physical Review D 86 (2012) 124030 [ 1209.2056]

    2012 arXiv

  24. [32]

    A. J. Amsel and D. Gorbonos, A Wald-like Formula for Energy , Physical Review D 87 (2013) 024032 [ 1209.1603]

    2013 arXiv

  25. [33]

    L. F. Abbott and S. Deser, Stability of gravity with a cosmological constant , Nuclear Physics B 195 (1982) 76

    1982

  26. [34]

    Jacobson and R

    T. Jacobson and R. C. Myers, Entropy of Lovelock Black Holes , Physical Review Letters 70 (1993) 3684 [ hep-th/9305016]

    1993 arXiv

  27. [35]

    Harlow and J.-q

    D. Harlow and J.-q. Wu, Covariant phase space with boundaries , 1906.08616

    1906 arXiv

  28. [36]

    Olea, Mass, Angular Momentum and Thermodynamics in Four-Dimensi onal Kerr-AdS Black Holes , Journal of High Energy Physics 2005 (2005) 023 [ hep-th/0504233]

    R. Olea, Mass, Angular Momentum and Thermodynamics in Four-Dimensi onal Kerr-AdS Black Holes , Journal of High Energy Physics 2005 (2005) 023 [ hep-th/0504233]

    2005 arXiv

  29. [37]

    Deruelle, N

    N. Deruelle, N. Merino and R. Olea, Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term , Physical Review D 97 (2018) [ 1709.06478]

    2018 arXiv

  30. [38]

    Iyer and R

    V. Iyer and R. M. Wald, A comparison of Noether charge and Euclidean methods for Computing the Entropy of Stationary Black Holes , Physical Review D 52 (1995) 4430 [gr-qc/9503052]

    1995 arXiv

  31. [39]

    Arenas-Henriquez, O

    G. Arenas-Henriquez, O. Miskovic and R. Olea, Vacuum Degeneracy and Conformal Mass in Lovelock AdS Gravity , Journal of High Energy Physics 2017 (2017) 128 [ 1710.08512]

    2017 arXiv

  32. [40]

    Arenas-Henriquez, R

    G. Arenas-Henriquez, R. B. Mann, O. Miskovic and R. Olea, Mass in Lovelock Unique Vacuum gravity theories , arXiv:1905.10840 [gr-qc, physics:hep-th] (2019) [ 1905.10840]

    2019 arXiv

  33. [41]

    Arenas-Henriquez, Black Hole Energy in Lovelock Unique Vacuum theories , arXiv:1909.06716 [gr-qc, physics:hep-th] (2019) [ 1909.06716]

    G. Arenas-Henriquez, Black Hole Energy in Lovelock Unique Vacuum theories , arXiv:1909.06716 [gr-qc, physics:hep-th] (2019) [ 1909.06716]

    2019 arXiv

  34. [42]

    M. H. Dehghani, N. Bostani and A. Sheykhi, Counterterm Method in Lovelock Theory and Horizonless Solutions in Dimensionally Continued Gravity , Physical Review D 73 (2006) [hep-th/0603058]

    2006 arXiv

  35. [43]

    Yale, Simple counterterms for asymptotically AdS spacetimes in L ovelock gravity, Physical Review D 84 (2011) 104036

    A. Yale, Simple counterterms for asymptotically AdS spacetimes in L ovelock gravity, Physical Review D 84 (2011) 104036. – 23 –

    2011

  36. [44]

    Astefanesei, R

    D. Astefanesei, R. B. Mann and C. Stelea, Note on counterterms in asymptotically flat spacetimes, Physical Review D 75 (2007) 024007 [ hep-th/0608037]. – 24 –

    2007 arXiv

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