Pith. sign in

REVIEW 3 major objections 4 minor 50 references

Quasitopological Gravity with Matter: Modified Double-Copy Approach

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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

Pith's one-line read Matter-coupled quasitopological gravity reduces, in spherical symmetry, to a nonlinear electrodynamics on a flat spacetime one dimension higher, from which Kerr-Schild metrics are rebuilt.

desk verdict A promising extension of the QTG double copy to matter, currently undone by a power-of-r error in the central inversion formula. read the letter →

arxiv 2608.12596 v1 pith:CWB2WG5N submitted 2026-08-12 gr-qc hep-th

Valeri P. Frolov This is my paper · ORCID
classification gr-qchep-th
keywords quasitopologicalgravitymodifieddoublecopyKerr-SchildmetricnonlinearelectrodynamicsYang-MillsfieldsVaidyasolutionsregularblackholessphericalsymmetry
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 extends the modified double-copy formalism from vacuum quasitopological gravity (QTG) to QTG coupled to matter. Its central claim is that, for spherically symmetric configurations whose matter stress-energy has the form $T_{\mu\nu}=\tau\gamma_{\mu\nu}+\sigma k_\mu k_\nu$ with $k_\mu=v_{,\mu}$ null, the QTG field equations are equivalent to equations for an auxiliary nonlinear gauge field in a flat $(D+1)$-dimensional spacetime. The QTG generating function $h(p)$ fixes the auxiliary electrodynamics through $dL/dE=h(E)$, while the matter stress-energy determines the current. Restricting the auxiliary solution to a $D$-dimensional hyperplane and applying the modified double-copy prescription yields a Kerr-Schild metric that solves the QTG equations. The construction covers Maxwell, nonlinear electrodynamics, and spherically symmetric Yang-Mills sources, reproduces static solutions under a generalized Birkhoff theorem, and produces Vaidya-type metrics when null currents are present.

What carries the argument

The load-bearing object is the modified double-copy correspondence. In a flat $(D+1)$-dimensional spacetime with null coordinate $V=T+R$, an auxiliary nonlinear electrodynamics with Lagrangian $L(E)$, defined by $dL/dE=h(E)$ where $h$ is the QTG generating function, produces a reduced field $H=R^{D-1}h(E)$. Its equations of motion, $H_{,R}=-R^{D-1}J_V$ and $H_{,V}=R^{D-1}J_R$, restricted to the equatorial hyperplane $\Pi$ with identifications $E|_\Pi=p$ and $(H/R^{D-2})|_\Pi=h(p)$, become the QTG field equations (2.32). The metric is then assembled as a Kerr-Schild form $ds^2=ds_0^2+r^2p\,(k_\mu dx^\mu)^2$, with $f=1-r^2p$. Everything flows from requiring the auxiliary current to be the matter stress-energy, making the correspondence an exact rewriting, not an approximation.

What would settle it

Take a spherically symmetric fluid whose stress-energy tensor has a tangential pressure unrelated to the radial one, so it cannot be written as $\tau\gamma_{\mu\nu}+\sigma k_\mu k_\nu$, and solve the QTG field equations directly; if a solution exists that is not reproduced by the auxiliary equations (3.9) under the hyperplane restriction, the claimed equivalence fails for that source class.

Watch

Extended reading notes

Core claim

The central discovery is an exact correspondence between matter-coupled QTG and a nonlinear gauge theory in flat space, valid for spherically symmetric configurations. With the stress-energy ansatz (2.24)-(2.25), the QTG field equations reduce to $H_{,v}=\frac{2\kappa}{D-2}\sigma$ and $H_{,r}=-\frac{2\kappa}{D-2}\tau$, where $H=r^{D-1}h(p)$. These are precisely the equations (3.9) satisfied by the auxiliary gauge field in the flat $(D+1)$-dimensional spacetime, after restriction to the hyperplane $\Pi: X^D=0$ and identification of the electric field $E$ with the primary curvature invariant $p$ and $H/R^{D-2}$ with $h(p)$. The metric function follows as $f=1-r^2p$, with $p$ obtained by inverting $h(p)=H/r^{D-2}$. Thus the hard gravitational problem is traded for a gauge-field problem whose Lagrangian is the QTG generating function; in the Einstein limit $h(p)=p$ the auxiliary theory becomes Maxwell's equations.

Load-bearing premise

The construction requires the matter stress-energy tensor to be of the form $T_{\mu\nu}=\tau\gamma_{\mu\nu}+\sigma k_\mu k_\nu$ with null $k_\mu=v_{,\mu}$, and the identification $E|_\Pi=p$ to hold; if a physical source does not admit this decomposition, the mapping to the auxiliary gauge field does not apply.

Editorial extensions

If this is right

  • Every matter source that fits the ansatz (2.24)-(2.25), including Maxwell fields, nonlinear electrodynamics, and a broad class of spherically symmetric Yang-Mills fields, generates exact QTG solutions through the auxiliary gauge-field construction.
  • Sources without null fluxes ($\sigma=0$) yield static geometries protected by a generalized Birkhoff theorem; Vaidya-type solutions arise precisely when $\sigma\neq 0$.
  • In the Einstein limit $h(p)=p$, the auxiliary nonlinear electrodynamics reduces to Maxwell theory, so the classical Kerr-Schild double copy is recovered as a special case.
  • The construction provides a practical route to exact regular black-hole solutions with matter in QTG, extending previously known vacuum regular black holes.

Reading between the lines

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

  • Editorial inference: the dictionary between $h(p)$ and the auxiliary Lagrangian suggests that QTG models can be classified by the nonlinear electrodynamics they emulate, potentially linking black-hole regularity to properties of the gauge theory.
  • Editorial inference: if the identification $E|_\Pi=p$ holds beyond the reduced equations, the formalism may extend to non-spherical configurations where the same identification is imposed along a congruence, a possible path toward rotating solutions.
  • Editorial inference: the conservation constraint $\tau_{,r}=r^{-1}T$ shows the allowed matter sector is narrower than generic anisotropic fluids; testing the double-copy mapping against a non-conforming fluid would delimit the true scope of the method.
  • Editorial inference: the correspondence could be inverted to design QTG models for a given matter source by choosing the generating function $h(p)$ that makes the auxiliary gauge theory solvable.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes a modified double-copy construction for quasitopological gravity (QTG) coupled to matter. After reducing spherically symmetric QTG to a two-dimensional dilaton-gravity system in null coordinates, the author introduces an auxiliary nonlinear electrodynamics in a flat (D+1)-dimensional spacetime with H=R^{D-1}h(E), defines currents through smooth extensions of the matter variables, and restricts the auxiliary solution to a D-dimensional equatorial hyperplane. The claim is that the restricted auxiliary equations reproduce the QTG field equations (2.32), and that inverting h(p)=H/r^{D-2} and setting f=1-r^2p yields Kerr–Schild metrics solving QTG with matter. Maxwell, nonlinear electrodynamics, and Yang–Mills sources are discussed as compatible matter models, together with Birkhoff and Vaidya-type consequences.

Significance. If the construction were correct, it would give a genuine solution-generating technique for a nontrivial higher-curvature gravity with matter, reducing the problem to a gauge-field system in flat spacetime. The paper is clearly written, the 2D reduction is standard, and the idea of encoding the QTG model through h(p)=dL/dE is elegant. The explicit statements of the stress-energy ansatz and the roles of null fluxes are useful. However, the central algebraic identification contains a dimensional error that invalidates the inversion procedure as written, so the main claim does not currently hold; the error appears to be locally fixable.

major comments (3)
  1. [Sec. 2, after Eq. (2.32); Eq. (3.16)] The inversion formula has the wrong power of r. Equation (2.23) defines H=r^{D-1}h(p) and Eq. (3.10) defines H=R^{D-1}h(E). On the hyperplane Pi, R=r, so H|_Pi = r^{D-1}h(E|_Pi). The text after Eq. (2.32) and the second identification in Eq. (3.16) instead state h(p)=H/r^{D-2}; this would imply r h(p)=h(p), which is impossible except at r=1. The correct inversion is p=h^{-1}(H/r^{D-1}), so f=1-r^2 p = 1 - r^2 h^{-1}(H/r^{D-1}). In the Einstein limit h(p)=p with D=5 and vacuum, the paper's formula gives f=1-H/r, whereas the correct Schwarzschild-Tangherlini result is f=1-2M/r^2, obtained from p=H/r^4. This is a load-bearing error: the central mapping and the claimed reduction to Maxwell theory in the Einstein limit fail as written until D-2 is replaced by D-1 in both places.
  2. [Sec. 3, Eq. (3.16)] The identification E|_Pi = p is asserted rather than derived. Since the auxiliary theory is deliberately engineered by setting dL/dE = h(E) and H=R^{D-1}h(E), the matching of equations (3.9) to (2.32) is enforced by construction once E|_Pi=p is imposed. If this identification is intended as a postulate of the double-copy ansatz, that should be stated explicitly; if it is meant to follow from the field equations, a derivation is needed. As written, the phrase 'the identifications ... are made' presents a central assumption as though it were a conclusion, which weakens the claim that QTG equations are mapped rather than merely reproduced by definition.
  3. [Sec. 2.3, Eqs. (2.24)-(2.25)] The scope of the construction is narrower than the abstract's 'broad class of matter sources' suggests. The matter stress-energy must admit the decomposition T_mu_nu = tau gamma_mu_nu + sigma k_mu k_nu with k_mu=v,mu null, and conservation then forces tau,r = r^{-1} T and sigma,r = -tau,v. This excludes generic anisotropic matter and is a substantive restriction. The examples in Section 4 are consistent with this ansatz, but the limitation should be stated at the outset rather than only in the discussion section.
minor comments (4)
  1. [Eq. (3.5)] Equation (3.5) contains the typo 'L(E)\approx= 1/2 E^2 + ...'; the double equals sign should be removed.
  2. [Fig. 1 and surrounding text] The figure caption and the text around it contain garbled characters (for example, 'DX 1X 1DX :0 DX'), which should be corrected before publication.
  3. [Section 2 heading] The heading 'QTG DILATON 2D ACTION' is awkward; a clearer title would be 'QTG as a two-dimensional dilaton action'.
  4. [References] The paper relies on reference [33], an arXiv preprint, for the reduced gravitational equations (2.22) and for the generalized Birkhoff theorem; since these are load-bearing, the relevant derivations should be summarized or the dependence on the preprint should be explicitly flagged.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the auxiliary-field dictionary is deliberately definitional, and no fitted output is relabeled as a prediction.

full rationale

The central mapping is built by explicit definition rather than by hidden reuse of data: Eq. (3.10) sets H = R^(D-1) h(E) with h(E) = dL/dE, and Eqs. (2.23)/(2.32) use the same h through H = r^(D-1) h(p); after the stated identifications E|Pi = p and, correctly, H/R^(D-1) = h(p), the auxiliary equations (3.9) coincide with the QTG equations (2.32) term by term. This is the announced purpose of the modified double-copy dictionary, not a claim that independent input produced the output. The Einstein-limit statement ('h(p) = p implies L = E^2/2, Maxwell') is a consistency check of the definition, not a prediction. The matter ansatz (2.24)-(2.25) and the Birkhoff theorem are imported from [33], and the modified-double-copy method comes from [22]; these are same-author citations, but the present paper restates the equations and verifies the matching directly, so the citations are not load-bearing evidence for the claimed reduction. A separate, non-circularity concern is that Eq. (2.23) defines H = r^(D-1) h, yet the text inverts h = H/r^(D-2) and repeats H/R^(D-2) in (3.16); those displayed powers are dimensionally inconsistent and would break the Einstein-limit example, but this is a correctness slip, not a circularity.

Assumptions & free parameters 1 free parameters · 4 assumptions · 1 invented entities

There are no numerical fits. The main dependencies are the prior reduced equations from [33], the invertibility of h(p), the restrictive matter ansatz, and the definitional choice that the auxiliary NED Lagrangian derive from h(E). These are stated or cited, but the matter ansatz and the dL/dE = h(E) definition carry the construction by construction rather than by independent derivation.

free parameters (1)
  • Generating function h(p) (coefficients alpha_j) = unspecified; arbitrary analytic invertible function
    The construction works for any admissible h(p). No numerical values are fitted, but the entire auxiliary nonlinear electrodynamics is defined by h(p), so this is a hand-chosen model input that the central claim depends on.
assumptions (4)
  • domain assumption The reduced QTG field equations (2.22), taken from [33], are correct.
    Section 2.2 uses G_vv + N f G_vr = N H,v, G_vr = -N H,r, and G_rr = 2 r^(D-3) N,r/N h'(p) from [33] without rederivation.
  • domain assumption The generating function h(p) is analytic and invertible over the relevant domain.
    Section 1 and the inversion step h(p) = H/r^(D-2) require h to be invertible; this is stated but not proved for the matter-coupled case.
  • ad hoc to paper The matter stress-energy tensor admits the decomposition (2.24)-(2.25) with smooth extensions to M^(D+1).
    Section 2.3 and Eq. (3.13). The mapping to the auxiliary current depends on this special form and on the existence of smooth extensions satisfying tau,V + sigma,R = 0.
  • ad hoc to paper The auxiliary nonlinear electrodynamics is defined by dL/dE = h(E).
    Section 3, Eq. (3.10). This is chosen so that the auxiliary equations reproduce the QTG equations; it is a definition rather than a derived property.
invented entities (1)
  • Auxiliary flat (D+1)-dimensional spacetime M^(D+1) with auxiliary gauge field A_a
    purpose: Hosts nonlinear electrodynamics equations whose solutions map to QTG metrics in D dimensions; purely a calculational device.
    The extra dimension is introduced solely to make the field equations tractable and is not claimed to be physical. No falsifiable prediction is attached to it.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quasitopological Gravity with Matter: Modified Double-Copy Approach." pith.science (2026). https://pith.science/paper/CWB2WG5N

@misc{pith2026260812596,
  author       = {Pith},
  title        = {Pith review of: Quasitopological Gravity with Matter: Modified Double-Copy Approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CWB2WG5N}},
  note         = {Machine review of arXiv:2608.12596}
}
abstract

We extend the recently proposed modified double-copy formalism to quasitopological gravity (QTG) coupled to matter. For spherically symmetric configurations, the QTG field equations in $D-$dimensional curved spacetime with a broad class of matter sources are mapped to equations for an auxiliary nonlinear gauge field in a flat $(D+1)$-dimensional spacetime. The nonlinear electrodynamics governing this auxiliary field is determined entirely by the generating function $h(p)$ that specifies the QTG model, while the corresponding current is determined by the matter stress-energy tensor. Restricting the auxiliary solution to a $D$-dimensional hyperplane and applying the modified double-copy prescription yields the Kerr--Schild metric solving the QTG equations. We show that Maxwell and nonlinear electrodynamics, as well as a broad class of spherically symmetric Yang--Mills fields, provide physical matter sources compatible with this construction. In the absence of null currents, the resulting solutions satisfy a generalized Birkhoff theorem and are static, whereas null charged currents naturally generate Vaidya-type solutions. In the Einstein limit, $h(p)=p$, the auxiliary nonlinear electrodynamics reduces to Maxwell theory.

Figures

Figures reproduced from arXiv: 2608.12596 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic illustration of the modified double-copy [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

50 extracted references · 22 canonical work pages

  1. [1]

    Quasitopological Gravity with Matter: Modified Double-Copy Approach

    INTRODUCTION A broad class of important solutions of the Einstein equations can be written in the Kerr–Schild form [1] ds2 =ds 2 0 + Φ (kµdxµ)2,(1.1) whereds 2 0 is the flat spacetime metric andk µ is a shear- free null congruence. The vector fieldk µ is null with respect to both the background metricds 2 0 and the full metricds 2. A remarkable property o...

    work page Pith review arXiv 2026

  2. [2]

    Spherically reduced QTG equations We first summarize the geometrical conventions em- ployed in the spherical reduction of the QTG theory

    QTG DILATON 2D ACTION AND FIELD EQUATIONS 2.1. Spherically reduced QTG equations We first summarize the geometrical conventions em- ployed in the spherical reduction of the QTG theory. Let MD denote aD-dimensional curved spacetime endowed with the metricg AB, ds2 =g ABdXAdXB, A,B= 0,1,...,D−1.(2.1) We restrict attention to geometries that split into a two...

    work page

  3. [3]

    Within this framework, solutions of the QTG field equations on the curvedD-dimensional spacetimeM D are obtained indi- rectly

    MODIFIED DOUBLE-COPY METHOD OF SOLVING QTG EQUATIONS In this section we apply the modified double-copy formalism proposed in [22] to quasitopological gravity (QTG) in the presence of a matter source. Within this framework, solutions of the QTG field equations on the curvedD-dimensional spacetimeM D are obtained indi- rectly. The construction begins by sol...

    work page

  4. [4]

    EXAMPLES It should be emphasized that, up to this point, the matter source has been treated as a prescribed exter- nal distribution constrained only by the assumed ansatz. In fact, stress-energy tensors of the form (2.24)–(2.25) arise naturally in a broad class of field theories, includ- ing Maxwell electrodynamics, nonlinear electrodynamics, and Yang–Mil...

    work page

  5. [5]

    DISCUSSION We have developed a modified double-copy formula- tion of quasitopological gravity in the presence of mat- ter sources. The construction replaces the direct so- lution of the nonlinear gravitational field equations in a curved spacetimeM D by the solution of gauge-field equations in an auxiliary flat (D+ 1)-dimensional space- time. The gravitat...

    work page

  6. [6]

    The double copy: gravity from gluons,

    C. D. White, “The double copy: gravity from gluons,” Contemporary Physics59, 109 (2018)

    2018

  7. [7]

    Some algebraically degenerate solutions of einstein’s gravitational field equations,

    R. P. Kerr and A. Schild, “Some algebraically degenerate solutions of einstein’s gravitational field equations,” Pro- ceedings of Symposia in Applied Mathematics17, 199 (1965)

    work page 1965

  8. [8]

    Pertur- bative quantum gravity as a double copy of gauge the- ory,

    Z. Bern, J. J. M. Carrasco, and H. Johansson, “Pertur- bative quantum gravity as a double copy of gauge the- ory,” Physical Review Letters105(2010), 10.1103/phys- revlett.105.061602

    doi:10.1103/phys- 2010

Show all 50 references
  1. [9]

    Black holes and the double copy,

    R. Monteiro, D. O’Connell, and C. D. White, “Black holes and the double copy,” Journal of High Energy Physics2014(2014), 10.1007/jhep12(2014)056

    2014 doi

  2. [10]

    The classical double copy for taub–NUT spacetime,

    A. Luna, R. Monteiro, D. O’Connell, and C. D. White, “The classical double copy for taub–NUT spacetime,” Physics Letters B750, 272 (2015)

    2015

  3. [11]

    Kerr-Schild Double Copy and Complex Worldlines,

    I. Bah, R. Dempsey, and P. Weck, “Kerr-Schild Double Copy and Complex Worldlines,” JHEP02, 180 (2020), arXiv:1910.04197 [hep-th]

    2020 arXiv

  4. [12]

    Generalized quasi-topological gravities: the whole shebang,

    P. Bueno, P. A. Cano, R. A. Hennigar, M. Lu, and J. Moreno, “Generalized quasi-topological gravities: the whole shebang,” Class. Quant. Grav.40, 015004 (2023), arXiv:2203.05589 [hep-th]

    2023 arXiv

  5. [13]

    The duality between color and kine- matics and its applications,

    Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson, and R. Roiban, “The duality between color and kine- matics and its applications,” (2019), arXiv:1909.01358 [hep-th]

    2019 arXiv

  6. [14]

    The sagex review on scattering ampli- tudes, chapter 2: An invitation to color-kinematics dual- ity and the double copy,

    Z. Bern, J. J. Carrasco, M. Chiodaroli, H. Johansson, and R. Roiban, “The sagex review on scattering ampli- tudes, chapter 2: An invitation to color-kinematics dual- ity and the double copy,” (2022), arXiv:2203.13013 [hep- th]

    2022 arXiv

  7. [15]

    The Kerr spacetime: A brief introduction,

    M. Visser, “The Kerr spacetime: A brief introduction,” arXiv e-prints (2007), arXiv:0706.0622 [gr-qc]

    2007 arXiv

  8. [16]

    (Generalized) quasi-topological gravities at all or- ders,

    P. Bueno, P. A. Cano, and R. A. Hennigar, “ (Generalized) quasi-topological gravities at all or- ders,” Classical and Quantum Gravity37, 015002 (2019), arXiv:1909.07983 [hep-th]

    2019 arXiv

  9. [17]

    All higher-curvature gravities as Generalized quasi-topological gravities,

    P. Bueno, P. A. Cano, J. Moreno, and A. Mur- cia, “All higher-curvature gravities as Generalized quasi-topological gravities,” JHEP11, 062 (2019), arXiv:1906.00987 [hep-th]

    2019 arXiv

  10. [18]

    Regular black holes inspired by quasitopological grav- ity,

    V. P. Frolov, A. Koek, J. P. Soto, and A. Zelnikov, “Regular black holes inspired by quasitopological grav- ity,” Phys. Rev. D111, 044034 (2025). 9

    2025

  11. [19]

    A new cubic theory of gravity in five dimensions: black hole, Birkhoff’s theorem and c- function,

    J. Oliva and S. Ray, “A new cubic theory of gravity in five dimensions: black hole, Birkhoff’s theorem and c- function,” Classical and Quantum Gravity27, 225002 (2010)

    2010

  12. [20]

    Gener- alized quasitopological gravity,

    R. A. Hennigar, D. Kubizˇ n´ ak, and R. B. Mann, “Gener- alized quasitopological gravity,” Phys. Rev. D95, 104042 (2017), arXiv:1703.01631 [hep-th]

    2017 arXiv

  13. [21]

    Black Holes in Quasi-topological Gravity,

    R. C. Myers and B. Robinson, “Black Holes in Quasi-topological Gravity,” JHEP08, 067 (2010), arXiv:1003.5357 [gr-qc]

    2010 arXiv

  14. [22]

    Classification of generalized quasitopological gravities,

    J. Moreno and A. J. Murcia, “Classification of generalized quasitopological gravities,” Phys. Rev. D108, 044016 (2023), arXiv:2304.08510 [gr-qc]

    2023 arXiv

  15. [23]

    Regular black holes from pure gravity,

    P. Bueno, P. A. Cano, and R. A. Hennigar, “Regular black holes from pure gravity,” Physics Letters B861, 139260 (2025)

    2025

  16. [24]

    Cos- mic Inflation From Regular Black Holes,

    K. Sueto, R. Yoshimoto, and P. A. Cano, “Cos- mic Inflation From Regular Black Holes,” (2026), arXiv:2604.04601 [gr-qc]

    2026 arXiv

  17. [25]

    J. A. Pinedo Soto,Modified Gravity and Regular Black Hole Models, Ph.D. thesis, University of Alberta (2025), arXiv:2511.12902 [gr-qc]

    2025

  18. [26]

    Buchdahl limits in theories with reg- ular black holes,

    P. Bueno, R. A. Hennigar, ´Angel J. Murcia, and A. Vicente-Cano, “Buchdahl limits in theories with reg- ular black holes,” (2026), arXiv:2512.19796 [gr-qc]

    2026

  19. [28]

    Quasitopological gravity and double- copy formalism,

    V. P. Frolov, “Quasitopological gravity and double- copy formalism,” Phys. Rev. D113, 064023 (2026), arXiv:2512.14674 [gr-qc]

    2026 arXiv

  20. [29]

    Regular geometries from singu- lar matter in quasi-topological gravity,

    P. Bueno, R. A. Hennigar, ´Angel J. Murcia, and A. Vicente-Cano, “Regular geometries from singu- lar matter in quasi-topological gravity,” (2026), arXiv:2603.10110 [gr-qc]

    2026

  21. [30]

    C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravi- tation(W. H. Freeman, San Francisco, 1973)

    1973

  22. [31]

    All 2D generalized dilaton theories from d≥4 gravities,

    J. Borissova, “All 2D generalized dilaton theories from d≥4 gravities,” Phys. Rev. D113, 124088 (2026), arXiv:2603.06786 [hep-th]

    2026 arXiv

  23. [32]

    Regular black holes from pure gravity in four dimensions,

    J. Borissova and R. Carballo-Rubio, “Regular black holes from pure gravity in four dimensions,” Phys. Rev. D113, 124004 (2026), arXiv:2602.16773 [gr-qc]

    2026 arXiv

  24. [33]

    (2.22) Here, h=h(p) is a function of the primary curvature in- variant

    for more details) Gvv +NfG vr =NH ,v, Gvr =−NH ,r, Grr = 2rD−3N,r N h′(p). (2.22) Here, h=h(p) is a function of the primary curvature in- variant. It specifies the particular QTG model under consideration. For the time being, we leave this function arbitrary. We also introduce...

  25. [34]

    g ttgrr =−1 black hole thermody- namics in extended quasi-topological gravity,

    J. Borissova, “g ttgrr =−1 black hole thermody- namics in extended quasi-topological gravity,” (2026), arXiv:2604.24101 [gr-qc]

    2026 arXiv

  26. [35]

    Birkhoff implies quasi-topological,

    P. Bueno, R. A. Hennigar, and ´A. J. Murcia, “Birkhoff implies quasi-topological,” Class. Quant. Grav.43, 095020 (2026), arXiv:2510.25823 [gr-qc]

    2026

  27. [36]

    Regular black hole formation in four-dimensional non-polynomial gravities,

    P. Bueno, P. A. Cano, R. A. Hennigar, and ´Angel J. Mur- cia, “Regular black hole formation in four-dimensional non-polynomial gravities,” (2025), arXiv:2509.19016 [gr- qc]

    2025

  28. [37]

    The scalar invari- ants of a general gravitational metric,

    V. V. Narlikar and K. R. Karmarkar, “The scalar invari- ants of a general gravitational metric,” Proceedings of the Indian Academy of Sciences, Section A29, 91 (1949)

    1949

  29. [38]

    Regular black holes from Oppenheimer-Snyder collapse,

    P. Bueno, P. A. Cano, R. A. Hennigar, A. J. Mur- cia, and A. Vicente-Cano, “Regular black holes from Oppenheimer-Snyder collapse,” Phys. Rev. D112, 064039 (2025), arXiv:2505.09680 [gr-qc]

    2025 arXiv

  30. [39]

    Vaidya-Type Solutions of Quasitopological Gravity Interacting with Nonlinear Electrodynamics,

    V. P. Frolov, C.-M. Yoo, and A. Zelnikov, “Vaidya-Type Solutions of Quasitopological Gravity Interacting with Nonlinear Electrodynamics,” (2026), arXiv:2607.22856 [gr-qc]

    2026 arXiv

  31. [40]

    Foundations of the new field the- ory,

    M. Born and L. Infeld, “Foundations of the new field the- ory,” Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character144, 425 (1934)

    1934

  32. [41]

    Many faces of Born-Infeld theory,

    S. V. Ketov, “Many faces of Born-Infeld theory,” in 7th International Wigner Symposium (Wigsym 7)(2001) arXiv:hep-th/0108189

    2001 arXiv

  33. [42]

    Topics in Born-Infeld electrodynamics,

    R. Kerner, A. L. Barbosa, and D. V. Gal’tsov, “Topics in Born-Infeld electrodynamics,” AIP Conf. Proc.589, 377 (2001), arXiv:hep-th/0108026

    2001 arXiv

  34. [43]

    Introductory Notes on Non-linear Elec- trodynamics and its Applications,

    D. P. Sorokin, “Introductory Notes on Non-linear Elec- trodynamics and its Applications,” Fortsch. Phys.70, 2200092 (2022), arXiv:2112.12118 [hep-th]

    2022 arXiv

  35. [44]

    Born–infeld theory of electromagnetism,

    Y. Yang, “Born–infeld theory of electromagnetism,” in Mathematical Physics with Differential Equations(Ox- ford University Press, 2023) Chap. 14, pp. 323–428

    2023

  36. [45]

    Constraints on sin- gularity resolution by nonlinear electrodynamics,

    A. Bokuli´ c, I. Smoli´ c, and T. Juri´ c, “Constraints on sin- gularity resolution by nonlinear electrodynamics,” Phys. Rev. D106, 064020 (2022)

    2022

  37. [46]

    Space-time symmetries in gauge theories,

    P. Forg´ acs and N. S. Manton, “Space-time symmetries in gauge theories,” Communications in Mathematical Physics72, 15 (1980)

    1980

  38. [47]

    On the spherically symmetric gauge fields,

    C. Gu and H. Hu, “On the spherically symmetric gauge fields,” Communications in Mathematical Physics79, 75 (1981)

    1981

  39. [48]

    On symmetric gauge fields for arbitrary gauge and symmetry groups,

    O. Brodbeck, “On symmetric gauge fields for arbitrary gauge and symmetry groups,” Helvetica Physica Acta69, 321 (1996), arXiv:gr-qc/9610024 [gr-qc]

    1996 arXiv

  40. [49]

    Group actions on principal bundles and invariance conditions for gauge fields,

    J. Harnad, S. Shnider, and L. Vinet, “Group actions on principal bundles and invariance conditions for gauge fields,” Journal of Mathematical Physics21, 2719 (1980)

    1980

  41. [50]

    Local existence proofs for the boundary value problem for static spheri- cally symmetric einstein–yang–mills fields with compact gauge groups,

    T. A. Oliynyk and H. P. K¨ unzle, “Local existence proofs for the boundary value problem for static spheri- cally symmetric einstein–yang–mills fields with compact gauge groups,” Journal of Mathematical Physics43, 2363 (2002)

    2002

  42. [51]

    On all possible static spherically symmetric einstein–yang–mills solitons and black holes,

    T. A. Oliynyk and H. P. K¨ unzle, “On all possible static spherically symmetric einstein–yang–mills solitons and black holes,” Classical and Quantum Gravity19, 457 (2002)

    2002

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.