On the consistency of non-commutative geometry inspired Reissner-Nordstr\"{o}m black hole solution

Gokhan Alkac; Gonul Unal; Murat Mesta

REVIEW 3 major objections 3 minor 24 references

On the consistency of non-commutative geometry inspired Reissner-Nordstr\"{o}m black hole solution

T0 review · 3 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The Gaussian-smeared Reissner-Nordström solution does not satisfy the full Einstein equations.

desk verdict A real, checkable inconsistency in a widely cited noncommutative charged black hole solution, with a repair that is mathematically consistent but physically underdetermined. read the letter →

arxiv 2507.16780 v2 pith:PIDXZPME submitted 2025-07-22 gr-qc hep-th

Gokhan Alkac , Murat Mesta , Gonul Unal This is my paper · ORCID

classification gr-qchep-th MSC 83C5783C2283C6583C75

keywords noncommutativegeometryblackholeReissner-NordströmGaussiansmearingenergy-momentumtensorEinsteinequationsstrongenergyconditionCauchyhorizon

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 revisits the noncommutative-geometry-inspired Reissner-Nordström black hole, built by smearing the point mass and point charge with Gaussian distributions. It argues that the standard construction, which reads the metric off the $tt$-component of Einstein's equations, does not produce a full solution: the $\theta\theta$ and $\phi\phi$ components fail because the smeared scalar potential is not Coulomb. The authors show that only a Coulomb potential satisfies the transverse-pressure consistency condition required by the diagonal stress-tensor form, and they construct an improved electromagnetic energy-momentum tensor that imposes this condition by hand. The improved tensor makes all Einstein equations hold but breaks the conformal symmetry of Maxwell theory, and it changes the predicted region where the strong energy condition is violated, possibly placing that violation outside the Cauchy horizon.

What carries the argument

The load-bearing mechanism is a consistency relation for the energy-momentum tensor in a static, spherically symmetric spacetime. Writing $T^{\mu}_{\nu}=\mathrm{diag}\{-\epsilon,p_r,p_{\perp},p_{\perp}\}$, the Einstein tensor's structure forces $p_r=-\epsilon$ and $p_{\perp}=-\epsilon-\frac{r}{2}\epsilon'$. For the electromagnetic part with $\epsilon=-\frac{1}{2}\phi'^2$ (from the Maxwell tensor), this relation reduces to a differential equation whose only solution is the Coulomb potential $\phi=c/r$. The smeared potential from the Gaussian charge density, $\phi=\frac{Q}{4\pi^{3/2}r}\gamma(1/2,r^2/4\theta)$, fails this test, which is why the $\theta\theta$ and $\phi\phi$ equations break. The paper's repair is the improved tensor (31): it keeps $\epsilon=\frac{1}{2}\phi'^2$ and $p_r=-\epsilon$ but imposes $p_{\perp}=-\epsilon-\frac{r}{2}\partial_r\epsilon$ by hand, producing a nonzero trace and a different strong-energy condition.

What would settle it

Evaluate the $\theta\theta$ (equivalently $\phi\phi$) component of Einstein's equations directly for the metric (30), the smeared potential (28), and the standard Maxwell stress tensor (22); the paper's claim is that the left-hand side minus the right-hand side is nonzero, and this substitution can be checked by hand or with computer algebra.

Watch

Extended reading notes

Core claim

The central claim is that the Gaussian-smeared Reissner-Nordström solution is inconsistent as a solution of the full Einstein equations. Solving the $tt$-component alone gives the metric function (30), and the thermodynamics derived from that metric remain unaffected. But when the electromagnetic energy-momentum tensor is built from the Maxwell form (22) evaluated on the smeared potential (28), the $\theta\theta$ and $\phi\phi$ components of Einstein's equations are not satisfied. The reason is a structural constraint: for a static, spherically symmetric diagonal stress tensor, the transverse pressure must obey $p_{\perp}=-\epsilon-\frac{r}{2}\epsilon'$, a relation satisfied only by the Coulomb potential among Maxwell fields. The paper therefore supplies an improved electromagnetic tensor with that relation imposed by hand; all components of Einstein's equations then hold, at the cost of a nonzero trace that breaks the four-dimensional conformal invariance of Maxwell theory.

Load-bearing premise

The argument assumes that the electromagnetic energy-momentum tensor must be the standard Maxwell form evaluated on the smeared potential, so that imposing the transverse-pressure relation by hand is a legitimate physical improvement rather than an arbitrary choice.

Editorial extensions

If this is right

The metric function (30) and the black-hole thermodynamics derived from it remain unchanged, since they follow from the $tt$-component alone.
For the standard Maxwell tensor, the $\theta\theta$ and $\phi\phi$ Einstein equations are violated; with the improved tensor they are satisfied exactly.
The improved tensor has nonzero trace, so the four-dimensional conformal invariance of Maxwell theory is lost in this construction.
For $M=2\sqrt{\theta}$ and $Q=5\sqrt{\theta}$, the strong-energy violation radius moves from $r_*\simeq 0.61\sqrt{\theta}$ to $r_*\simeq 2.95\sqrt{\theta}$, crossing the Cauchy horizon at $r_-\simeq 2.32\sqrt{\theta}$.
Parameter choices that look safe under the standard treatment can violate the strong energy condition outside the Cauchy horizon when the improved tensor is used, so the causal structure of these solutions may need revision.

Reading between the lines

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

If the improved tensor cannot be derived from an action, then the new strong-energy prediction is a property of the hand-imposed repair rather than of noncommutativity itself; deriving the same tensor from a nonlinear electrodynamics Lagrangian would test this.
The same inconsistency should appear in any smeared-charge solution whose scalar potential is not Coulomb, including higher-dimensional and Gauss-Bonnet extensions; checking their $\theta\theta$/ $\phi\phi$ components would show whether the repair generalizes.
Observational signatures that depend on energy conditions, such as horizon structure, photon-ring location, or the possibility of traversable wormholes, should be recomputed with the improved tensor before drawing conclusions from the original solution.
Alternatively, defining the matter stress tensor directly from the Einstein tensor $T_{\mu\nu}=G_{\mu\nu}/8\pi$ would dissolve the inconsistency by construction, at the price of leaving the electromagnetic interpretation less clear.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: the paper is right about a real gap in the standard noncommutative Reissner-Nordström solution, and the repair it offers is mathematically consistent but physically underdetermined. The one-line takeaway: don't use the old smeared-charge solution with the standard Maxwell stress tensor and expect all Einstein equations to hold; either use their improved tensor or allow a two-function metric.

The new part is Eqs. (22)-(26): for a static spherically symmetric metric written in Schwarzschild form g_tt = -1/g_rr, the Einstein tensor forces any diagonal matter tensor to obey p_perp = -epsilon - r/2 epsilon'. The standard Maxwell tensor has p_perp = +epsilon for a radial electric field, and the two match only when phi is Coulomb. For the smeared Gaussian charge, phi is not Coulomb, so the theta-theta and phi-phi Einstein equations fail. That's a clean, checkable result, and the paper deserves credit for stating the limitation honestly: the metric function and thermodynamics from the original papers survive; the problem is in the stress tensor.

The soft spots are real but not fatal to the main observation. The improved tensor in (31)-(32) is chosen to enforce the consistency condition; no action, star product, or noncommutative field theory produces it. The trace is nonzero, so it breaks Maxwell conformal symmetry without a Lagrangian explanation. That means the headline SEC result — violation outside the Cauchy horizon at r* = 2.95 sqrt(theta) — is a property of this particular completion, not a robust prediction. The paper acknowledges the ad hoc nature, but a reader should not walk away thinking the SEC boundary is a theorem. There is also a larger gap the paper doesn't address: the inconsistency may be an artifact of insisting on g_tt g_rr = -1. In a general static spherically symmetric metric with two independent functions, the standard Maxwell T could be accommodated by letting the metric relax. The authors don't discuss that, so the "full solution status" of the original model is less clean than they claim.

Minor: the explicit failure calculation is asserted but not shown; it's simple enough to reproduce, but a referee should ask for it.

Bottom line: an important subfield-specific correction, not a breakthrough. Deserves a serious referee; the referee should push for a Lagrangian derivation of the improved tensor or an explicit statement that it is an effective model, and should ask the authors to discuss the two-function metric alternative. I'd take the inconsistency result and leave the SEC prediction on the shelf.

Referee Report

3 major / 3 minor

Summary. The paper revisits the non-commutative geometry inspired Reissner-Nordström black hole solution obtained by replacing point mass and charge with Gaussian smeared sources. Its central claim is that the standard construction, which determines the metric function from the tt-component of the Einstein equations, does not solve the θθ and φφ components when the electromagnetic sector is represented by the standard Maxwell tensor built from the smeared scalar potential. The paper gives a short algebraic argument that the transverse-pressure consistency condition p⊥ = −ε − (r/2)ε′ can hold only for the Coulomb potential, and it therefore concludes that the smeared potential of Eq. (28) and the metric of Eq. (30) are inconsistent with the full set of Einstein equations. It then proposes an improved electromagnetic energy-momentum tensor, Eq. (31)-(32), which imposes the transverse-pressure relation by hand and satisfies all components. Using this tensor, the strong energy condition violation radius shifts from r∗ = 0.61√θ to r∗ = 2.95√θ for Q = 5√θ and M = 2√θ, placing the violation outside the Cauchy horizon. The paper states that the metric function and thermodynamic properties remain unchanged.

Significance. If the inconsistency diagnosis is correct, it is a useful clarification of a widely used class of non-commutative geometry inspired charged black hole solutions: the metric and its thermodynamics are unaffected, but any application that uses the energy-momentum tensor as an independent physical object must be reconsidered. The core algebraic observation—only the Coulomb potential satisfies the consistency condition (25) for the standard Maxwell tensor—is simple, credible, and easy to verify. However, the improved tensor is constructed by hand rather than derived from an action, a star-product, or a noncommutative field theory, and the paper itself acknowledges this. Consequently the strong energy condition prediction is a property of one particular completion, not a robust consequence of noncommutative geometry. The paper is honest about the ad hoc nature of the repair in the body, but the abstract and conclusions use 'predicts' language that overstates the model independence of the result.

major comments (3)

[§3, Eqs. (28)–(30)] The central claim that the θθ and φφ components of the Einstein equations fail is asserted rather than demonstrated: the text says 'An explicit calculation shows that this is indeed the case' but does not display the calculation. Since this is the load-bearing evidence for the paper's main result, please include the explicit failure, for example the nonzero value of p⊥|el + ε|el + (r/2)ε′|el evaluated with Eqs. (28)-(29), or the residual of the θθ component of Gμν − 8π(T_matt + T_el).
[§4, Eqs. (31)–(32)] The improved electromagnetic tensor is imposed by hand and is not unique. It is one minimal completion that preserves the t-r sector of the Maxwell tensor and forces conservation via Eq. (25), but it is not derived from any action, star-product, or noncommutative field theory, and other consistent completions (e.g., nonlinear electrodynamics, which the paper mentions) will generically give different energy conditions. Therefore the abstract's and Section 4's claim that the proposal 'predicts' violation of the strong energy condition outside the Cauchy horizon is too strong. The authors should either derive T from a concrete Lagrangian or explicitly reframe the r∗ = 2.95√θ result as an example of model dependence rather than a prediction.
[§4, Eq. (33)] The trace calculation in Eq. (33) is presented as evidence that the improvement breaks the conformal symmetry of Maxwell's theory, but the derivation is not shown and the displayed expression appears inconsistent with the improved tensor defined in Eqs. (31)-(32). With ε = φ′^2/2 and φ′ from Eq. (29), the trace of the improved electromagnetic tensor alone is −Q² γ(3/2, r²/4θ) e^{−r²/4θ} / (16π³ θ^{3/2} r). Eq. (33) is missing the exponential factor and also includes the matter trace; the matter sector already has a nonzero trace, so the inference drawn from Eq. (33) needs to be recomputed and the electromagnetic and matter traces must be separated.

minor comments (3)

[§3, after Eq. (25)] The sentence that reads 'taking p⊥|el = 1/2 φ′^2 and ε|el = −1/2 φ′^2' has a sign error: from Eq. (22), T t t = −1/2 φ′^2, so with T t t = −ε|el one should have ε|el = +1/2 φ′^2, not −1/2 φ′^2.
[§3, heading text] There is a typo in 'Reissnerr–Nordström' immediately before Eq. (28); it should read 'Reissner–Nordström'.
[§4, Fig. 1] The caption could state explicitly that the strong-energy curve is p⊥ (or equivalently ε + p_r + 2p⊥) in units of the appropriate θ powers, since the reader must currently infer this from Eq. (34).

Circularity Check

2 steps flagged · score 6.0 of 10

Transparent inconsistency diagnosis; the improved stress tensor and SEC prediction are imposed by construction.

self definitional [Equations (31)-(32), after the claim that the θθ and φφ components fail]
"In order to satisfy these components, an improvement of the electromagnetic tensor is required such that the constraint on the transverse pressure p⊥|el. in (25) is imposed by hand. In terms of the scalar potential, the improved electromagnetic energy-momentum tensor is given by ... However, all the components of the Einstein equations Gμν = 8π (Tμν|matt. + T μν|el.) are now satisfied."

Equation (32) sets p⊥|el. = −ε|el. − (r/2)∂_r ε|el., which is exactly the consistency condition (25) that the paper had just shown to be violated by the Maxwell tensor. Since the metric ansatz (5) has G^r_r = G^t_t, this choice of transverse pressure makes the θθ and φφ Einstein equations algebraic consequences of the tt equation. The claim that all components are now satisfied is therefore true by construction, not an independent check. The authors explicitly concede that the constraint is imposed by hand, so this is a valid completion but not a derivation from Maxwell theory or noncommutative geometry.
fitted input called prediction [After Eq. (34), Figure 1(b), and Conclusion]
"for the type of energy-momentum tensors that we study, the strong energy condition reduces to the positivity of the transverse pressure as follows ε+pr+2p⊥ ≥ 0 ⇒ p⊥ ≥ 0, since pr = −ε. Therefore, the improved energy-momentum tensor that we propose predicts a different region where the energy condition is violated."

The new SEC-violation boundary r* = 2.95√θ is a direct algebraic consequence of the hand-imposed transverse pressure in (32). Because (32) was chosen solely to make the Einstein equations hold, the predicted violation outside the Cauchy horizon is not an independent output of noncommutative geometry; it is forced by the chosen completion. The paper even notes that alternative regularizations such as nonlinear electrodynamics could differ, confirming that the observational-signature claim is underdetermined by the physical principles, even though the underlying inconsistency diagnosis is not circular.

full rationale

The paper's central negative result — that the standard smeared Maxwell tensor (22) with potential (28) does not satisfy the θθ and φφ Einstein equations — is a direct, self-contained calculation and is not circular. The circularity lies downstream. The proposed 'improved' tensor (31)-(32) is defined by taking p⊥ = −ε − (r/2)ε′, which is precisely the consistency condition (25) that the authors had just shown to be violated by the Maxwell tensor. Consequently, verifying that all Einstein equations are satisfied is a tautology: the transverse pressure was chosen to make them hold. Likewise, the SEC boundary r* = 2.95√θ is not an independent prediction of noncommutative geometry; it is a mathematical consequence of this hand-imposed completion, as the authors concede by noting that the conformal symmetry of Maxwell theory is broken and that alternative regularizations such as nonlinear electrodynamics could be considered. There is no load-bearing self-citation; the appeal to prior work is contextual. The underdetermination of the SEC result, not the inconsistency diagnosis, is the reason for the nonzero score.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The central inconsistency check uses only the metric ansatz, Einstein equations, and the standard Maxwell stress tensor. The new SEC prediction additionally rests on a hand-imposed stress tensor. M, Q and θ are model inputs, not fitted parameters. No numerical fitting is performed.

free parameters (3)

θ (noncommutativity scale)
Input length-squared scale from the Gaussian smearing; central to all formulas but not fitted.
M (black hole mass) = 2√θ in Figure 1
Chosen for the demonstration; the critical radius r* for SEC violation depends on M.
Q (electric charge) = 5√θ in Figure 1
Chosen for the demonstration; the SEC region and horizon structure depend on Q.

assumptions (5)

domain assumption Static, spherically symmetric metric ansatz (Eq. 5): ds^2 = -f(r) dt^2 + f(r)^-1 dr^2 + r^2 dΩ^2.
Assumed from the start for all solutions discussed.
standard math Einstein equations G^μ_ν = 8π T^μ_ν with the diagonal anisotropic tensor structure (Eqs. 8-10).
Background theory of general relativity; the paper derives consequences from it.
domain assumption Gaussian smearing substitution for point sources (Eq. 4).
Imported from coherent-state results of Smailagic and Spallucci [11,12]; not derived here.
domain assumption Standard Maxwell action and stress tensor (Eqs. 18, 22) for the electromagnetic sector.
The prior solution is assumed to be Einstein-Maxwell theory; the inconsistency claim depends on this identification.
ad hoc to paper Consistency condition p⊥ = -ε - (r/2) ε' is imposed on the improved electromagnetic tensor by hand (Eqs. 31-32).
The paper states the improvement is 'based on imposing the constraints on the energy-momentum tensor by hand'; no action or derivation is provided.

invented entities (1)

Improved electromagnetic energy-momentum tensor T^μ_ν|el (Eqs. 31-32)
purpose: Make the θθ and φφ Einstein equations hold with the smeared scalar potential (28) while keeping the metric function unchanged.
The transverse pressure p⊥ is set by the consistency condition rather than by Maxwell theory; the tensor is not derived from an action and has no outside falsifiable handle.

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Pith. "Pith review of On the consistency of non-commutative geometry inspired Reissner-Nordstr\"{o}m black hole solution." pith.science (2026). https://pith.science/paper/PIDXZPME

@misc{pith2026250716780,
  author       = {Pith},
  title        = {Pith review of: On the consistency of non-commutative geometry inspired Reissner-Nordstr\"om black hole solution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PIDXZPME}},
  note         = {Machine review of arXiv:2507.16780}
}

read the original abstract

We revisit the non-commutative geometry inspired Reissner-Nordstr\"{o}m black hole solution obtained by smearing the point sources with a Gaussian distribution. We show that while the form of the metric function and the physical properties derived from that remain valid, not all the components of Einstein equations are satisfied. We construct an improved energy-momentum tensor that consistently satisfies Einstein equations and show that it leads to a different prediction for the region where the strong energy condition is violated. For certain choice of parameters, our proposal predicts the violation of the energy condition outside the Cauchy horizon, which might be important for observational signatures.

Figures

Figures reproduced from arXiv: 2507.16780 by the authors.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

24 extracted references · 12 canonical work pages

[1]

Quantized space-time,

H. S. Snyder, “Quantized space-time,”Phys. Rev.71 (1947) 38–41

work page 1947
[2]

The Electromagnetic Field in Quantized Space-Time,

H. S. Snyder, “The Electromagnetic Field in Quantized Space-Time,”Phys. Rev.72(1947) 68–71

work page 1947
[3]

ConnesInst

A. ConnesInst. Hautes Études Sci. Publ. Math. Phys.22 (1985) 257

work page 1985
[4]

S. L. WoronowiczPubl. Res. Inst. Math. Sci. Kyoto23(1987) 117

work page 1987
[5]

S. L. WoronowiczCommun. Math. Phys.111 (1987) 613

work page 1987
[6]

Connes,Noncommutative Geometry

A. Connes,Noncommutative Geometry. Academic Press, 1994

1994
[7]

Bound states of strings and p-branes,

E. Witten, “Bound states of strings and p-branes,”Nucl. Phys. B460 (1996) 335–350, arXiv:hep-th/9510135

arXiv 1996
[8]

String theory and noncommutative geometry,

N. Seiberg and E. Witten, “String theory and noncommutative geometry,”JHEP 09(1999) 032, arXiv:hep-th/9908142

arXiv 1999

Show all 24 references

[9]

On the Principles of elementary quantum mechanics,

H. J. Groenewold, “On the Principles of elementary quantum mechanics,”Physica 12 (1946) 405–460

1946
[10]

Quantum mechanics as a statistical theory,

J. E. Moyal, “Quantum mechanics as a statistical theory,”Proc. Cambridge Phil. Soc.45(1949) 99–124

1949
[11]

Feynman path integral on the noncommutative plane,

A. Smailagic and E. Spallucci, “Feynman path integral on the noncommutative plane,”J. Phys. A36 (2003) L467,arXiv:hep-th/0307217

2003 arXiv
[12]

UV divergence free QFT on noncommutative plane,

A. Smailagic and E. Spallucci, “UV divergence free QFT on noncommutative plane,”J. Phys. A36 (2003) L517–L521,arXiv:hep-th/0308193

2003 arXiv
[13]

Lorentz invariance, unitarity in UV-finite of QFT on noncommutative spacetime,

A. Smailagic and E. Spallucci, “Lorentz invariance, unitarity in UV-finite of QFT on noncommutative spacetime,”J. Phys. A37(2004) 7169,arXiv:hep-th/0406174

2004 arXiv
[14]

Noncommutative geometry inspired Schwarzschild black hole,

P. Nicolini, A. Smailagic, and E. Spallucci, “Noncommutative geometry inspired Schwarzschild black hole,”Phys. Lett. B632 (2006) 547–551,arXiv:gr-qc/0510112

2006 arXiv
[15]

Noncommutative geometry inspired charged black holes,

S. Ansoldi, P. Nicolini, A. Smailagic, and E. Spallucci, “Noncommutative geometry inspired charged black holes,”Phys. Lett. B645 (2007) 261–266,arXiv:gr-qc/0612035

2007 arXiv
[16]

Noncommutative Inspired Black Holes in Extra Dimensions,

T. G. Rizzo, “Noncommutative Inspired Black Holes in Extra Dimensions,”JHEP 09(2006) 021, arXiv:hep-ph/0606051

2006 arXiv
[17]

Non-commutative geometry inspired higher-dimensional charged black holes,

E. Spallucci, A. Smailagic, and P. Nicolini, “Non-commutative geometry inspired higher-dimensional charged black holes,”Phys. Lett. B670 (2009) 449–454,arXiv:0801.3519 [hep-th]

2009 arXiv
[18]

BTZ black holes inspired by noncommutative geometry,

F. Rahaman, P. K. F. Kuhfittig, B. C. Bhui, M. Rahaman, S. Ray, and U. F. Mondal, “BTZ black holes inspired by noncommutative geometry,”Phys. Rev. D87no. 8, (2013) 084014,arXiv:1301.4217 [gr-qc]

2013 arXiv
[19]

Noncommutative Black Holes, The Final Appeal To Quantum Gravity: A Review,

P. Nicolini, “Noncommutative Black Holes, The Final Appeal To Quantum Gravity: A Review,”Int. J. Mod. Phys. A24(2009) 1229–1308,arXiv:0807.1939 [hep-th] . 7

2009 arXiv
[20]

Noncommutative geometry inspired Einstein–Gauss–Bonnet black holes,

S. G. Ghosh, “Noncommutative geometry inspired Einstein–Gauss–Bonnet black holes,”Class. Quant. Grav. 35 no. 8, (2018) 085008,arXiv:1707.08174 [gr-qc]

2018 arXiv
[21]

Thermodynamics and evaporation of the noncommutative black hole,

Y. S. Myung, Y.-W. Kim, and Y.-J. Park, “Thermodynamics and evaporation of the noncommutative black hole,”JHEP 02(2007) 012,arXiv:gr-qc/0611130

2007 arXiv
[22]

Noncommutative Schwarzschild Black Hole and Area Law,

R. Banerjee, B. R. Majhi, and S. K. Modak, “Noncommutative Schwarzschild Black Hole and Area Law,”Class. Quant. Grav.26 (2009) 085010,arXiv:0802.2176 [hep-th]

2009 arXiv
[23]

Thermodynamic similarity between the noncommutative Schwarzschild black hole and the Reissner-Nordstrom black hole,

W. Kim, E. J. Son, and M. Yoon, “Thermodynamic similarity between the noncommutative Schwarzschild black hole and the Reissner-Nordstrom black hole,”JHEP 04(2008) 042, arXiv:0802.1757 [gr-qc]

2008 arXiv
[24]

Hawking Radiation as Quantum Tunneling from Noncommutative Schwarzschild Black Hole,

K. Nozari and S. H. Mehdipour, “Hawking Radiation as Quantum Tunneling from Noncommutative Schwarzschild Black Hole,”Class. Quant. Grav.25 (2008) 175015,arXiv:0801.4074 [gr-qc] . 8

2008 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Quantized space-time,

H. S. Snyder, “Quantized space-time,”Phys. Rev.71 (1947) 38–41

work page 1947

[2] [2]

The Electromagnetic Field in Quantized Space-Time,

H. S. Snyder, “The Electromagnetic Field in Quantized Space-Time,”Phys. Rev.72(1947) 68–71

work page 1947

[3] [3]

ConnesInst

A. ConnesInst. Hautes Études Sci. Publ. Math. Phys.22 (1985) 257

work page 1985

[4] [4]

S. L. WoronowiczPubl. Res. Inst. Math. Sci. Kyoto23(1987) 117

work page 1987

[5] [5]

S. L. WoronowiczCommun. Math. Phys.111 (1987) 613

work page 1987

[6] [6]

Connes,Noncommutative Geometry

A. Connes,Noncommutative Geometry. Academic Press, 1994

1994

[7] [7]

Bound states of strings and p-branes,

E. Witten, “Bound states of strings and p-branes,”Nucl. Phys. B460 (1996) 335–350, arXiv:hep-th/9510135

arXiv 1996

[8] [8]

String theory and noncommutative geometry,

N. Seiberg and E. Witten, “String theory and noncommutative geometry,”JHEP 09(1999) 032, arXiv:hep-th/9908142

arXiv 1999