pith. sign in

arxiv: 2605.23047 · v1 · pith:TYHPWU4Nnew · submitted 2026-05-21 · ✦ hep-th

On Thermodynamics of Charged Black Holes, Swampland, and Dark Matter

Saad Eddine Baddis , Adil Belhaj , Hajar Belmahi , Salah Eddine Ennadif This is my paper

Pith reviewed 2026-05-25 05:16 UTC · model grok-4.3

classification ✦ hep-th
keywords black hole thermodynamicsswampland conjecturesdark matterdark dimensionscalar fieldsKaluza-Kleincosmological constantcharged black holes
0
0 comments X

The pith

Treating the cosmological constant as dynamical in charged black hole thermodynamics connects swampland conjectures to the dark dimension and dark matter via scalar fields.

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

The paper proposes viewing the cosmological constant as varying in black hole systems, using the radial metric function at the horizon to define an equation of state. This setup reveals structural transitions and coexistence curves in the thermodynamics of charged black holes. An effective potential involving a quasi-static scalar field then links this to swampland conjectures from string theory. Through Kaluza-Klein interpretations of the scalar fields, the approach extends to explanations for the dark dimension and dark matter. A sympathetic reader would care because it suggests a unified thermodynamic origin for these seemingly disparate ideas in high-energy physics and cosmology.

Core claim

By dealing with the radial metric function at the horizon as an equation of state for black holes with dynamical cosmological constant, and introducing an effective potential with a quasi-static scalar field, the work establishes a connection between certain swampland conjectures and approaches the dark dimension and dark matter using Kaluza-Klein interpretations of scalar fields.

What carries the argument

The radial metric function at the horizon treated as an equation of state, combined with an effective potential for a quasi-static scalar field.

If this is right

  • Structural transitions and coexistence curves appear in the thermodynamics of charged black holes when the cosmological constant is dynamical.
  • An effective potential with a quasi-static scalar field places the thermodynamic setup in string theory and links to swampland conjectures.
  • Kaluza-Klein interpretations of the scalar fields provide a thermodynamic approach to the dark dimension and dark matter.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The thermodynamic transitions might predict observable signatures in cosmological data related to dark energy variation.
  • This framework could be tested by checking whether black hole phase diagrams match constraints from extra-dimensional models.
  • Extending the scalar field treatment to other black hole charges might reveal additional swampland connections.

Load-bearing premise

The cosmological constant can be treated as a dynamical quantity whose variation is captured by the radial metric function at the horizon serving as an equation of state.

What would settle it

A calculation demonstrating that the effective potential with the quasi-static scalar field violates the connected swampland conjectures would falsify the proposed bridge.

Figures

Figures reproduced from arXiv: 2605.23047 by Adil Belhaj, Hajar Belmahi, Saad Eddine Baddis, Salah Eddine Ennadif.

Figure 1
Figure 1. Figure 1: (ϕ − r+)-diagrams in the AdS case for different small phase sizes rs. Integrating out this equation, we get the following charge solution Q = √ 2 ℓp r 2 s e −aϕ (III.11) interpreted as a coexistence curve separating large black hole phases and small ones. Equipped with GPU accelerated CUDA computing techniques and in order to illustrate the present proposition, we consider the (ϕ − r+)-diagram playing a si… view at source ↗
read the original abstract

Inspired by the idea that the cosmological constant can be considered as a dynamical quantity, we present a scenario bridging certain swampland conjectures from a new look at thermodynamics of black holes. Dealing with the radial metric function at the horizon as an equation of state, we discuss structural transitions and coexistence curves. By considering an effective potential with a quasi-static scalar field that could find a place in string theory, we then establish a connection between certain swampland conjectures. Relying on Kaluza Klein interpretations of scalar fields, we approach the dark dimension and dark matter through such a thermodynamic approach to charged black holes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes treating the radial metric function at the horizon of charged black holes as an equation of state to model a dynamical cosmological constant, discusses structural transitions and coexistence curves in this thermodynamic framework, introduces a quasi-static scalar field in an effective potential to connect to swampland conjectures, and invokes Kaluza-Klein interpretations of the scalar to relate the setup to the dark dimension and dark matter.

Significance. If the key identifications were rigorously derived from the Einstein-scalar action and the mappings to swampland conjectures were made explicit, the work could provide a novel thermodynamic route to string-theory constraints on the dark sector. The approach of linking black-hole thermodynamics to swampland ideas is potentially interesting, but the manuscript supplies no derivations, explicit equations, or on-shell action variations to support the central claims.

major comments (3)
  1. [Abstract and thermodynamic analysis] The central construction (abstract and introduction) identifies the radial metric function evaluated at the horizon as an equation of state that encodes the variation of Lambda. For the RN-AdS metric f(r)=1-2M/r+Q²/r²-(Lambda/3)r² this identification is asserted without deriving the first law from the Einstein-scalar action; the standard extended-phase-space term V dP acquires extra contributions from scalar stress-energy and horizon-radius variation that are not shown to vanish or be absorbed.
  2. [Swampland connection paragraph] The connection between the effective potential of the quasi-static scalar field and specific swampland conjectures is stated as established (abstract) but no explicit steps, equations, or mapping from thermodynamic quantities to the conjectures are supplied, rendering the claimed bridge uncheckable.
  3. [Dark dimension and dark matter discussion] The Kaluza-Klein interpretation linking the scalar to the dark dimension and dark matter is presented without any derivation or quantitative relation between the black-hole thermodynamic quantities and the dark-sector observables.
minor comments (2)
  1. [Abstract] The abstract and introduction would benefit from explicit statements of which swampland conjectures are being connected and which equations define the effective potential.
  2. [Thermodynamic setup] Notation for the metric function and the equation-of-state identification should be introduced with an equation number rather than described only in prose.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful review and valuable comments on our manuscript. The work proposes a thermodynamic approach to connect black hole physics with swampland conjectures and the dark sector. We address each of the major comments below, providing clarifications and indicating where revisions will be made to strengthen the derivations.

read point-by-point responses

  1. Referee: [Abstract and thermodynamic analysis] The central construction (abstract and introduction) identifies the radial metric function evaluated at the horizon as an equation of state that encodes the variation of Lambda. For the RN-AdS metric f(r)=1-2M/r+Q²/r²-(Lambda/3)r² this identification is asserted without deriving the first law from the Einstein-scalar action; the standard extended-phase-space term V dP acquires extra contributions from scalar stress-energy and horizon-radius variation that are not shown to vanish or be absorbed.

    Authors: We agree that an explicit derivation of the first law from the Einstein-scalar action would strengthen the central construction. In the revised manuscript, we will include a detailed derivation in the thermodynamic analysis section. Starting from the action with the quasi-static scalar field, we will show that the contributions from the scalar stress-energy and horizon variations are either absorbed into the effective pressure term or vanish under the quasi-static approximation, justifying the identification of f(r) at the horizon as the equation of state for dynamical Lambda. revision: yes

  2. Referee: [Swampland connection paragraph] The connection between the effective potential of the quasi-static scalar field and specific swampland conjectures is stated as established (abstract) but no explicit steps, equations, or mapping from thermodynamic quantities to the conjectures are supplied, rendering the claimed bridge uncheckable.

    Authors: The connection is based on identifying the effective potential parameters with thermodynamic quantities from the black hole horizon. To make this explicit, we will add a dedicated subsection with the step-by-step mapping: relating the scalar field value to the horizon radius via the equation of state, and then applying the swampland distance conjecture to the field displacement in terms of the thermodynamic variables. This will allow readers to verify the bridge to the conjectures. revision: yes

  3. Referee: [Dark dimension and dark matter discussion] The Kaluza-Klein interpretation linking the scalar to the dark dimension and dark matter is presented without any derivation or quantitative relation between the black-hole thermodynamic quantities and the dark-sector observables.

    Authors: The KK interpretation is invoked to relate the scalar field to a modulus in the dark dimension scenario, with the thermodynamic pressure setting the scale for dark matter candidates. We acknowledge the lack of quantitative relations in the current draft. In the revision, we will provide explicit expressions linking the black hole mass and charge (from the thermodynamic analysis) to the compactification scale and dark matter mass, making the connection more quantitative while noting the phenomenological nature of the approach. revision: yes

Circularity Check

0 steps flagged

No circularity: central identification presented as modeling choice rather than derived prediction

full rationale

The manuscript introduces the treatment of the radial metric function at the horizon as an equation of state for a dynamical cosmological constant as an inspired modeling step, then uses an effective potential for a quasi-static scalar to link to swampland conjectures and Kaluza-Klein interpretations. No quoted equation or step reduces a claimed first-principles result or prediction to the input by construction (e.g., no fitted parameter renamed as output, no self-citation chain supplying the uniqueness of the identification, and no ansatz smuggled via prior author work). The derivation chain remains self-contained against external benchmarks once the initial modeling choice is granted; the provided abstract and context exhibit no self-definitional or fitted-input circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

Review performed on abstract alone; full derivations, parameter counts, and explicit assumptions are not visible. The ledger therefore records only the assumptions stated or implied in the abstract.

axioms (2)
  • domain assumption The cosmological constant can be treated as a dynamical quantity.
    Stated in the first sentence of the abstract as the starting inspiration.
  • ad hoc to paper The radial metric function at the horizon functions as an equation of state.
    Introduced without further justification in the abstract.
invented entities (1)
  • quasi-static scalar field in effective potential no independent evidence
    purpose: Bridge between black-hole thermodynamics and swampland conjectures
    Introduced in the abstract as the object that 'could find a place in string theory'.

pith-pipeline@v0.9.0 · 5637 in / 1479 out tokens · 20545 ms · 2026-05-25T05:16:28.661104+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

66 extracted references · 45 canonical work pages · 23 internal anchors

  1. [1]

    Event Horizon Telescope Collaboration.First M87 Event Horizon Telescope results. I. The shadow of the supermassive black hole, the Astrophysical Journal Letters, 875 1 L1 (2019)17

    2019

  2. [2]

    Event Horizon Telescope Collaboration.First Sagittarius A Event Horizon Telescope results. I. The shadow of the supermassive black hole in the center of the Milky Way the Astrophysical Journal Letters, 930 2 L12 (2022)21

    2022

  3. [3]

    First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole

    K. Akiyama and al.,First M87 Event Horizon Telescope Results. IV. Imaging the Cen- tral Supermassive Black Hole, Astrophys. J. 875 L4 (2019),arXiv:1906.11241

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  4. [4]

    Akiyama and al.,First M87 Event Horizon Telescope Results

    K. Akiyama and al.,First M87 Event Horizon Telescope Results. VI. Imaging the Cen- tral Supermassive Black Hole, Astrophys. J. 875 L6 (2019)

    2019

  5. [5]

    S. W. Hawking and D. N. Page,Thermodynamics of black holes in anti- de Sitter space, Communications in Mathematical Physics, 87 (1983)577

    1983

  6. [7]

    On Thermodynamics of AdS Black Holes in Arbitrary Dimensions

    A. Belhaj, M. Chabab, H. El Moumni and M. B. Sedra,On Thermodynamics of AdS Black Holes in Arbitrary Dimensions, Chin. Phys. Lett. 29 (2012) 100401, arXiv:1210.4617 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  7. [8]

    Chamblin, R

    A. Chamblin, R. Emparan, C. Johnson C and R. Myers,Holography, Thermodynamics and Fluctuations of Charged AdS Black Holes, Phys. Rev. D 60 (1999) 104026

    1999

  8. [9]

    Cvetic M, G

    M. Cvetic M, G. W. Gibbons, D. Kubiznak and C. N. Pope,Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume, Phys. Rev. D 84 (2011) 024037

    2011

  9. [10]

    Dolan,Compressibility of rotating black holes, Phys

    B.P. Dolan,Compressibility of rotating black holes, Phys. Rev. D 84 (2011) 127503

    2011

  10. [11]

    J. L. Zhang, R. G. Cai and H. Yu,Phase transition and thermodynamical geome- try for Schwarzschild AdS black hole in AdS5 x S5 spacetime, JHEP 1502 (2015)143, [arXiv:1409.5305 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  11. [12]

    Belhaj, M

    A. Belhaj, M. Chabab, H. El Moumni, K. Masmar, M. Sedra,On Thermodynamics of AdS Black Holes in M-Theory, Eur. Phys. J. C76(2)(2016)73

    2016

  12. [13]

    The String Landscape and the Swampland

    C. Vafa,The String Landscape and the Swampland, arXiv:hep-th/0509212

    work page internal anchor Pith review Pith/arXiv arXiv

  13. [14]

    N. B. Agmon, A. Bedroya, M. J. Kang, C. Vafa,Lectures on the string landscape and the Swampland, arXiv:2212.06187

    work page arXiv

  14. [15]

    Palti, C

    E. Palti, C. Vafa, Timo Weigand,Supersymmetric Protection and the Swampland, arXiv:2003.10452

    work page arXiv 2003

  15. [17]

    D. Lust, E. Palti and C. Vafa, AdS and the Swampland, Phys. Lett. B 797 (2019) 134867, arXiv:1906.05225

    work page arXiv 2019

  16. [18]

    M. V. Beest, J. C. Infante, D. Mirfendereski, I. Valenzuela,Lectures on the Swampland Program in String Compacti cations, arXiv:2102.01111

    work page arXiv

  17. [19]

    Montero, C

    M. Montero, C. Vafa, I. Valenzuela,The Dark Dimension and the Swampland, J. High Energ. Phys. 02, 22(2023)

    2023

  18. [20]

    J. A. P. Law-Smith, G. Obied, A. Prabhu, C. Vafa,Astrophysical Constraints on De- caying Dark Gravitons, arXiv:2307.11048[hep-ph]

    work page arXiv

  19. [21]

    Anchordoqui, I

    L. Anchordoqui, I. Antoniadis, D. Lust,The Dark Dimension, the Swampland, and the Dark Matter Fraction Composed of Primordial Black Holes, Phys. Rev. D, 1061(2022)086001, arXiv:2206.07071[hep-th]. 11

    work page arXiv 2022

  20. [22]

    V. K. Oikonomou, Konstantinos-Rafail Revis, Ilias C. Papadimitriou, Maria-Myrto Pe- gioudi,Swampland Criteria and Constraints on Inflation in a f(R,T) Gravity Theory, Int. J. Mod. Phys. D3,(2023) 2350034

    2023

  21. [23]

    V. K. Oikonomou, I. Giannakoudi, A. Gitsis, K-R Revis,Rescaled Einstein-Hilbert Grav- ity: Inflation and the Swampland Criteria, Int.J.Mod.Phys.D 31, 02 (2022)2250001, arXiv:2105.11935

    work page arXiv 2022

  22. [24]

    V. K. Oikonomou,Rescaled Einstein-Hilbert Gravity from f(R) Gravity: Inflation, Dark Energy and the Swampland Criteria, Phys. Rev. D 103, 124028(2021), arXiv:2012.01312

    work page arXiv 2021

  23. [25]

    S. E. Baddis, A. Belhaj,Hypergeometric Potential Inflation and Swampland Pro- gram in Rescaled Gravity with Stringy Corrections, Eur.Phys.J.Plus 139 (2024) 7, 612, arXiv:2407.06070

    work page arXiv 2024

  24. [26]

    S. E. Baddis, A. Belhaj,Swampland Program for Hypergeometric Inflation Scenarios in Rescaled Gravity, Mod.Phys.Lett.A 39 (2024) 21n22, 2450096, arXiv:2407.00785

    work page arXiv 2024

  25. [27]

    N. A. Hamed, L. Motl, A. Nicolis, C. Vafa,The String landscape, black holes and gravity as the weakest force, JHEP 06(2007)060, arXiv:hep-th/0601001

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  26. [28]

    A Tower Weak Gravity Conjecture from Infrared Consistency

    S. Andriolo, D. Junghans, T. Noumi, G. Shiu,A Tower Weak Gravity Conjecture from Infrared Consistency, Fortsch. Phys. 66(2018)1800020, arXiv:1802.04287

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  27. [29]

    Hamada, T

    Y. Hamada, T. Noumi, G. Shiu,Weak Gravity Conjecture from Unitarity and Causality, Phys. Rev. Lett. 123(2019)051601, arXiv:1810.03637

    work page arXiv 2019

  28. [30]

    Quantum Gravity Constraints from Unitarity and Analyticity

    B. Bellazzini, C. Cheung, G. N. Remmen,Quantum Gravity Constraints from Unitarity and Analyticity, Phys. Rev. D93(2016)6, arXiv:1509.00851

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  29. [31]

    Causality, Analyticity and an IR Obstruction to UV Completion

    A. Adams, N. A. Hamed, S. Dubovsky, A. Nicolis, R. Rattazzi,Causality, analyticity and an IR obstruction to UV completion, JHEP 10(2006)014, arXiv:hep-th/0602178

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  30. [32]

    Bellazzini, M

    B. Bellazzini, M. Lewandowski, J. Serra,Positivity of Amplitudes, Weak Gravity Con- jecture, and Modified Gravity, Phys. Rev. Lett. 123(2019)251103, arXiv:1902.03250

    work page arXiv 2019

  31. [33]

    N. A. Hamed, Y. Huang, J. Liu, G. N. Remmen,Causality, unitarity, and the weak gravity conjecture, JHEP 03(2022)083, arXiv:2109.13937

    work page arXiv 2022

  32. [34]

    Proof of the Weak Gravity Conjecture from Black Hole Entropy

    C. Cheung, J. Liu, G. N. Remmen,Proof of the Weak Gravity Conjecture from Black Hole Entropy, JHEP 10(2018)004, arXiv:1801.08546

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  33. [35]

    P. T. W. Grimm, I. Valenzuela,The Swampland Distance Conjecture for Kahler moduli, JHEP 08(2019)075, arXiv:1812.07584

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  34. [36]

    T. W. Grimm, E. Palti, I. Valenzuela,Infinite Distances in Field Space and Massless Towers of States,JHEP 08(2018)143, arXiv:1802.08264. 12

    work page arXiv 2018

  35. [38]

    On the Geometry of the String Landscape and the Swampland

    H. Ooguri and C. Vafa,On the Geometry of the String Landscape and the Swampland, Nucl. Phys. B766(2007)21, arXiv:hep-th/0605264

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  36. [39]

    Etheredge, B

    M. Etheredge, B. Heidenreich, S. Kaya, Y. Qiu, T. Rudelius,Sharpening the Distance Conjecture in Diverse Dimensions,JHEP 12(2022)114, arXiv:2206.04063

    work page arXiv 2022

  37. [40]

    S. J. Lee, W. Lerche, T. Weigand,Emergent strings from infinite distance limits,JHEP 02(2022)190, arXiv:1910.01135

    work page arXiv 2022

  38. [41]

    Bedroya and C

    A. Bedroya, C. Vafa,Trans-Planckian Censorship and the Swampland,JHEP 09(2020)123, arXiv:1909.11063

    work page arXiv 2020

  39. [42]

    Andriot, N

    D. Andriot, N. Cribiori, and D. Erkinger,The web of swampland conjectures and the TCC bound, JHEP 07(2020)162, arXiv:2004.00030

    work page arXiv 2020

  40. [43]

    Bedroya,Holographic origin of TCC and the Distance Conjecture, JHEP 06(2024)016, arXiv:2211.09128

    A. Bedroya,Holographic origin of TCC and the Distance Conjecture, JHEP 06(2024)016, arXiv:2211.09128

    work page arXiv 2024

  41. [44]

    Sola,Cosmologies with a time dependent vacuum, J

    J. Sola,Cosmologies with a time dependent vacuum, J. Phys.: Conf. Ser. 283 (2011) 012033

    2011

  42. [45]

    M. B. Green, J. H. Schwarz, E. Witten,Superstring Theory(Vol. 1 & 2) Cambridge University Press (1987)

    1987

  43. [46]

    Polchinski,String Theory, Vol

    J. Polchinski,String Theory, Vol. 2: Superstring Theory and Beyond(Cambridge, 1998)

    1998

  44. [47]

    Klein,Quantum Theory and Five-Dimensional Theory of Relativity, Zeitschrift f¨ ur Physik 37, (1926) 895–906

    O. Klein,Quantum Theory and Five-Dimensional Theory of Relativity, Zeitschrift f¨ ur Physik 37, (1926) 895–906

    1926

  45. [48]

    Edmund, M

    J. Edmund, M. Copeland, M. Sami, S. Tsujikawa,Dynamics of Dark Energy, Interna- tional Journal of Modern Physics D 15, 1753–1935 (2006)

    1935

  46. [49]

    The Dark Matter Halo of the Milky Way, AD 2013

    F. Nesti and P. Salucci,The Dark Matter halo of the Milky Way, AD 2013, Journal of Cosmology and Astroparticle Physics 07 (2013) 016, arXiv:1304.5127 [astro-ph.GA]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  47. [50]

    Symmetries and Strings in Field Theory and Gravity

    T. Banks and N. Seiberg,Symmetries and Strings in Field Theory and Gravity, Phys. Rev. D 084019 (2011) 83, arXiv:1011.5120 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  48. [51]

    Heidenreich1, J

    B. Heidenreich1, J. McNamara, M. Montero, M. Reece, T. Rudelius, and I. Valenzuela, Non-invertible global symmetries and completeness of the spectrum, JHEP 09 (2021) 203, arXiv:2104.07036 [hep-th]

    work page arXiv 2021

  49. [52]

    P-V criticality of charged AdS black holes

    D. Kubiznak, R. B. Mann,P-V criticality of charged AdS black holes, JHEP 1207(2012)033, arXiv:1205.0559. 13

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  50. [53]

    Clapeyron equations and fitting formula of the coexistence curve in the extended phase space of charged AdS black holes

    S. Wei and Y. Liu,Clapeyron equations and fitting formula of the coexistence curve in the extended phase space of charged AdS black holes, Phys.Rev.D 91 (2015) 4, arXiv:1411.5749 [hep-th]. [54]CUDA C++ Programming Guide, Nvidia

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  51. [54]

    Elafrou, G

    A. Elafrou, G. Thomas Collignon,Introduction to CUDA Performance Optimization, Nvidia

  52. [55]

    W. W. Hwu, D. B. Kirk, I. El Hajj,Programming Massively Parallel Processors, 4th Edition May 28, 2022

    2022

  53. [56]

    Rennich,CUDA C/C++ Streams and Concurrency, Nvidia

    S. Rennich,CUDA C/C++ Streams and Concurrency, Nvidia

  54. [57]

    G. D. QuirogaMALBEC: a new CUDA-C ray-tracer in General Relativity, Gen.Rel.Grav. 50 (2018) 6, 75, arXiv:1803.08320

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  55. [58]

    A. G. M. Lewis, H. P. Pfeiffer1,4GPU-Accelerated Simulations of Isolated Black Holes, Class.Quant.Grav. 35, 9(2018) 095017, arXiv:1804.09101

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  56. [59]

    A. Y. Chen, M. Luepker, Y. YuanIntroducing APERTURE: A GPU-based General Relativistic Particle-in-Cell Simulation Framework, arXiv:2503.04558

    work page arXiv

  57. [60]

    D. J. Gross, M. J. Perry, L. G. Yaffe,Instability of flat space at finite temperature, Phys. Rev. D25 (1982)330

    1982

  58. [61]

    J. I. Kapusta,Nucleation rate for black holes, Phys. Rev. D30(1984)831

    1984

  59. [62]

    Black Hole Remnants and the Information Loss Paradox

    P. Chen, Y.Chin Ong, D.han Yeom,Black Hole Remnants and the Information Loss Paradox, Phys. Rept. 603(2015)1, arXiv:1412.8366

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  60. [63]

    Trouble For Remnants

    L. Susskind,Trouble For Remnants, arXiv:hep-th/9501106

    work page internal anchor Pith review Pith/arXiv arXiv

  61. [64]

    S. B. GiddingsConstraints on Black Hole RemnantsPhys.Rev.D49 (1994) 947

    1994

  62. [65]

    Generalized Global Symmetries

    D. Gaiottoa, A. Kapustinb1, N. Seibergc, and B. Willett,Generalized Global Symme- tries,JHEP 02 (2015) 172, arXiv:1412.5148 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  63. [66]

    Aharony, N

    O. Aharony, N. Seiberg and Y. Tachikawa,Reading between the lines of four- dimensional gauge theories,, JHEP 08 (2013) 115, arXiv:1305.0318 [hep-th]

    work page arXiv 2013

  64. [67]

    Coupling a QFT to a TQFT and Duality

    A. Kapustina and N. Seiberg,Coupling a QFT to a TQFT and Duality, JHEP 04 (2014) 001, arXiv:1401.0740 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  65. [68]

    Rigid Surface Operators

    S. Gukova and E. Witten,Rigid Surface Operators,Adv.Theor.Math.Phys. 14 (2010) 1, arXiv: 0804.1561 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  66. [69]

    On the local dark matter density

    J. Bovy and S. Tremaine,On the local dark matter density, The Astrophysical Journal 756 (2012) 89, arXiv:1205.4033 [astro-ph.GA]. 14

    work page internal anchor Pith review Pith/arXiv arXiv 2012