pith. sign in

arxiv: 2606.27992 · v1 · pith:YC4BNNXNnew · submitted 2026-06-26 · 🌀 gr-qc · hep-ph· hep-th

Probing Two Dark Dimensions through Primordial Black Holes, Gravitational Waves, and Colliders

Waqas Ahmed , George K. Leontaris This is my paper

Pith reviewed 2026-06-29 03:36 UTC · model grok-4.3

classification 🌀 gr-qc hep-phhep-th
keywords primordial black holesdark matterextra dimensionsgravitational wavesmemory-burden effectbrane-worldcollidersstochastic background
0
0 comments X

The pith

In the two-dark-dimensions framework the memory-burden effect with p=2 suppresses evaporation enough for primordial black holes as light as 10^{-3} g to survive to the present and comprise all dark matter.

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

The paper examines primordial black holes as dark matter candidates inside a six-dimensional brane-world model that has two compact extra dimensions and a fundamental gravity scale near 10 TeV. It incorporates the recently proposed memory-burden effect and shows that an exponent p=2 reduces the evaporation rate so strongly that black holes with initial masses around 10^{-3} g remain intact today. This opens a wide mass window from 10^{-3} g to 10^{21} g in which such objects can account for the observed dark matter density. The same curvature perturbations that form the black holes also generate a stochastic gravitational-wave background whose calculation remains valid in the standard four-dimensional formalism across the relevant range. The low gravity scale further allows microscopic black holes to be produced at future colliders, supplying an independent probe.

Core claim

In the two-dark-dimensions scenario, applying the memory-burden effect with p=2 to higher-dimensional primordial black holes strongly suppresses their evaporation, permitting initial masses as small as ∼10^{-3} g to survive to the present epoch and thereby account for the observed dark matter over the mass range 10^{-3} g to 10^{21} g. The stochastic gravitational-wave background induced by the required curvature perturbations can be computed with the conventional four-dimensional formalism and lies within reach of LISA, DECIGO and pulsar timing arrays, while the TeV-scale gravity also allows microscopic black hole production at colliders.

What carries the argument

The memory-burden effect with exponent p=2, which modifies the evaporation rate of higher-dimensional black holes in the two-dark-dimensions brane-world model.

If this is right

  • PBHs with initial masses from 10^{-3} g to 10^{21} g can constitute the entire dark matter density.
  • The scalar-induced gravitational wave background from PBH formation is accessible to LISA, DECIGO, and pulsar timing arrays.
  • Fisher forecasts indicate that gravitational-wave data can tightly constrain PBH mass, dark-matter fraction, and the width of the primordial curvature spectrum.
  • Microscopic black holes can be produced at future high-energy colliders owing to the low fundamental gravity scale.

Where Pith is reading between the lines

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

  • Similar evaporation suppression could operate in other extra-dimension models and thereby enlarge the viable PBH mass window beyond the specific two-dark-dimensions case.
  • Independent astrophysical searches for long-lived small black holes could test the memory-burden mechanism without relying on early-universe cosmology.
  • Joint analysis of collider events and gravitational-wave spectra might distinguish different values of the memory exponent p.

Load-bearing premise

The quantum-gravitational memory-burden effect with memory exponent p=2 holds for primordial black holes evolving in the two-dark-dimensions framework.

What would settle it

An observation that black holes with initial mass near 10^{-3} g have fully evaporated by the present epoch, or a null result for the predicted scalar-induced gravitational-wave background in the LISA frequency band under the assumption that these black holes make up the dark matter.

Figures

Figures reproduced from arXiv: 2606.27992 by George K. Leontaris, Waqas Ahmed.

Figure 1
Figure 1. Figure 1: FIG. 1: Lifetime of primordial black holes as a function of the initial PBH mass in four and six dimensions. The [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Illustration of the charged Nariai limit in six-dimensional Reissner–Nordstr¨om–de Sitter geometry. Left: [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Regimes of validity for scalar-induced gravitational waves in the six-dimensional two-dark-dimensions [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Scalar-induced gravitational-wave spectra associated with primordial black holes in the six-dimensional [PITH_FULL_IMAGE:figures/full_fig_p021_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Corner plots for the Fisher forecasts of LISA, DECIGO, and BBO using the zero-mode benchmark SIGW [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Benchmark production cross sections for microscopic six-dimensional black holes. The left panel shows the [PITH_FULL_IMAGE:figures/full_fig_p024_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Hawking temperature and estimated primary multiplicity of a six-dimensional microscopic black hole. The [PITH_FULL_IMAGE:figures/full_fig_p026_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Illustrative missing-transverse-momentum templates for bulk graviton emission from a six-dimensional [PITH_FULL_IMAGE:figures/full_fig_p027_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Theoretical logarithmic Hawking temperature–mass relation for different numbers of extra dimensions. Its [PITH_FULL_IMAGE:figures/full_fig_p028_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Schematic dependence of the monojet plus missing-momentum rate on the fundamental gravity scale in the [PITH_FULL_IMAGE:figures/full_fig_p029_10.png] view at source ↗
read the original abstract

We study primordial-black-hole (PBH) dark matter in the two-dark-dimensions (2DD) framework, a six-dimensional brane-world scenario with two compact extra dimensions and a fundamental gravity scale of order $10\,\mathrm{TeV}$. We calculate the evolution of higher-dimensional PBHs including the recently proposed quantum-gravitational memory-burden effect. For a memory exponent $p=2$, the evaporation rate is strongly suppressed, allowing PBHs with initial masses as small as $\sim10^{-3}\,\mathrm{g}$ to survive until the present epoch. Consequently, PBHs can account for the observed dark matter over a mass range extending from $10^{-3}\,\mathrm{g}$ to $10^{21}\,\mathrm{g}$. We further compute the stochastic gravitational-wave background generated at second order by the primordial curvature perturbations responsible for PBH formation. We show that the conventional four-dimensional formalism for scalar-induced gravitational waves remains applicable throughout the mass range accessible to current and future gravitational wave experiments. The resulting signals can be probed by LISA, DECIGO, and pulsar timing arrays. Using Fisher forecasts, we find that these observations can constrain the PBH mass, dark-matter fraction, and width of the primordial curvature spectrum with high precision. The low fundamental gravity scale of the 2DD framework also permits the production of microscopic black holes at future high-energy colliders. Their decay signatures, together with gravitational-wave measurements, provide complementary tests of higher-dimensional gravity, the memory-burden mechanism, and primordial-black-hole dark matter.

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

2 major / 1 minor

Summary. The manuscript claims that in the two-dark-dimensions (2DD) framework—a six-dimensional brane-world model with two compact extra dimensions and a fundamental gravity scale of order 10 TeV—incorporation of the memory-burden effect with exponent p=2 strongly suppresses primordial black hole (PBH) evaporation. This allows PBHs with initial masses as small as ∼10^{-3} g to survive to the present epoch and account for all dark matter over the range 10^{-3} g to 10^{21} g. The paper further states that the standard four-dimensional formalism for scalar-induced gravitational waves remains valid across the relevant mass window, computes the resulting stochastic background, and uses Fisher forecasts to show that LISA, DECIGO, and pulsar timing arrays can tightly constrain PBH mass, dark-matter fraction, and the width of the primordial curvature spectrum. Collider production of microscopic black holes is noted as a complementary probe.

Significance. If the central assumptions on the memory-burden effect and the applicability of the four-dimensional gravitational-wave formalism hold after explicit derivation, the work would link higher-dimensional gravity, quantum-gravitational evaporation suppression, and multi-messenger observations in a single framework. The quantitative Fisher forecasts for gravitational-wave constraints on PBH parameters constitute a concrete strength that enables direct comparison with future data.

major comments (2)
  1. [Abstract and PBH evolution section] Abstract and the section on PBH evolution: the claim that the evaporation rate is strongly suppressed for p=2, allowing initial masses ∼10^{-3} g to survive until today, is asserted without a derivation of the modified evaporation law that incorporates the six-dimensional metric, bulk effects, or the ∼10 TeV fundamental scale; this step is load-bearing for the entire dark-matter mass-range conclusion.
  2. [Gravitational waves section] Section on gravitational waves: the statement that the conventional four-dimensional formalism for scalar-induced gravitational waves remains applicable is presented without an explicit check or equation demonstrating that curvature-perturbation sourcing and tensor propagation receive no corrections from the extra dimensions at the wavenumbers corresponding to the quoted PBH mass window.
minor comments (1)
  1. [Abstract] The abstract would benefit from a short statement of the numerical value adopted for the fundamental scale and the motivation for fixing the memory exponent at p=2 rather than treating it as a free parameter.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract and PBH evolution section] Abstract and the section on PBH evolution: the claim that the evaporation rate is strongly suppressed for p=2, allowing initial masses ∼10^{-3} g to survive until today, is asserted without a derivation of the modified evaporation law that incorporates the six-dimensional metric, bulk effects, or the ∼10 TeV fundamental scale; this step is load-bearing for the entire dark-matter mass-range conclusion.

    Authors: We agree that an explicit derivation of the modified evaporation law is required. In the revised manuscript we will add a dedicated subsection deriving the memory-burden-suppressed evaporation rate from the six-dimensional brane-world metric, incorporating bulk graviton emission and the ∼10 TeV fundamental scale for p=2. This derivation will directly support the survival of PBHs with initial masses down to ∼10^{-3} g and the resulting dark-matter mass window. revision: yes

  2. Referee: [Gravitational waves section] Section on gravitational waves: the statement that the conventional four-dimensional formalism for scalar-induced gravitational waves remains applicable is presented without an explicit check or equation demonstrating that curvature-perturbation sourcing and tensor propagation receive no corrections from the extra dimensions at the wavenumbers corresponding to the quoted PBH mass window.

    Authors: We acknowledge that an explicit verification is needed. The revised version will include a new subsection (or appendix) that supplies the required check: we will derive the conditions under which the six-dimensional corrections to curvature-perturbation sourcing and tensor-mode propagation remain negligible at the wavenumbers set by the PBH mass window, confirming the validity of the four-dimensional scalar-induced gravitational-wave formalism throughout the relevant range. revision: yes

Circularity Check

0 steps flagged

No circularity; central results rest on external input assumptions

full rationale

The paper presents the memory-burden exponent p=2 as an input taken from recent external proposals and applies it to calculate PBH evolution in the 2DD framework. The resulting mass range for dark matter follows directly from this suppression combined with higher-dimensional evaporation formulas. The assertion that 4D scalar-induced GW formalism remains applicable is stated as a check without reducing to a self-derived quantity. No quoted step shows a prediction equivalent to a fitted parameter by construction, a self-citation load-bearing the central claim, or any of the enumerated circular patterns. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim depends on the memory-burden effect (p=2) and the validity of four-dimensional gravitational-wave methods in the higher-dimensional setting; the fundamental scale of order 10 TeV is an input from the 2DD framework.

free parameters (2)
  • memory exponent p = 2
    Set to 2 to produce strong suppression of evaporation allowing survival of 10^{-3} g black holes; chosen rather than derived.
  • fundamental gravity scale = 10 TeV
    Order-of-magnitude input for the two-dark-dimensions model that enables collider production.
axioms (2)
  • domain assumption The conventional four-dimensional formalism for scalar-induced gravitational waves remains applicable throughout the mass range accessible to current and future gravitational wave experiments.
    Invoked without derivation to justify the stochastic gravitational-wave background calculation.
  • domain assumption The quantum-gravitational memory-burden effect with exponent p=2 applies to higher-dimensional primordial black holes in the two-dark-dimensions framework.
    Central to the survival of small-mass black holes; referenced as recently proposed but not re-derived.

pith-pipeline@v0.9.1-grok · 5818 in / 1618 out tokens · 55575 ms · 2026-06-29T03:36:15.004865+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

92 extracted references · 5 linked inside Pith

  1. [1]

    The Nariai limit corresponds to the degeneracy of the black-hole and cosmological horizons [63, 64]

    The Nariai limit inddimensions Consider thed-dimensional Reissner–Nordstr¨ om–de Sitter (RNdS) geometry [62, 63], ds2 =−U(r)dt 2 + dr2 U(r) +r 2dΩ2 d−2,(63) with U(r) = 1− µ rd−3 + Q2 d r2d−6 − r2 ℓ2 ,(64) where µ≡ 2M M d−2 P , Q 2 d ≡ g2q2 4πM d−2 P .(65) HereMis the black-hole mass,qis the charge quantum number,gis the gauge coupling,M P is thed-dimensi...

  2. [2]

    With the same normalization used in Eq

    Electric field on the Nariai horizon The discharge of a charged near-Nariai black hole proceeds through Schwinger pair production in the background electric field [60, 65, 66]. With the same normalization used in Eq. (64), we define Q2 d ≡ g2q2 4πM d−2 P ,(79) so that the electric field may be written as E(r) = Qd 2√π rd−2 .(80) At the Nariai horizon, EN ...

  3. [3]

    (88) Thus, avoiding rapid Schwinger discharge of charged Nariai black holes requires parametricallym 2 ≳e physEN /π, up to order-one corrections

    Schwinger pair production and the Festina–Lente bound In a locally constant electric fieldE, the Schwinger pair-production rate for a particle of massmand physical chargee phys has the schematic form [65] ΓSchw ∼ (ephysE)d/2 (2π)d−1 exp − πm2 ephysE ,(87) up to spin-dependent, curvature-dependent, and geometry-dependent prefactors, the Schwinger exponent ...

  4. [4]

    6: Benchmark production cross sections for microscopic six-dimensional black holes

    Proton–proton production rate The proton–proton cross section is obtained by convoluting the partonic result with the parton luminosities, σpp→BH(s) = X i,j Z 1 τmin dτ dLij dτ ˆσij→BH(τ s),(141) where τmin = M2 min s , dLij dτ = Z 1 τ dx x fi(x, Q)fj τ x , Q ,(142) 24 25 50 75 100 125 150 175 200 √ ˆs (TeV) 102 ˆσBH (pb) Mmin = 5M ∗ ˆσBH ≃ πr2 h rh = kn ...

  5. [5]

    The black hole therefore resolves the higher-dimensional bulk, and bulk graviton emission is not kinematically suppressed by the small KK mass gap

    Bulk emission and missing transverse momentum The compactification scale is much larger than the microscopic horizon,r h ≪R, while the Hawking temperature is much greater than the KK mass spacing. The black hole therefore resolves the higher-dimensional bulk, and bulk graviton emission is not kinematically suppressed by the small KK mass gap. The power em...

  6. [6]

    Their relative emission rates are determined by the corresponding couplings and polarization-dependent greybody factors

    Illustrative polarization dependence of bulk emission From a four-dimensional viewpoint, a massive KK spin-2 excitation contains helicity-±2, helicity-±1, and helicity-0 components. Their relative emission rates are determined by the corresponding couplings and polarization-dependent greybody factors. In principle, their different angular distributions ca...

  7. [7]

    Sensitivity to the number of extra dimensions Fornextra dimensions, the temperature–mass relation has the logarithmic slope dlogT BH dlogM BH =− 1 n+ 1 .(152) A slope near−1/3 would therefore be consistent with two extra dimensions. In practice, the reconstructed mass is affected by invisible energy, while the inferred temperature is distorted by greybody...

  8. [8]

    KK decomposition of the tensor perturbation We consider a six-dimensional spacetime compactified on a square two-torus, M4 ×T 2,(A1) with compactification length L≡2πR.(A2) 31 The tensor perturbation of the higher-dimensional metric can be decomposed into eigenmodes of the compact space. Schematically, hij(x, y) =h (0) ij (x) + X ⃗ n̸=0 h(⃗ n) ij (x)Y ⃗ n...

  9. [9]

    Energy density of a massive tensor mode The energy density carried by a tensor perturbation follows from the quadratic action. For a massive KK tensor mode, the kinetic, gradient, and mass terms give schematically ρ(⃗ n) GW ≃ M2 Pl 8a2 X λ h hλ′ ⃗ n 2 + k2 +a 2m2 ⃗ n hλ ⃗ n 2i .(A17) For an oscillating mode, one may average over several oscillations. The ...

  10. [10]

    The functionI ⃗ nis the massive Green- function kernel and differs from the standard massless kernelI 0

    F ull six-dimensional spectrum The full six-dimensional gravitational-wave spectrum is obtained by summing over the massless zero mode and all massive KK modes: Ω6d GW(k, η) = Ω(0) GW(k, η) + X ⃗ n̸=0 Ω(⃗ n) GW(k, η).(A26) The zero-mode contribution is the standard four-dimensional scalar-induced gravitational-wave spectrum: Ω(0) GW,0(k) = Ω(4d) GW,0(k).(...

  11. [11]

    Nima Arkani-Hamed, Savas Dimopoulos, and G. R. Dvali. The Hierarchy problem and new dimensions at a millimeter. Phys. Lett. B, 429:263–272, 1998

    1998

  12. [12]

    Ignatios Antoniadis, Nima Arkani-Hamed, Savas Dimopoulos, and G. R. Dvali. New dimensions at a millimeter to a Fermi and superstrings at a TeV.Phys. Lett. B, 436:257–263, 1998

    1998

  13. [13]

    Nima Arkani-Hamed, Savas Dimopoulos, and G. R. Dvali. Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity.Phys. Rev. D, 59:086004, 1999

    1999

  14. [14]

    The string landscape and the swampland

    Cumrun Vafa. The string landscape and the swampland. 2005. arXiv:hep-th/0509212

    Pith/arXiv arXiv 2005

  15. [15]

    On the Geometry of the String Landscape and the Swampland.Nucl

    Hirosi Ooguri and Cumrun Vafa. On the Geometry of the String Landscape and the Swampland.Nucl. Phys. B, 766:21–33, 2007

    2007

  16. [16]

    The Swampland: Introduction and Review.Fortsch

    Eran Palti. The Swampland: Introduction and Review.Fortsch. Phys., 67(6):1900037, 2019

    2019

  17. [17]

    Lectures on the Swampland Program in String Compactifications.Phys

    Marieke van Beest, Jos´ e Calder´ on-Infante, Delaram Mirfendereski, and Irene Valenzuela. Lectures on the Swampland Program in String Compactifications.Phys. Rept., 989:1–50, 2022

    2022

  18. [18]

    Lectures on the String Landscape and the Swampland

    Nathan Benjamin Agmon, Alek Bedroya, Monica Jinwoo Kang, and Cumrun Vafa. Lectures on the String Landscape and the Swampland. , 12 2022. arXiv:2212.06187 [hep-th]

    arXiv 2022

  19. [19]

    Anchordoqui and Dieter Lust

    Luis A. Anchordoqui and Dieter Lust. Breaking Free from the Swampland of Impossible Universes through the DESI Portal. , 5 2026. arXiv:2605.10476 [astro-ph.CO]

    Pith/arXiv arXiv 2026

  20. [20]

    The dark dimension and the Swampland.JHEP, 02:022, 2023

    Miguel Montero, Cumrun Vafa, and Irene Valenzuela. The dark dimension and the Swampland.JHEP, 02:022, 2023

    2023

  21. [21]

    Anchordoqui, Ignatios Antoniadis, and Dieter Lust

    Luis A. Anchordoqui, Ignatios Antoniadis, and Dieter Lust. Dark dimension, the swampland, and the dark matter fraction composed of primordial near-extremal black holes.Phys. Rev. D, 109(9):095008, 2024

    2024

  22. [22]

    Leontaris and George Prampromis

    George K. Leontaris and George Prampromis. 5D rotating black holes as dark matter in dark dimension scenario: Hawking radiation versus the memory burden effect.JCAP, 05:014, 2026. 34

    2026

  23. [23]

    Leontaris

    Waqas Ahmed and George K. Leontaris. Secondary Gravitational Wave Signatures from 5D Rotating Primordial Black Holes in the Dark Dimension. 5 2026. arXiv:2605.12948 [hep-ph]

    Pith/arXiv arXiv 2026

  24. [24]

    Anchordoqui, Ignatios Antoniadis, and Dieter Lust

    Luis A. Anchordoqui, Ignatios Antoniadis, and Dieter Lust. Two Micron-Size Dark Dimensions.Fortsch. Phys., 73(8):e70015, 2025

    2025

  25. [25]

    Leontaris and George Prampromis

    George K. Leontaris and George Prampromis. Micron-sized Extra Dimensions and Primordial Black Holes: Charged, Rotating, and Memory Burdened. 4 2026. arXiv:2605.00252 [hep-ph]

    Pith/arXiv arXiv 2026

  26. [26]

    Benedikt et al

    M. Benedikt et al. Future Circular Collider Feasibility Study Report: Volume 1, Physics, Experiments, Detectors.Eur. Phys. J. C, 85(12):1468, 2025

    2025

  27. [27]

    Abada et al

    A. Abada et al. FCC-hh: The Hadron Collider: Future Circular Collider Conceptual Design Report Volume 3.Eur. Phys. J. ST, 228(4):755–1107, 2019

    2019

  28. [28]

    Benedikt et al

    M. Benedikt et al. Future Circular Hadron Collider FCC-hh: Overview and Status. 3 2022. arXiv:2203.07804 [physics.acc- ph]

    arXiv 2022

  29. [29]

    King, Alexander Merle, Stefano Morisi, Yusuke Shimizu, and Morimitsu Tanimoto

    Stephen F. King, Alexander Merle, Stefano Morisi, Yusuke Shimizu, and Morimitsu Tanimoto. Neutrino Mass and Mixing: from Theory to Experiment.New J. Phys., 16:045018, 2014

    2014

  30. [30]

    Carr and S

    Bernard J. Carr and S. W. Hawking. Black holes in the early Universe.Mon. Not. Roy. Astron. Soc., 168:399–415, 1974

    1974

  31. [31]

    Gravitationally collapsed objects of very low mass.Mon

    Stephen Hawking. Gravitationally collapsed objects of very low mass.Mon. Not. Roy. Astron. Soc., 152:75, 1971

    1971

  32. [32]

    Constraints on primordial black holes.Rept

    Bernard Carr, Kazunori Kohri, Yuuiti Sendouda, and Jun’ichi Yokoyama. Constraints on primordial black holes.Rept. Prog. Phys., 84(11):116902, 2021

    2021

  33. [33]

    Black Hole’s Quantum N-Portrait.Fortsch

    Gia Dvali and Cesar Gomez. Black Hole’s Quantum N-Portrait.Fortsch. Phys., 61:742–767, 2013

    2013

  34. [34]

    Black hole metamorphosis and stabilization by memory burden.Phys

    Gia Dvali, Lukas Eisemann, Marco Michel, and Sebastian Zell. Black hole metamorphosis and stabilization by memory burden.Phys. Rev. D, 102(10):103523, 2020

    2020

  35. [35]

    Ananda, Chris Clarkson, and David Wands

    Kishore N. Ananda, Chris Clarkson, and David Wands. The Cosmological gravitational wave background from primordial density perturbations.Phys. Rev. D, 75:123518, 2007

    2007

  36. [36]

    Steinhardt, Keitaro Takahashi, and Kiyotomo Ichiki

    Daniel Baumann, Paul J. Steinhardt, Keitaro Takahashi, and Kiyotomo Ichiki. Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations.Phys. Rev. D, 76:084019, 2007

    2007

  37. [37]

    Yanagida

    Kazunori Kohri, Takahiro Terada, and Tsutomu T. Yanagida. Induced gravitational waves probing primordial black hole dark matter with the memory burden effect.Phys. Rev. D, 111(6):063543, 2025

    2025

  38. [38]

    Gravitational waves induced by scalar perturbations as probes of the small-scale primordial spectrum.Phys

    Keisuke Inomata and Tomohiro Nakama. Gravitational waves induced by scalar perturbations as probes of the small-scale primordial spectrum.Phys. Rev. D, 99(4):043511, 2019

    2019

  39. [39]

    Giudice, Riccardo Rattazzi, and James D

    Gian F. Giudice, Riccardo Rattazzi, and James D. Wells. Quantum gravity and extra dimensions at high-energy colliders. Nucl. Phys. B, 544:3–38, 1999

    1999

  40. [40]

    Anchordoqui, Jonathan L

    Luis A. Anchordoqui, Jonathan L. Feng, Haim Goldberg, and Alfred D. Shapere. Inelastic black hole production and large extra dimensions.Phys. Lett. B, 594:363–367, 2004

    2004

  41. [41]

    Landsberg

    Savas Dimopoulos and Greg L. Landsberg. Black holes at the LHC.Phys. Rev. Lett., 87:161602, 2001

    2001

  42. [42]

    Giddings and Scott D

    Steven B. Giddings and Scott D. Thomas. High-energy colliders as black hole factories: The End of short distance physics. Phys. Rev. D, 65:056010, 2002

    2002

  43. [43]

    Black holes in theories with large extra dimensions: A Review.Int

    Panagiota Kanti. Black holes in theories with large extra dimensions: A Review.Int. J. Mod. Phys. A, 19:4899–4951, 2004

    2004

  44. [44]

    New mass window for primordial black holes as dark matter from the memory burden effect.Phys

    Ana Alexandre, Gia Dvali, and Emmanouil Koutsangelas. New mass window for primordial black holes as dark matter from the memory burden effect.Phys. Rev. D, 110(3):036004, 2024

    2024

  45. [45]

    Memory burden effect in black holes and solitons: Implications for PBH.Phys

    Gia Dvali, Juan Sebasti´ an Valbuena-Berm´ udez, and Michael Zantedeschi. Memory burden effect in black holes and solitons: Implications for PBH.Phys. Rev. D, 110(5):056029, 2024

    2024

  46. [46]

    Gravitational wave background as a probe of the primordial black hole abundance

    Ryo Saito and Jun’ichi Yokoyama. Gravitational wave background as a probe of the primordial black hole abundance. Phys. Rev. Lett., 102:161101, 2009. [Erratum: Phys.Rev.Lett. 107, 069901 (2011)]

    2009

  47. [47]

    Scalar Induced Gravitational Waves Review.Universe, 7(11):398, 2021

    Guillem Dom` enech. Scalar Induced Gravitational Waves Review.Universe, 7(11):398, 2021

    2021

  48. [48]

    Flanagan

    Curt Cutler and Eanna E. Flanagan. Gravitational waves from merging compact binaries: How accurately can one extract the binary’s parameters from the inspiral wave form?Phys. Rev. D, 49:2658–2697, 1994

    1994

  49. [49]

    Karhunen-Loeve eigenvalue problems in cosmology: How should we tackle large data sets?Astrophys

    Max Tegmark, Andy Taylor, and Alan Heavens. Karhunen-Loeve eigenvalue problems in cosmology: How should we tackle large data sets?Astrophys. J., 480:22, 1997

    1997

  50. [50]

    Laser Interferometer Space Antenna.arXiv, 2 2017

    Pau Amaro-Seoane et al. Laser Interferometer Space Antenna.arXiv, 2 2017. arXiv:1702.00786 [astro-ph.IM]

    Pith/arXiv arXiv 2017

  51. [51]

    Possibility of direct measurement of the acceleration of the universe using 0.1-Hz band laser interferometer gravitational wave antenna in space.Phys

    Naoki Seto, Seiji Kawamura, and Takashi Nakamura. Possibility of direct measurement of the acceleration of the universe using 0.1-Hz band laser interferometer gravitational wave antenna in space.Phys. Rev. Lett., 87:221103, 2001

    2001

  52. [52]

    Torsion-Bar Antenna for Low-Frequency Gravitational-Wave Observations.Phys

    Masaki Ando, Koji Ishidoshiro, Kazuhiro Yamamoto, Kent Yagi, Wataru Kokuyama, Kimio Tsubono, and Akiteru Takamori. Torsion-Bar Antenna for Low-Frequency Gravitational-Wave Observations.Phys. Rev. Lett., 105:161101, 2010

    2010

  53. [53]

    Vincent Corbin and Neil J. Cornish. Detecting the cosmic gravitational wave background with the big bang observer. Class. Quant. Grav., 23:2435–2446, 2006

    2006

  54. [54]

    Giudice, Riccardo Rattazzi, and James D

    Gian F. Giudice, Riccardo Rattazzi, and James D. Wells. Transplanckian collisions at the LHC and beyond.Nucl. Phys. B, 630:293–325, 2002

    2002

  55. [55]

    Black hole formation in the grazing collision of high-energy particles.Phys

    Hirotaka Yoshino and Yasusada Nambu. Black hole formation in the grazing collision of high-energy particles.Phys. Rev. D, 67:024009, 2003

    2003

  56. [56]

    Hirotaka Yoshino and Vyacheslav S. Rychkov. Improved analysis of black hole formation in high-energy particle collisions. Phys. Rev. D, 71:104028, 2005. [Erratum: Phys.Rev.D 77, 089905 (2008)]

    2005

  57. [57]

    Greybody factors for scalar fields emitted by a higher-dimensional Schwarzschild–de Sitter black hole.Phys

    Panagiota Kanti, Thomas Pappas, and Nikolaos Pappas. Greybody factors for scalar fields emitted by a higher-dimensional Schwarzschild–de Sitter black hole.Phys. Rev. D, 90(12):124077, 2014. 35

    2014

  58. [58]

    Th. Kaluza. Zum Unit¨ atsproblem der Physik.Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys. ), 1921:966–972, 1921

    1921

  59. [59]

    Quantum Theory and Five-Dimensional Theory of Relativity

    Oskar Klein. Quantum Theory and Five-Dimensional Theory of Relativity. (In German and English).Z. Phys., 37:895–906, 1926

    1926

  60. [60]

    Appelquist, A

    T. Appelquist, A. Chodos, and P. G. O. Freund, editors.Modern Kaluza–Klein Theories. Addison-Wesley, Reading, MA, 1987

    1987

  61. [61]

    F. R. Tangherlini. Schwarzschild field in n dimensions and the dimensionality of space problem.Nuovo Cim., 27:636–651, 1963

    1963

  62. [62]

    Roberto Emparan and Harvey S. Reall. Black Holes in Higher Dimensions.Living Rev. Rel., 11:6, 2008

    2008

  63. [63]

    S. W. Hawking. Particle Creation by Black Holes.Commun. Math. Phys., 43:199–220, 1975. [Erratum: Com- mun.Math.Phys. 46, 206 (1976)]

    1975

  64. [64]

    Bekenstein

    Jacob D. Bekenstein. Black holes and entropy.Phys. Rev. D, 7:2333–2346, 1973

    1973

  65. [65]

    Black Hole Particle Emission in Higher-Dimensional Spacetimes

    Vitor Cardoso, Marco Cavaglia, and Leonardo Gualtieri. Black Hole Particle Emission in Higher-Dimensional Spacetimes. Phys. Rev. Lett., 96:071301, 2006. [Erratum: Phys.Rev.Lett. 96, 219902 (2006)]

    2006

  66. [66]

    Myers and M

    Robert C. Myers and M. J. Perry. Black Holes in Higher Dimensional Space-Times.Annals Phys., 172:304, 1986

    1986

  67. [67]

    Rotating black holes at future colliders: Greybody factors for brane fields.Phys

    Daisuke Ida, Kin-ya Oda, and Seong Chan Park. Rotating black holes at future colliders: Greybody factors for brane fields.Phys. Rev. D, 67:064025, 2003. [Erratum: Phys.Rev.D 69, 049901 (2004)]

    2003

  68. [68]

    Rotating black holes at future colliders

    Daisuke Ida, Kin-ya Oda, and Seong Chan Park. Rotating black holes at future colliders. II. Anisotropic scalar field emission.Phys. Rev. D, 71:124039, 2005

    2005

  69. [69]

    Marc Casals, S. R. Dolan, P. Kanti, and E. Winstanley. Brane Decay of a (4+n)-Dimensional Rotating Black Hole. III. Spin-1/2 particles.JHEP, 03:019, 2007

    2007

  70. [70]

    Festina Lente: EFT Constraints from Charged Black Hole Evaporation in de Sitter.JHEP, 01:039, 2020

    Miguel Montero, Thomas Van Riet, and Victoria Venken. Festina Lente: EFT Constraints from Charged Black Hole Evaporation in de Sitter.JHEP, 01:039, 2020

    2020

  71. [71]

    The FL bound and its phenomenological impli- cations.JHEP, 10:009, 2021

    Miguel Montero, Cumrun Vafa, Thomas Van Riet, and Victoria Venken. The FL bound and its phenomenological impli- cations.JHEP, 10:009, 2021

    2021

  72. [72]

    G. W. Gibbons and S. W. Hawking. Cosmological Event Horizons, Thermodynamics, and Particle Creation.Phys. Rev. D, 15:2738–2751, 1977

    1977

  73. [73]

    Raphael Bousso and Stephen W. Hawking. Pair creation of black holes during inflation.Phys. Rev. D, 54:6312–6322, 1996

    1996

  74. [74]

    On a New Cosmological Solution of Einstein’s Field Equations of Gravitation.Gen

    Hidekazu Nariai. On a New Cosmological Solution of Einstein’s Field Equations of Gravitation.Gen. Rel. Grav., 31(6):963– 971, 1999

    1999

  75. [75]

    Schwinger

    Julian S. Schwinger. On gauge invariance and vacuum polarization.Phys. Rev., 82:664–679, 1951

    1951

  76. [76]

    J. Garriga. Pair production by an electric field in (1+1)-dimensional de Sitter space.Phys. Rev. D, 49:6343–6346, 1994

    1994

  77. [77]

    Enhancement of Gravitational Waves Induced by Scalar Perturbations due to a Sudden Transition from an Early Matter Era to the Radiation Era.Phys

    Keisuke Inomata, Kazunori Kohri, Tomohiro Nakama, and Takahiro Terada. Enhancement of Gravitational Waves Induced by Scalar Perturbations due to a Sudden Transition from an Early Matter Era to the Radiation Era.Phys. Rev. D, 100:043532, 2019. [Erratum: Phys.Rev.D 108, 049901 (2023)]

    2019

  78. [78]

    Gravitational Waves Induced by Scalar Perturbations with a Lognormal Peak.JCAP, 09:037, 2020

    Shi Pi and Misao Sasaki. Gravitational Waves Induced by Scalar Perturbations with a Lognormal Peak.JCAP, 09:037, 2020

    2020

  79. [79]

    Fierz and W

    M. Fierz and W. Pauli. On relativistic wave equations for particles of arbitrary spin in an electromagnetic field.Proc. Roy. Soc. Lond. A, 173:211–232, 1939

    1939

  80. [80]

    Theoretical Aspects of Massive Gravity.Rev

    Kurt Hinterbichler. Theoretical Aspects of Massive Gravity.Rev. Mod. Phys., 84:671–710, 2012

    2012

Showing first 80 references.