Pith. sign in

REVIEW 1 major objections 6 minor 75 references

Transportable Optical Lattice Clocks and General Relativity

T0 review · 1 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

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

Pith's one-line read This review reports that two transportable optical lattice clocks separated by 450 m in height at Tokyo Skytree measured the gravitational redshift with $\alpha = (1.4 \pm 9.1)\times 10^{-5}$, the best constraint on the redshift obtained…

desk verdict Accurate review of the authors' own OLC gravitational-redshift experiments; no new results, but a reliable synthesis worth peer review. read the letter →

arxiv 2502.06104 v1 pith:46WDTO3D submitted 2025-02-10 gr-qc

Hisaaki Shinkai , Masao Takamoto , Hidetoshi Katori This is my paper · ORCID
classification gr-qc
keywords opticallatticeclocksgravitationalredshiftlocalpositioninvarianceequivalenceprincipletransportablechronometriclevelingrelativisticgeodesystrontium-87
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

Optical lattice clocks keep time with fractional uncertainty near $10^{-18}$, two orders of magnitude better than the cesium clocks that define the second. This review argues that such clocks have turned the gravitational redshift—the slowing of time in a deeper gravitational potential—into a ground-level laboratory observable. The load-bearing experimental result is a comparison of two transportable strontium clocks at Tokyo Skytree with a 450 m height difference, which gives the local-position-invariance parameter $\alpha = (1.4 \pm 9.1)\times 10^{-5}$, the tightest constraint on gravitational redshift obtained on the ground. A second comparison over a 15 m height difference between two sites in Japan demonstrates that clock networks can measure geopotential differences in real time. If these results hold, optical lattice clocks are not just better clocks; they are gravity sensors that test Einstein's equivalence principle and open relativistic geodesy.

What carries the argument

The carrying object is the optical lattice clock: neutral $^{87}$Sr atoms confined in a one-dimensional standing-wave laser trap, interrogated on the $5s^2\,{}^1S_0 \to 5s5p\,{}^3P_0$ clock transition. The lattice laser is tuned to the magic frequency (and, in the transportable version, to the operational magic condition) so that the trapping light's a.c. Stark shift cancels to high order; a four-stage Peltier-cooled blackbody-radiation shield at 245 K suppresses the thermal shift, and a bow-tie cavity transports atoms into the shield while controlling lattice intensity. Frequency comparison between the two clocks runs through a phase-noise-canceled optical fiber, and the geopotential difference is pinned down independently by GNSS leveling, laser ranging, spirit leveling, and gravity measurements. The argument then uses the redshift relation $\Delta\nu/\nu = (1+\alpha)\Delta U/c^2$ to convert the measured fractional frequency difference into a constraint on $\alpha$.

What would settle it

Re-analyze the Skytree data with an independently recalibrated $^{87}$Sr blackbody-radiation shift coefficient, or place one of the transportable clocks beside a third clock of a different atomic species at the same location; if the inferred $\alpha$ leaves $(1.4 \pm 9.1)\times 10^{-5}$, the no-hidden-offset assumption is false.

Watch

Extended reading notes

Core claim

The paper's central claim is that transportable optical lattice clocks can measure the gravitational redshift on Earth's surface with an accuracy previously available only to space missions. Writing the redshift as $\Delta\nu/\nu_1 = (1+\alpha)\Delta U/c^2$, with $\alpha=0$ in general relativity, the Skytree experiment with a height difference of approximately 450 m yields $\alpha = (1.4 \pm 9.1)\times 10^{-5}$; the same setup, after returning both clocks to the same height, reproduced the frequency ratio to $(-0.3 \pm 4.7)\times 10^{-18}$. An earlier comparison over a 15 m height difference, with the clocks connected by a phase-noise-canceled optical fiber, gave $\alpha = (2.9 \pm 3.6)\times 10^{-3}$ and agreed with conventional leveling, demonstrating chronometric leveling at the 5 cm level. The authors therefore present the ground-based clock comparison as a complement to satellite redshift tests: it covers the short, near-surface range of gravitational potential rather than the $10^4$ km range probed by Galileo satellites.

Load-bearing premise

The extraction of $\alpha$ assumes the two transportable clocks have no hidden frequency errors at the level of a few parts in $10^{18}$, especially from heat radiation from the walls and from the laser light that traps the atoms; if those corrections are wrong by more than claimed, the derived $\alpha$ moves by more than its uncertainty.

Editorial extensions

If this is right

  • The Skytree value $\alpha = (1.4 \pm 9.1)\times 10^{-5}$ is consistent with general relativity and sets the best ground-based constraint on the gravitational redshift, at a level comparable to satellite clock experiments.
  • The 15 m fiber-linked comparison demonstrates chronometric leveling: a frequency comparison at $10^{-18}$ resolves about 1 cm of height, and the experiment measured the height difference to about 5 cm.
  • A network of optical lattice clocks would allow real-time monitoring of the geopotential, with applications in geodetic leveling, seismology, and volcanology.
  • Placing optical lattice clocks on spacecraft at Sun–Earth Lagrange points (the proposed INO configuration) would use Doppler tracking to detect low-frequency gravitational waves from supermassive black hole mergers with currently available technology.

Reading between the lines

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

  • The same 450 m baseline would yield a ground $\alpha$ constraint near $10^{-6}$ if clock uncertainty improves one order of magnitude, pushing the paper's second-order PPN discussion from space down to ground scale.
  • A permanent Skytree-style clock pair could double as a geopotential observatory: the same-height reproducibility check would be the calibration that converts clock noise into a height-equivalent signal for tracking subsurface mass shifts.
  • Because the laser-ranging and GNSS geopotential errors are about 1.3 cm in height while the clock comparison resolves about 5 cm, the next gain in $\alpha$ should come from clock systematics, not from better surveying.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 6 minor

Summary. The paper by Shinkai, Takamoto, and Katori reviews optical lattice clocks (OLCs) and their use in tests of general relativity, concentrating on two experiments by the authors: a fiber-linked comparison of clocks at RIKEN and the University of Tokyo (15 m height difference), giving α = (2.9 ± 3.6) × 10^-3, and the Tokyo Skytree experiment with two transportable clocks separated by about 450 m, giving α = (1.4 ± 9.1) × 10^-5. The paper also discusses future applications of OLCs, including chronometric leveling, tests of the second-order parametrized post-Newtonian (PPN) potential, and the proposed Interplanetary Network of Optical Lattice Clocks (INO) for gravitational-wave detection. The central experimental assertion is that the Skytree measurement provides the best ground-based gravitational redshift constraint at the 10^-5 level.

Significance. If the reported results are correct, the paper demonstrates that transportable OLCs can test local position invariance on Earth at the 10^-5 level, complementary to space-borne tests such as the Galileo satellite experiments. The paper serves as a useful consolidated review of the authors' previously published work (refs. 7, 8, 20), and the quoted numerical values are consistent with those sources. The treatment of systematics is not reproduced here, but the authors explicitly defer to the original publications, which is appropriate for a review article. The future-applications sections are speculative but clearly identified as proposals. The main strength of the paper is its clear presentation of the state of the art and the explicit connection between clock technology and fundamental physics tests.

major comments (1)
  1. [4.2] The description of the Skytree measurement states that a single clock laser located on the ground floor was used to interrogate the clock at the observatory floor through a phase-noise-canceled optical fiber. In a vertical setup, the laser light itself undergoes a gravitational frequency shift of the same order (gΔh/c² ≈ 4.93 × 10^-14) as the atomic transition difference being measured, which could introduce a factor-of-two ambiguity in the derived Δν if not explicitly accounted for. The paper does not explain how this light-propagation effect is separated from the atomic redshift; please clarify the analysis or explicitly state that it is treated as in Ref. 8, so that the derivation of the reported α is unambiguous.
minor comments (6)
  1. [Title page] The title reads "T ransportable optical lattice clocks and general relativity" with a stray space after "T", and the abstract contains "W e also discuss" with a stray space; these should be corrected.
  2. [3.2] Under "Test of WEP", the word "Threfore" is a typo for "Therefore".
  3. [Figure 3 caption] The caption contains the typo "uncertanites" (should be "uncertainties"), and the sentence "Colored points are of the largest uncertanites in α, while black ones are from Ref.57" is confusing; it should be rephrased to indicate which points have the largest uncertainties.
  4. [4.2] The quoted frequency shift "Δν = ν2−ν1 ≈ 21.18 Hz" combined with the quoted geopotential difference implies α ≈ 1.4 × 10^-4, not the reported α = (1.4 ± 9.1) × 10^-5; the authors should either provide the unrounded frequency difference or state that α is derived from the full fit, since the rounding to 0.01 Hz is too coarse to determine α at the 10^-5 level.
  5. [5.2] The phrase "the second-order effect is 10th-order smaller than that of the first-order" is ambiguous; it should be rephrased as "ten orders of magnitude smaller".
  6. [5.2] The sentence "The direct comparison ... is critically reachable with current technology" is overly optimistic for the current state of clock uncertainties (around 10^-18); it should be qualified as "will be critically reachable" or "is within reach of near-future technology".

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the LPI parameter α is measured from independent clock-frequency and geodetic-potential data, not derived from a fitted input.

full rationale

The paper's central result, α = (1.4 ± 9.1) × 10⁻⁵ at Tokyo Skytree, is obtained by inserting two independently measured quantities into eq. (3): the clock frequency ratio Δν/ν₁ determined from Ramsey spectroscopy at the two tower floors, and the geopotential difference ΔU/c² = gΔh/c² determined separately by laser ranging, GNSS leveling, spirit leveling, and gravimetry. Neither quantity is fitted to the other; α is the residual after comparing them, so the derivation does not reduce to its inputs by construction. The RIKEN–University of Tokyo result is analogous: the measured frequency offset is compared with conventional leveling, giving α = (2.9 ± 3.6) × 10⁻³. The self-citations (refs. 7, 8, 11) support the quoted experimental values and the INO proposal, but the experimental values are externally published, peer-reviewed, and externally falsifiable data, not assumptions introduced for this paper; they therefore do not constitute load-bearing self-citation. No uniqueness theorem, smuggled ansatz, or renaming of a known empirical pattern is used. The remaining systematic-uncertainty discussion (BBR shield, operational magic condition, same-height reproducibility check) is standard experimental support and not circular. The paper is a review/experimental report whose claims are self-contained against the reported measurements and external comparisons.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No new free parameters are introduced; the paper reports measured values of α and applies standard GR formulas. The main axioms are standard PPN theory and the assumed accuracy of the clock system as characterized in prior work by the same group.

assumptions (4)
  • standard math The PPN metric for a static spherical mass (Eq. 4) applies to the Earth's gravitational field.
    Used as the basis for computing gravitational redshift and the second-order PPN time-dilation estimates in Section 5.2.
  • standard math The gravitational redshift between two clocks is parameterized by alpha as in Eq. (3): Δν/ν1 = (1+α)ΔU/c^2.
    Standard parametrization for LPI tests; the experimental results are expressed in terms of alpha.
  • domain assumption The transportable optical lattice clocks achieve the claimed fractional uncertainties near 10^-18, relying on the BBR shield and operational magic condition.
    This is a premise for the experimental α values; the calibrations are detailed in refs. 8, 14, and 20, not fully reproduced in this paper.
  • domain assumption For the PPN second-order estimates in Table 2, each satellite is on a Keplerian circular orbit and ISS orbital radius variations are neglected.
    The table is illustrative; the paper explicitly notes ISS height loss and that the numbers exclude orbital radius shifts.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Transportable Optical Lattice Clocks and General Relativity." pith.science (2026). https://pith.science/paper/46WDTO3D

@misc{pith2026250206104,
  author       = {Pith},
  title        = {Pith review of: Transportable Optical Lattice Clocks and General Relativity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/46WDTO3D}},
  note         = {Machine review of arXiv:2502.06104}
}
abstract

Optical lattice clocks (OLCs) enable us to measure time and frequency with a fractional uncertainty at $10^{-18}$ level, which is 2 orders of magnitude better than Cs clocks. In this article, after briefly reviewing OLCs and the history of testing the fundamental principles of general relativity, we report our experiments of measuring the gravitational redshift between RIKEN and The University of Tokyo, and at Tokyo Skytree using transportable OLCs. We also discuss a couple of future applications of OLCs, such as detecting gravitational waves in space and relativistic geodesy. The possibility of testing second-order parametrized post-Newtonian potential around the Earth is also mentioned.

Figures

Figures reproduced from arXiv: 2502.06104 by the authors.

Figure 1
Figure 1. A schematic of an optical lattice clock. (a) Optical l [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Transportable OLCs using 87Sr atoms. (a) Two transportable OLCs. The frequencies of the clocks are compared via a phase-noise-canceled optical fiber. (b) A schematic of the vacuum chamber inside the physics package. (c) The relevant energy diagram of Sr atoms. (d) A schematic of the clock spectroscopy in a bow-tie optical cavity for the lattice. probability, the frequency of the clock laser is stabilized to the reso… view at source ↗
Figure 3
Figure 3. Comparison of selected tests of the LPI with gravitat [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Chronometric leveling demonstrated by frequency co [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: Test of GR at Tokyo skytree. (a) The gravitational pot [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: A planned location of the INO spacecrafts: Lagrangia [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]
Figure 7
Figure 7. Figure 7: Sensitivity of Doppler-tracking spacecrafts and ex [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

75 extracted references · 74 canonical work pages

  1. [1]

    Katori, Proceedings of the 6th Symposium on Frequency S tandards and Metrology, edited by P

    H. Katori, Proceedings of the 6th Symposium on Frequency S tandards and Metrology, edited by P. Gill (World Scientific, Singapore, 2002) (2002) 323

    work page 2002

  2. [2]

    Katori, M

    H. Katori, M. Takamoto, V. G. Pal’chikov and V. D. Ovsianni kov, Phys. Rev. Lett. 91 (2003) 173005

    work page 2003

  3. [3]

    Takamoto and H

    M. Takamoto and H. Katori, Phys. Rev. Lett. 91 (2003) 223001

    work page 2003

  4. [4]

    Ushijima, M

    I. Ushijima, M. Takamoto, M. Das, T. Ohkubo, and H. Katori, Nat. Photon. 9 (2015) 185

    work page 2015

  5. [5]

    Katori, V

    H. Katori, V. D. Ovsiannikov, S. I. Marmo and V. G. Pal’chik ov, Phys. Rev. A 91(2015) 052503

    work page 2015

  6. [6]

    C. W. Chou, D.B. Hume, T. Rosenband, and D. J. Wineland, Sci ence 329 (2010) 1630

    work page 2010

  7. [7]

    Takano, M

    T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka , A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, & H. Katori, Nat. Photon . 10 (2016) 662. February 11, 2025 2:12 WSPC/INSTRUCTION FILE OLCGR Transportable Optical Lattice Clocks and General Relativi ty 21

    work page 2016

  8. [8]

    Takamoto, I

    M. Takamoto, I. Ushijima, N. Ohmae, T. Yahagi, K. Kokado, H . Shinkai and H. Katori, Nat. Photon. 14 (2020) 411

    work page 2020

Show all 75 references
  1. [9]

    Denker, et al

    H. Denker, et al. J. Geodesy 92 (2017) 487

    2017

  2. [10]

    Tanaka and H

    Y. Tanaka and H. Katori, J. Geodesy 95 (2021) 93

    2021

  3. [11]

    Ebisuzaki, H

    T. Ebisuzaki, H. Katori, J. Makino, A. Noda, H. Shinkai, a nd T. Tamagawa, Int. J. Modern Phys. D 28 (2019) 1940002

    2019

  4. [12]

    R. H. Dicke, Phys. Rev. 89 (1953) 472

    1953

  5. [13]

    W. F. McGrew et al. Nature 564 (2018) 87

    2018

  6. [14]

    Ushijima, M

    I. Ushijima, M. Takamoto, H. Katori, Phys. Rev. Lett. 121 (2018) 263202

    2018

  7. [15]

    Haensch, Rev

    T.W. Haensch, Rev. Mod. Phys. 78 (2006) 1297

    2006

  8. [16]

    Hall, Rev

    J.L. Hall, Rev. Mod. Phys. 78 (2006) 1279

    2006

  9. [17]

    Itano et al

    W.M. Itano et al. , Phys. Rev. A 47 (1993) 3554

    1993

  10. [18]

    Aeppli, K

    A. Aeppli, K. Kim, W. Warfield, M. S. Safronova and J. Ye, Ph ys. Rev. Lett. 2 (2024) 133

    2024

  11. [19]

    Dimarcq et al

    N. Dimarcq et al. , Metrologia 61 (2024) 012001

    2024

  12. [20]

    Ohmae et al

    N. Ohmae et al. , Adv. Quantum Technol. 4 (2021) 2100015

    2021

  13. [21]

    T. L. Nicholson et al. Nat. Commun. 6 (2015) 6896

    2015

  14. [22]

    C. M. Will, Theory and Experiment in Gravitational Physics , (Cambridge University Press, Cambridge; New York, 1993), 2nd edition (2018)

    2018

  15. [23]

    C. M. Will, Liv. Rev. Rel. 17 (2014), 4

    2014

  16. [24]

    C. M. Will, Am. J. Phys. 78 (2010), 1240

    2010

  17. [25]

    T. A. Wagner, S. Schlamminger, J. H. Gundlach, & E. G. Adel berger, Class. Quant. Grav. 29 (2012) 184002

    2012

  18. [26]

    Berg´ e, P

    J. Berg´ e, P. Touboul, M. Rodrigues, J. Phys.: Conf. Ser. 610 (2015) 012009

    2015

  19. [27]

    Bonnin, N

    A. Bonnin, N. Zahzam, Y. Bidel, & A. Bresson, Phys. Rev. A 88 (2013) 043615

    2013

  20. [28]

    Touboul et al , Phys

    P. Touboul et al , Phys. Rev. Lett. 129 (2022) 121102

    2022

  21. [29]

    Damour, Class

    T. Damour, Class. Quant. Grav. 29 (2012) 184001

    2012

  22. [30]

    Overduin, F

    J. Overduin, F. Everitt, P. Worden, & J. Mester, Class. Qu ant. Grav. 29 (2012) 184012

    2012

  23. [31]

    T. E. Chupp, et al. , Phys. Rev. Lett. 63 (1989) 1541

    1989

  24. [32]

    M. S. Safronova, D. Budker, D. DeMille, D. F. J. Kimball, A . Derevianko, and C. W. Clark, Rev. Mod. Phys. 90 (2018) 025008

    2018

  25. [33]

    J. G. Williams, S. G. Turyshev, D. H. Boggs, Phys. Rev. Let t. 93 (2004) 261101

    2004

  26. [34]

    J. G. Williams, S. G. Turyshev, D. H. Boggs, Int. J. Mod. Ph ys. D18 (2009) 1129

    2009

  27. [35]

    T. W. Murphy, Jr. et al. Class. Quant. Grav. 29 (2012) 184005

    2012

  28. [36]

    Milani, D

    A. Milani, D. Vokrouhlicky, D. Villani, C. Bonanno, and A . Rossi, Phys. Rev. D 66 (2002) 082001

    2002

  29. [37]

    Shao, Phys

    L. Shao, Phys. Rev. D 93 (2016) 084023

    2016

  30. [38]

    Congedo, and F

    G. Congedo, and F. De Marchi, Phys. Rev. D 93 (2016) 102003

    2016

  31. [39]

    R. V. Pound, & G. A. Rebka, Phys. Rev. Lett. 3 (1959) 439

    1959

  32. [40]

    R. V. Pound, & J. L. Snider, Phys. Rev. 140 (1965) B788

    1965

  33. [41]

    R. F. C. Vessot et al. , Phys. Rev. Lett. 45 (1980) 2081

    1980

  34. [42]

    L. L. Smarr et al. , Gen. Relativ. Gravit. 15 (1983) 129

    1983

  35. [43]

    Delva et al

    P. Delva et al. , Phys. Rev. Lett. 121 (2018) 231101

    2018

  36. [44]

    Herrmann et al

    S. Herrmann et al. , Phys. Rev. Lett. 121 (2018) 231102

    2018

  37. [45]

    Grotti et al

    J. Grotti et al. , Nat. Phys. 14 (2018) 437

    2018

  38. [46]

    Grotti, et al

    J. Grotti, et al. , Phys. Rev. Appl. 21 (2024) L061001

    2024

  39. [47]

    J. C. Hafele, & R. E. Keating, Science 177 (1972) 166; Science 177 (1972) 168

    1972

  40. [48]

    T. P. Krisher, J. D. Anderson, and J. K. Campbell, Phys. Re v. Lett. 64 (1990) 1322

    1990

  41. [49]

    J. W. Brault, The Gravitational Red Shift in the Solar Spe ctrum, Ph.D. thesis, Prince- February 11, 2025 2:12 WSPC/INSTRUCTION FILE OLCGR 22 H. Shinkai, M. Takamoto, & H. Katori ton University, 1962

    2025

  42. [50]

    J. L. Snider, Phys. Rev. Lett. 28 (1972) 853

    1972

  43. [51]

    J. C. LoPresto, C. Schrader, & A.K. Pierce, Astrophys. J. 376 (1991) 757

    1991

  44. [52]

    J. P. Turneaure, C. M. Will, B. F. Farrell, E. M. Mattison, and R. F. C. Vessot, Phys. Rev. D 27 (1983) 1705

    1983

  45. [53]

    Godone, C

    A. Godone, C. Novero, and P. Tavella, Phys. Rev. D 51 (1995) 319

    1995

  46. [54]

    Bauch and S

    A. Bauch and S. Weyers, Phys. Rev. D 65 (2002) 081101

    2002

  47. [55]

    Ashby, T

    N. Ashby, T. P. Heavner, S. R. Jefferts, T. E. Parker, A. G. R adnaev, and Y.O. Dudin, Phys. Rev. Lett. 98 (2007) 070802

    2007

  48. [56]

    S. Peil, S. Crane, J. L. Hanssen, T. B. Swanson, and C. R. Ek strom, Phys. Rev. A 87 (2013) 010102

    2013

  49. [57]

    Amorim et al

    A. Amorim et al. , Phys. Rev. Lett. 122 (2019) 101102

    2019

  50. [58]

    Vermeer, Rep

    M. Vermeer, Rep. Finnish Geodetic Inst. 83 (1983) 1

    1983

  51. [59]

    Schioppo et al

    M. Schioppo et al. , Nat. Commun. 13 (2022) 212

    2022

  52. [60]

    A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik and P. O. Schmidt, Re v. Mod. Phys. 87 (2015) 637

    2015

  53. [61]

    Katori, Appl

    H. Katori, Appl. Phys. Express 14 (2021) 072006

    2021

  54. [62]

    Takeuchi, H

    R. Takeuchi, H. Chiba, S. Okaba, M. Takamoto, S. Tsuji and H. Katori, Appl. Phys. Express 16 (2023) 042003

    2023

  55. [63]

    Okaba, R

    S. Okaba, R. Takeuchi, S. Tsuji and H. Katori, Phys. Rev. A ppl. 21 (2024) 034006

    2024

  56. [64]

    Riehle, P

    F. Riehle, P. Gill, F. Arias and L. Robertsson, Metrologi a 55 2018 188

    2018

  57. [65]

    LIGO and Virgo Scientific Collaborations (B. P. Abbott, et al. ), Phys. Rev. Lett. 116 (2016) 061102

    2016

  58. [66]

    LIGO and Virgo Scientific Collaborations (B. P. Abbott, et al. ), Phys. Rev. Lett. 119 (2017) 161101

    2017

  59. [67]

    LIGO, Virgo, and KAGRA Scientific Collaborations (B. P. A bbott, et al. ), Phys. Rev. X 13 (2023) 041039

    2023

  60. [68]

    Matsubayashi, H

    T. Matsubayashi, H. Shinkai, and T. Ebisuzaki, Astrophy s. J. 614 (2004) 864

    2004

  61. [69]

    Shinkai, N

    H. Shinkai, N. Kanda, and T. Ebisuzaki, Astrophys. J. 835 (2017) 276

    2017

  62. [70]

    W.-T. Ni, Int. J. Mod. Phys. D 25 (2016) 1630001

    2016

  63. [71]

    Ni, arXiv:2409.00927

    W.-T. Ni, arXiv:2409.00927

    arXiv

  64. [72]

    Jennrich, et al., NGO (New Gravitational wave Observa tory) assessment study report, ESA/SRE (2011) 19

    O. Jennrich, et al., NGO (New Gravitational wave Observa tory) assessment study report, ESA/SRE (2011) 19

    2011

  65. [73]

    Nakamura, et al., Prog

    T. Nakamura, et al., Prog. Theor. Exp. Phys. 2016 (2016) 093E01

    2016

  66. [74]

    J. W. Armstrong, Liv. Rev. Rel. 9 (2006) 1

    2006

  67. [75]

    Armano, et al., Phys

    M. Armano, et al., Phys. Rev. Lett. 118 (2017) 171101

    2017

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.