Pith. sign in

REVIEW 2 major objections 4 minor 1 cited by

Elliptically Polarized Plane Gravitational Waves

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read Elliptically polarized gravitational waves drive most free test particles into a near-light-speed cosmic jet.

desk verdict Solid exact-solutions paper with a clean derivation of the cosmic jet for elliptically polarized plane waves, but the jet limit is taken at the BJR coordinate boundary where the measurement frame degenerates, so the central claim needs a caveat or a Brinkmann-coordinate continuation. read the letter →

arxiv 2501.11503 v4 pith:6FUFUY53 submitted 2025-01-20 gr-qc

Masoud Molaei , Shant Baghram , Bahram Mashhoon This is my paper · ORCID
classification gr-qc
keywords planegravitationalwavesellipticalpolarizationcosmicjetsexactsolutionstimelikegeodesicsnullgravitoelectromagnetismKillingvectors
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 claims that exact elliptically polarized plane gravitational waves display a cosmic jet property: relative to the preferred observers who are spatially at rest, most free test particles, both timelike and null, asymptotically line up with the direction of wave propagation, and the jet's speed approaches the speed of light. It establishes this for two Ricci-flat exact solutions of Einstein's equations, one nonsingular and one with a curvature singularity, by writing the geodesics in terms of the constants of motion supplied by the plane wave's Killing vectors and then reading off the measured velocity components in the comoving tetrad. The result matters because it shows that a phenomenon previously found for linearly polarized and twisted plane waves is generic to the most general monochromatic polarization state, and it gives an invariant formulation in terms of measured velocity components. The central calculations are carried out in the wave-front coordinate system, and the jet limit is reached precisely at the boundary where that coordinate system and the adapted tetrad become singular.

What carries the argument

The central object is the exact plane-wave metric $ds^2 = -dt^2 + dz^2 + P^2(u)\, dx^2 + 2R(u)\, dx\, dy + Q^2(u)\, dy^2$ with the Ricci-flat field equation (27). The two special elliptically polarized solutions are the nonsingular one (87), where $P = e^{S/2}$, $Q = e^{-S/2}$, $R = S$ with $S = \sin(\eta u + \varphi)$, and the singular one (117), where $P = \cos(\eta_0 u + \varphi_0)\, e^{\gamma \eta_0 u}$, $Q = \cos(\eta_0 u + \varphi_0)\, e^{-\gamma \eta_0 u}$, $R = \alpha \cos^2(\eta_0 u + \varphi_0)$. The mechanism that produces the jet is the combination of the plane wave's five Killing vectors, which supply the constants $C_1, C_2, C_u$ (or $D_1, D_2, D_u$) that integrate the geodesic equations, and the adapted tetrad (30) used by the preferred observers; the denominators $1-S^2$ and $\cos^2(\eta_0 u + \varphi_0)$ in the measured velocity components force the transverse components to vanish while the longitudinal component tends to 1 at the coordinate boundary.

What would settle it

Extend the nonsingular solution through $S^2 = 1$ in a nonsingular chart such as Brinkmann coordinates and integrate a generic timelike geodesic across the boundary, measuring its velocity against a parallel-propagated frame on both sides; if the transverse components do not vanish as the Lorentz factor diverges, the cosmic jet claim fails. A concrete starting point is the geodesic with $C_1 = C_2 = 1$ in Eq. (110), whose transverse measured component diverges at $S = 1$ only because of the $1-S^2$ denominator; the boundary-crossing calculation decides whether this divergence is physical alignment or a coordinate artifact.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the cosmic jet is a property of elliptically polarized plane gravitational waves. For the nonsingular solution with metric $ds^2 = -dt^2 + dz^2 + e^{S} dx^2 + 2S\, dx\, dy + e^{-S} dy^2$, $S = \sin(\eta u + \varphi)$, every generic timelike or null geodesic has measured velocity components approaching $(0,0,1)$ with Lorentz factor $\Gamma \to \infty$ as $S^2 \to 1$; for the singular solution with $\cos(\eta_0 u + \varphi_0)$ in the metric, the same limit is approached as $\cos(\eta_0 u + \varphi_0) \to 0$. The wave's gravitoelectric and gravitomagnetic curvature components $K_1, K_2$ form null, transverse fields, and the associated GEM energy-momentum tensor has the form $\rho_g k^\mu k^\nu$, so the nonlinear wave behaves like a bundle of null rays. In this sense the paper claims the full electromagnetic analogy for elliptically polarized gravitational waves, including a polarization handedness set by the sign of $d(K_2/K_1)/du$.

Load-bearing premise

The jet limit is stated in the coordinate system that becomes singular exactly at the limit, and the paper assumes that this singular-frame limiting velocity $(0,0,1)$ with diverging Lorentz factor correctly describes the physical alignment of the geodesics, without extending the geodesics through the caustic.

Editorial extensions

If this is right

  • The cosmic jet effect, previously demonstrated for linearly polarized and twisted plane waves, holds for elliptically polarized waves as well.
  • Most timelike geodesics with arbitrary transverse constants join the jet, and null geodesics join it too, so the effect is generic rather than special to chosen initial data.
  • Preferred observers at rest in the wave see all jet particles moving along the propagation direction with diverging Lorentz factor, so the jet has no rest-frame speed below the speed of light.
  • The full analogy with electromagnetic waves—null transverse GEM fields, handedness, and energy transport along null rays—is valid for nonlinear elliptically polarized waves.
  • The nonsingular solution shows that a curvature singularity is not required for jet formation; the same alignment appears as its coordinate boundary is approached.

Reading between the lines

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

  • Editorial inference: If the geodesic integration is continued past the coordinate boundary in a nonsingular chart such as Brinkmann form, the jet alignment will likely persist; if so, the cosmic jet is a genuine physical focusing effect and the coordinate boundary is a caustic, not an artifact.
  • Editorial inference: The critical speed $1/\sqrt{2}$ in the transverse Fermi-frame equations is a natural separator: particles launched faster than this may be captured by the jet, while slower ones remain bounded; a phase-space survey of the Fermi equations could test whether the jet basin has this threshold.
  • Editorial inference: For the singular solution, the jet forms as the curvature singularity is approached, which suggests that in applications a gravitational wave carrying a caustic would produce a burst of ultra-relativistic particles at each singularity-crossing epoch, possibly observable as repeated jet pulses.
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

2 major / 4 minor

Summary. The paper studies exact elliptically polarized plane gravitational waves in Baldwin-Jeffrey-Rosen coordinates. It develops a gravitoelectromagnetic analogy, constructs two families of exact solutions (a nonsingular solution with S = sin(ηu+φ) and a singular solution with cos(η0u+φ0) factors), and analyzes timelike and null geodesics. The central claim is the cosmic jet property: as the BJR chart degenerates (S^2 → 1 for the nonsingular solution; cos(η0u+φ0) → 0 for the singular solution), generic geodesics acquire measured velocity components (V^1,V^2,V^3) → (0,0,1) with diverging Lorentz factor, so that most free test particles line up with the direction of wave propagation and approach the speed of light.

Significance. If the cosmic jet property holds, the paper extends a phenomenon previously established for linearly polarized and twisted gravitational waves to the elliptically polarized case, which is a useful addition to the exact plane-wave literature. The manuscript provides explicit formulas for the metric functions, curvature components, Killing constants, and geodesic integrals, making the calculations easy to check. The GEM framework and the explicit construction of the elliptic polarization are pedagogically valuable. However, the central claim rests on a limiting procedure at the boundary of the BJR coordinate chart, where both the metric and the observer tetrad become singular; the paper does not yet make the invariant status of this limit fully explicit.

major comments (2)
  1. [§IV C, Eqs. (100)–(112)] The cosmic jet limit for the nonsingular solution is taken as S^2 → 1 inside the BJR chart, but at that boundary the adapted tetrad (30), specialized in Eq. (108), contains the factor (1−S^2)^(−1/2), and the coordinate metric has determinant Δ = 1−S^2. Consequently, the measured velocity components in Eq. (111) are defined only for S^2 < 1 and diverge in the frame itself. The claim in the text that 'the jet structure has been invariantly specified' is asserted but not demonstrated. Please either extend the geodesics through the caustic in a regular coordinate system such as Brinkmann coordinates and verify the alignment there, or reformulate the result as a coordinate-invariant statement about the tangent vector (e.g., U^μ/(dt/dλ) → (1,0,0,1) in the BJR chart) and discuss what happens at the chart boundary. Without such an argument, the reader cannot rule out that the apparent jet is an artifact of Rosen-frame observers running to transverse infinity under the singular coordinate transformation.
  2. [§V, Eqs. (123)–(130)] The same issue affects the singular solution: the tetrad (126) contains 1/cos(η0u+φ0), which diverges at the curvature singularity, and the limiting statement (130) is again a limit of quantities defined in a frame that ceases to exist. In addition, in both solutions the limit occurs at finite affine parameter (u reaches a finite value), not at proper-time infinity. The abstract's phrase 'speed asymptotically approaches the speed of light' is therefore ambiguous: for the singular solution the geodesic terminates at the singularity, while for the nonsingular solution it reaches a coordinate singularity at finite proper time and the BJR chart cannot follow it further. Please state precisely the sense of 'asymptotic' intended, and specify whether the result describes the approach to the boundary, a late-time limit after extension, or both.
minor comments (4)
  1. [§III A, Eq. (73)] The hypergeometric solution for R(u) is stated without derivation; a brief outline or a reference to the standard reduction would help the reader verify that it indeed solves Eq. (72).
  2. [§II, Eq. (49)] The constant length scale ℓ entering the GEM energy-momentum tensor is introduced as an intrinsic scale but never given a physical identification; the paper should clarify whether ℓ is fixed by the averaging procedure or remains a free auxiliary parameter, and why that does not affect the geodesic results.
  3. [§IV D, Fig. 1] The caption of Figure 1 should state explicitly that the numerical integration of the Jacobi system continues smoothly beyond the BJR chart boundary ϖ = π/2, and the axes of the plots should be labeled.
  4. [§IV C, Eq. (112)] The text notes that exceptional geodesics with C1 = e C2 (or C2 = −e C1) do not join the jet, but it does not quantify the measure of such geodesics; a brief statement that these are a set of measure zero among initial data would make the 'most' in the abstract precise.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the cosmic-jet limit is derived from the exact geodesic equations and the adapted tetrad, not fed in as an assumption.

full rationale

The central claim, Eqs. (112) and (130), is obtained by direct integration of the geodesic equations in the exact solutions (87) and (117). The constants C1, C2, and Cu are constants of motion derived from the Killing vector fields, and the measured velocity components U^\hat{\alpha} in Eq. (110) are the projections of the geodesic 4-velocity onto the adapted orthonormal tetrad (30). The limits (V^\hat{1}, V^\hat{2}, V^\hat{3}) -> (0, 0, 1) and Gamma -> infinity as S^2 -> 1 (or cos(eta0 u + phi0) -> 0) follow algebraically from these expressions, with no parameter fitted to the target result. The polarization sense is defined through the sign of d(K2/K1)/du, but the cosmic-jet derivation does not presuppose the polarization sense; it holds for arbitrary values of the motion constants. The arbitrary length scale ell in the GEM energy-momentum tensor (49) is auxiliary and does not enter the jet derivation. Prior cosmic-jet papers are cited only as background and comparison, not as the justification of the result presented here. The coordinate-boundary issue at S^2 = 1 and at the curvature singularity is a question about the physical interpretation of a limit taken in the Baldwin-Jeffrey-Rosen chart, not a circularity in the derivation. Thus no circular step, by construction or by self-citation, is exhibited.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The central geodesic and cosmic jet claims rest on standard GR background results plus the specific metric ansatz (25). The only ad hoc parameter is the GEM length scale ℓ, which is auxiliary. No new particles, fields, or dimensions are introduced.

free parameters (1)
  • ℓ (GEM length scale) = unspecified
    Constant intrinsic lengthscale introduced in Eq. (49) to define the GEM energy-momentum tensor from the Bel-Robinson tensor. It is not fitted to data and does not affect the geodesic or cosmic jet claims.
assumptions (3)
  • domain assumption Metric ansatz (25) represents a general plane gravitational wave spacetime in Baldwin-Jeffrey-Rosen coordinates.
    The paper restricts to spacetimes with five Killing vectors, a standard subclass of pp-waves. This is an assumption on the form of the metric that underlies all later equations.
  • standard math The Ricci-flat condition (27) is the correct field equation for metric (25).
    Follows from Rμν = 0 for the given metric; stated without derivation but consistent with the standard plane-wave literature.
  • domain assumption The Fermi coordinate expansion (10)-(11) is valid to second order in spatial distance.
    Used to derive the generalized Jacobi equation (62)-(64). This is a standard approximation in the GEM framework but limits the validity of the Fermi-frame geodesic equations to a small neighborhood of the fiducial observer.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Elliptically Polarized Plane Gravitational Waves." pith.science (2026). https://pith.science/paper/6FUFUY53

@misc{pith2026250111503,
  author       = {Pith},
  title        = {Pith review of: Elliptically Polarized Plane Gravitational Waves},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6FUFUY53}},
  note         = {Machine review of arXiv:2501.11503}
}
read the original abstract

Exact plane gravitational radiation fields are presented within the framework of general relativity and their properties are described. The physics of nonlinear elliptically polarized plane gravitational waves is developed in close analogy with electromagnetic waves. The motion of free test particles in the dynamic gravitational fields of elliptically polarized plane waves is investigated. In particular, we demonstrate the cosmic jet property of these spacetimes, namely, most timelike geodesics tend to line up in the direction of wave propagation and produce a cosmic jet whose speed asymptotically approaches the speed of light.

Figures

Figures reproduced from arXiv: 2501.11503 by the authors.

Figure 1
Figure 1. FIG. 1: The results of the numerical integration of system ( [PITH_FULL_IMAGE:figures/full_fig_p025_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Cosmic Jets in General Relativity

    gr-qc 2025-06 conditional novelty 6.0 of 10

    Free particles and scalar waves in Kasner and plane-wave spacetimes asymptotically align into jets that move at nearly the speed of light relative to fiducial observers.

Reference graph

Works this paper leans on

67 extracted references · 29 canonical work pages · cited by 1 Pith paper

  1. [1]

    We return to this special nonsingular solution in Section IV

    Finally, we mention that in this special case the nonzero components of the acceleration tensor (41) can be obtained from Ω = 1 2 η [1 − sin(ηu + φ)] (76) and the corresponding angle of rotation (42) is given by Θ = 1 2 [ηu + φ + cos(ηu + φ) + φ′] , (77) where φ′ is an integration constant that depends on the particular fiducial observer under considerati...

    work page

  2. [2]

    , (50) where k = ∂t + ∂z. That is, the GEM energy-momentum tensor of a general elliptically polarized plane gravitational wave behaves like the energy-momentum tensor of a bundle of null rays with energy density given by ρg. Let us note that rotation (44) that maps ( K1, K2) to (K1, K2) implies ρg = 2ℓ2 (K2 1 + K2

    work page

  3. [3]

    , (51) 13 which can simplify the calculation of the radiation energy density. For linear waves of the previous section, for instance, we have ρg = 1 2 ℓ2ω4(h2 + + h2 ×), which agrees with the result obtained from the Landau-Lifshitz energy-momentum pseudotensor [13, 53] for ℓ = ( √ 8π ω)− 1 2 . Finally, relative to the observer in the Fermi frame fixed at...

    work page

  4. [4]

    (A7) Therefore, we can write T ˆα ˆβ = ρg k ˆα k ˆβ , k = ∂t + ∂z , (A8) where k is the covariantly constant null vector field that represents the propagation vector of the gravitational plane wave in the z direction at the speed of light. Appendix B: F ermi Connection Coefficients In this Appendix, Christoffel symbols Γ ˆµ ˆν ˆρ for the Fermi coordinate ...

    work page

  5. [5]

    Observation of Gravitational Waves from a Binary Black Hole Merger

    B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, R. X. Adhikari et al. (LIGO Scientific Collaboration and Virgo Col- laboration), “Observation of Gravitational Waves from a Binary Black Hole Merger”, Phys. Rev. Lett. 116, 061102 (2016)

    work page 2016

  6. [6]

    GW170817: Observation of gravitational waves from a binary neutron star inspiral

    B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), “GW170817: Observation of gravitational waves from a binary neutron star inspiral”, Phys. Rev. Lett. 119, 161101 (2017)

    work page 2017

  7. [7]

    Constraint likelihood analy- sis for a network of gravitational wave detectors

    S. Klimenko, S. Mohanty, M. Rakhmanov and G. Mitselmakher, “Constraint likelihood analy- sis for a network of gravitational wave detectors”, Phys. Rev. D 72, 122002 (2005). [arXiv:gr- qc/0508068 [gr-qc]]

    work page arXiv 2005

  8. [8]

    A coherent method for detection of gravitational wave bursts

    S. Klimenko, I. Yakushin, A. Mercer and G. Mitselmakher, “A coherent method for detection of gravitational wave bursts”, Classical Quantum Gravity 25, 114029 (2008)

    work page 2008

Show all 67 references
  1. [9]

    On the time lags of the LIGO signals

    J. Creswell, S. von Hausegger, A. D. Jackson, H. Liu and P. Naselsky, “On the time lags of the LIGO signals”, JCAP 08, 013 (2017). [arXiv:1706.04191 [astro-ph.IM]]

    2017 arXiv

  2. [10]

    Search for Tensor, Vector, and Scalar Po- larizations in the Stochastic Gravitational-Wave Background

    B. P. Abbott et al. [LIGO Scientific and Virgo], “Search for Tensor, Vector, and Scalar Po- larizations in the Stochastic Gravitational-Wave Background”, Phys. Rev. Lett. 120, no.20, 201102 (2018). [arXiv:1802.10194 [gr-qc]]

    2018 arXiv

  3. [11]

    Template Bank for Com- pact Binary Coalescence Searches in Gravitational Wave Data: A General Geometric Place- ment Algorithm

    J. Roulet, L. Dai, T. Venumadhav, B. Zackay and M. Zaldarriaga, “Template Bank for Com- pact Binary Coalescence Searches in Gravitational Wave Data: A General Geometric Place- ment Algorithm”, Phys. Rev. D 99, no.12, 123022 (2019). [arXiv:1904.01683 [astro-ph.IM]]

    2019 arXiv

  4. [12]

    A template-free approach for waveform extraction of gravitational wave events

    A. Akhshi, H. Alimohammadi, S. Baghram, S. Rahvar, M. R. R. Tabar and H. Arfaei, “A template-free approach for waveform extraction of gravitational wave events”, Sci. Rep. 11, no.1, 20507 (2021). 30

    2021

  5. [13]

    Gravitational-Wave Phasing of Quasicircular Compact Binary Systems to the Fourth-and-a-Half Post-Newtonian Order

    L. Blanchet, G. Faye, Q. Henry, F. Larrouturou and D. Trestini, “Gravitational-Wave Phasing of Quasicircular Compact Binary Systems to the Fourth-and-a-Half Post-Newtonian Order”, Phys. Rev. Lett. 131, no.12, 121402 (2023). [arXiv:2304.11185 [gr-qc]]

    2023 arXiv

  6. [14]

    Gravitational-wave flux and quadrupole modes from quasicircular nonspinning compact binaries to the fourth post- Newtonian order

    L. Blanchet, G. Faye, Q. Henry, F. Larrouturou and D. Trestini, “Gravitational-wave flux and quadrupole modes from quasicircular nonspinning compact binaries to the fourth post- Newtonian order”, Phys. Rev. D 108, no.6, 064041 (2023). [arXiv:2304.11186 [gr-qc]]

    2023 arXiv

  7. [15]

    Parametrizing gravitational-wave polarizations

    M. Isi, “Parametrizing gravitational-wave polarizations”, Classical Quantum Gravity 40, no.20, 203001 (2023). [arXiv:2208.03372 [gr-qc]]

    2023 arXiv

  8. [16]

    The NANOGrav 15 yr Data Set: Evidence for a Gravitational- wave Background

    G. Agazie et al.[NANOGrav], “The NANOGrav 15 yr Data Set: Evidence for a Gravitational- wave Background”, Astrophys. J. Lett.951, no.1, L8 (2023). [arXiv:2306.16213 [astro-ph.HE]]

    2023 arXiv

  9. [17]

    On the detection of a stochastic background of gravita- tional radiation by the Doppler tracking of spacecraft

    B. Mashhoon and L. P. Grishchuk, “On the detection of a stochastic background of gravita- tional radiation by the Doppler tracking of spacecraft”, Astrophys. J. 236, 990-999 (1980)

    1980

  10. [18]

    Pioneer 10 Search for Gravitational Waves—Limits on a Possible Isotropic Cosmic Background of Radiation in the Microhertz Region

    J. D. Anderson and B. Mashhoon, “Pioneer 10 Search for Gravitational Waves—Limits on a Possible Isotropic Cosmic Background of Radiation in the Microhertz Region”, Astrophys. J. 290, 445-448 (1985)

    1985

  11. [19]

    Exact solutions of the gravitational field equations

    J. Ehlers and W. Kundt, “Exact solutions of the gravitational field equations”, in Gravitation: An Introduction to Current Research, ed. L. Witten (Wiley, New York, 1962), pp. 49-101

    1962

  12. [20]

    Stephani, D

    H. Stephani, D. Kramer, M. A. H. MacCallum, C. Hoenselaers and E. Herlt, Exact Solutions of Einstein ’s Field Equations, 2nd edn (Cambridge University Press, Cambridge, UK, 2003)

    2003

  13. [21]

    J. B. Griffiths and J. Podolsky, Exact Space-Times in Einstein ’s General Relativity(Cambridge University Press, Cambridge, UK, 2009)

    2009

  14. [22]

    General polarization modes for the Rosen gravitational wave

    B. Cropp and M. Visser, “General polarization modes for the Rosen gravitational wave”, Classical Quantum Gravity 27, 165022 (2010). [arXiv:1004.2734 [gr-qc]]

    2010 arXiv

  15. [23]

    Optics in a nonlinear gravitational plane wave

    A. I. Harte, “Optics in a nonlinear gravitational plane wave”, Classical Quantum Gravity 32, no.17, 175017 (2015). [arXiv:1502.03658 [gr-qc]]

    2015 arXiv

  16. [24]

    The Memory Effect for Plane Gravitational Waves

    P. M. Zhang, C. Duval, G. W. Gibbons and P. A. Horvathy, “The Memory Effect for Plane Gravitational Waves”, Phys. Lett. B 772, 743-746 (2017). [arXiv:1704.05997 [gr-qc]]

    2017 arXiv

  17. [25]

    Soft gravitons and the memory effect for plane gravitational waves

    P. M. Zhang, C. Duval, G. W. Gibbons and P. A. Horvathy, “Soft gravitons and the memory effect for plane gravitational waves”, Phys. Rev. D 96, no.6, 064013 (2017). [arXiv:1705.01378 [gr-qc]]

    2017 arXiv

  18. [26]

    Velocity Memory Effect for 31 Polarized Gravitational Waves

    P. M. Zhang, C. Duval, G. W. Gibbons and P. A. Horvathy, “Velocity Memory Effect for 31 Polarized Gravitational Waves”, JCAP 05, 030 (2018). [arXiv:1802.09061 [gr-qc]]

    2018 arXiv

  19. [27]

    Scaling and conformal symmetries for plane gravitational waves

    P. M. Zhang, M. Cariglia, M. Elbistan and P. A. Horvathy, “Scaling and conformal symmetries for plane gravitational waves”, J. Math. Phys. 61, no.2, 022502 (2020). [arXiv:1905.08661 [gr- qc]]

    2020 arXiv

  20. [28]

    Singularities of plane gravitational waves in Einstein’s general relativity

    T. Wang, J. Fier, B. Li, G. L¨ u, Z. Wang, Y. Wu and A. Wang, “Singularities of plane gravitational waves in Einstein’s general relativity”, Gen. Relativ. Gravit. 52, no.2, 21 (2020). [arXiv:1807.09397 [gr-qc]]

    2020 arXiv

  21. [29]

    Persistent gravitational wave observables: Nonlinear plane wave spacetimes

    ´E. ´E. Flanagan, A. M. Grant, A. I. Harte and D. A. Nichols, “Persistent gravitational wave observables: Nonlinear plane wave spacetimes”, Phys. Rev. D 101, no.10, 104033 (2020). [arXiv:1912.13449 [gr-qc]]

    2020 arXiv

  22. [30]

    Twisted Gravitational Waves

    D. Bini, C. Chicone and B. Mashhoon, “Twisted Gravitational Waves”, Phys. Rev. D 97, no.6, 064022 (2018). [arXiv:1801.06003 [gr-qc]]

    2018 arXiv

  23. [31]

    Spinning Particles in Twisted Gravita- tional Wave Spacetimes

    D. Bini, C. Chicone, B. Mashhoon and K. Rosquist, “Spinning Particles in Twisted Gravita- tional Wave Spacetimes”, Phys. Rev. D 98, no.2, 024043 (2018). [arXiv:1805.07080 [gr-qc]]

    2018 arXiv

  24. [32]

    Twisted Gravitational Waves of Petrov Type D

    K. Rosquist, D. Bini and B. Mashhoon, “Twisted Gravitational Waves of Petrov Type D”, Phys. Rev. D 98, no.6, 064039 (2018). [arXiv:1807.09214 [gr-qc]]

    2018 arXiv

  25. [33]

    Twisted Gravitational Waves in the Presence of a Cosmo- logical Constant

    H. Firouzjahi and B. Mashhoon, “Twisted Gravitational Waves in the Presence of a Cosmo- logical Constant”, Phys. Rev. D 100, no.8, 084027 (2019). [arXiv:1904.01249 [gr-qc]]

    2019 arXiv

  26. [34]

    Vacuum gravitational fields with a null Killing vector

    G. Dautcourt, “Vacuum gravitational fields with a null Killing vector”, Gen. Relativ. Gravit. 52, no.2, 10 (2020). [arXiv:1910.00561 [gr-qc]]

    2020 arXiv

  27. [35]

    P. A. Hogan and D. Puetzfeld, Exact Space-Time Models of Gravitational Waves(Springer- Briefs in Physics, Springer, 2022)

    2022

  28. [36]

    Exact parallel waves in general relativity

    C. Roche, A. B. Aazami and C. Cederbaum, “Exact parallel waves in general relativity”, Gen. Relativ. Gravit. 55, no.2, 40 (2023). [arXiv:2207.03591 [gr-qc]]

    2023 arXiv

  29. [37]

    The generalized Jacobi equation

    C. Chicone and B. Mashhoon, “The generalized Jacobi equation”, Classical Quantum Gravity 19, 4231-4248 (2002). [arXiv:gr-qc/0203073 [gr-qc]]

    2002 arXiv

  30. [38]

    Explicit Fermi coordinates and tidal dynamics in de Sitter and G¨ odel spacetimes

    C. Chicone and B. Mashhoon, “Explicit Fermi coordinates and tidal dynamics in de Sitter and G¨ odel spacetimes”, Phys. Rev. D74, 064019 (2006). [arXiv:gr-qc/0511129 [gr-qc]]

    2006 arXiv

  31. [39]

    Gravitomagnetic helicity

    D. Bini, B. Mashhoon and Y. N. Obukhov, “Gravitomagnetic helicity”, Phys. Rev. D 105, no.6, 064028 (2022). [arXiv:2112.07550 [gr-qc]]

    2022 arXiv

  32. [40]

    On Tidal Resonance

    B. Mashhoon, “On Tidal Resonance”, Astrophys. J. 223, 285-298 (1978). 32

    1978

  33. [41]

    Helicity-rotation-gravity coupling for gravitational waves

    J. Ramos and B. Mashhoon, “Helicity-rotation-gravity coupling for gravitational waves”, Phys. Rev. D 73, 084003 (2006). [arXiv:gr-qc/0601054 [gr-qc]]

    2006 arXiv

  34. [42]

    Properties and Patterns of Polarized Gravitational Waves

    B. Mashhoon and S. Rahvar, “Properties and Patterns of Polarized Gravitational Waves”, Universe 9, no.1, 6 (2023). [arXiv:2211.01691 [gr-qc]]

    2023 arXiv

  35. [43]

    A note on the description of plane gravitational waves in Fermi coordinates

    M. L. Ruggiero, “A note on the description of plane gravitational waves in Fermi coordinates”, Eur. Phys. J. Plus 138, no.9, 792 (2023). [arXiv:2309.05599 [gr-qc]]

    2023 arXiv

  36. [44]

    Einstein spaces which are mapped conformally on each other

    H. W. Brinkmann, “Einstein spaces which are mapped conformally on each other”, Math. Ann. 94, 119-145 (1925)

    1925

  37. [45]

    The relativity theory of plane waves

    O. R. Baldwin and G. B. Jeffrey, “The relativity theory of plane waves”, Proc. Roy. Soc. London A 111, 95-104 (1926)

    1926

  38. [46]

    Plane polarized waves in the general theory of relativity

    N. Rosen, “Plane polarized waves in the general theory of relativity”, Phys. Z. Sowjetunion 12, 366-372 (1937)

    1937

  39. [47]

    Plane gravitational waves in general relativity

    H. Bondi, “Plane gravitational waves in general relativity”, Nature 179, 1072-1073 (1957)

    1957

  40. [48]

    Gravitational waves in general relativity. III. Exact plane waves

    H. Bondi, F. A. E. Pirani and I. Robinson, “Gravitational waves in general relativity. III. Exact plane waves”, Proc. Roy. Soc. London A 251, 519-533 (1959)

    1959

  41. [49]

    Generalized plane fronted gravitational waves in any dimension

    Y. N. Obukhov, “Generalized plane fronted gravitational waves in any dimension”, Phys. Rev. D 69, 024013 (2004). [arXiv:gr-qc/0310121 [gr-qc]]

    2004 arXiv

  42. [50]

    Gravitational superenergy tensor

    B. Mashhoon, J. C. McClune and H. Quevedo, “Gravitational superenergy tensor”, Phys. Lett. A 231, 47-51 (1997). [arXiv:gr-qc/9609018 [gr-qc]]

    1997 arXiv

  43. [51]

    On the Gravitoelectromagnetic stress-energy tensor

    B. Mashhoon, J. C. McClune and H. Quevedo, “On the Gravitoelectromagnetic stress-energy tensor”, Classical Quantum Gravity 16, 1137-1148 (1999). [arXiv:gr-qc/9805093 [gr-qc]]

    1999 arXiv

  44. [52]

    Gravitoelectromagnetism,

    B. Mashhoon, “Gravitoelectromagnetism,” in: Reference Frames and Gravitomagnetism, edited by J.-F. Pascual-Sanchez, L. Floria, A. San Miguel and F. Vicente (World Scientific, Singapore, 2001), pp. 121-132. [arXiv:gr-qc/0011014 [gr-qc]]

    2001 arXiv

  45. [53]

    Gravitoelectromagnetism: A brief review

    B. Mashhoon, “Gravitoelectromagnetism: A brief review”, in: The Measurement of Gravit- omagnetism: A Challenging Enterprise, edited by L. Iorio (Nova Science, New York, USA, 2007), pp. 29–39. [arXiv: gr-qc/0311030]

    2007 arXiv

  46. [54]

    On the energy content of electromagnetic and gravitational plane waves through super-energy tensors

    D. Bini and A. Geralico, “On the energy content of electromagnetic and gravitational plane waves through super-energy tensors”, Classical Quantum Gravity 35, no.16, 165006 (2018). [arXiv:1809.05305 [gr-qc]]

    2018 arXiv

  47. [55]

    Rotating Gravitational Waves

    B. Mashhoon and H. Quevedo, “Rotating Gravitational Waves”, Phys. Lett. A 151, 464-468 33 (1990)

    1990

  48. [56]

    On a class of rotating gravitational waves

    B. Mashhoon, J. C. McClune and H. Quevedo, “On a class of rotating gravitational waves”, Classical Quantum Gravity 17, 533-549 (2000). [arXiv: gr-qc/9609017]

    2000 arXiv

  49. [57]

    L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields(Pergamon Press, Oxford, 1971)

    1971

  50. [58]

    Abramowitz and I

    M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions(National Bureau of Standards, Washington, D.C., 1964)

    1964

  51. [59]

    Gravitomagnetic Jets

    C. Chicone and B. Mashhoon, “Gravitomagnetic Jets”, Phys. Rev. D 83, 064013 (2011). [arXiv:1005.1420 [gr-qc]]

    2011 arXiv

  52. [60]

    Gravitomagnetic Accelerators

    C. Chicone and B. Mashhoon, “Gravitomagnetic Accelerators”, Phys. Lett. A 375, 957-960 (2011). [arXiv:1005.2768 [gr-qc]]

    2011 arXiv

  53. [61]

    Cosmic Jets,

    C. Chicone, B. Mashhoon and K. Rosquist, “Cosmic Jets,” Phys. Lett. A 375, 1427-1430 (2011). [arXiv:1011.3477 [gr-qc]]

    2011 arXiv

  54. [62]

    Peculiar velocities in dynamic spacetimes

    D. Bini and B. Mashhoon, “Peculiar velocities in dynamic spacetimes”, Phys. Rev. D 90, no.2, 024030 (2014). [arXiv:1405.4430 [gr-qc]]

    2014 arXiv

  55. [63]

    Anisotropic Gravitational Collapse and Cosmic Jets

    D. Bini, C. Chicone and B. Mashhoon, “Anisotropic Gravitational Collapse and Cosmic Jets”, Phys. Rev. D 96, no.8, 084034 (2017). [arXiv:1708.01040 [gr-qc]]

    2017 arXiv

  56. [64]

    On the energy transported by exact plane gravitational-wave solutions

    Y. N. Obukhov, J. G. Pereira and G. F. Rubilar, “On the energy transported by exact plane gravitational-wave solutions”, Classical Quantum Gravity26, 215014 (2009). [arXiv:0909.4408 [gr-qc]]

    2009 arXiv

  57. [65]

    Tetrad Fields, Reference Frames, and the Gravitational Energy–Momentum in the Teleparallel Equivalent of General Relativity

    J. W. Maluf, F. L. Carneiro, S. C. Ulhoa and J. F. d. Rocha-Neto, “Tetrad Fields, Reference Frames, and the Gravitational Energy–Momentum in the Teleparallel Equivalent of General Relativity”, Ann. Phys. (Berlin) 535, no.12, 2300241 (2023). [arXiv:2306.03676 [gr-qc]]

    2023 arXiv

  58. [66]

    Energy of gravitational radiation and the background energy of the space-time

    J. W. Maluf, F. L. Carneiro, S. C. Ulhoa and J. F. da Rocha-Neto, “Energy of gravitational radiation and the background energy of the space-time”, Phys. Lett. B 858, 139041 (2024). [arXiv:2405.15499 [gr-qc]]

    2024 arXiv

  59. [67]

    Gravitational energy in pp-wave spacetimes

    R. D. Costa and J. B. Formiga, “Gravitational energy in pp-wave spacetimes”, [arXiv:2501.02290 [gr-qc]]

    arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.