Cosmic Jets in General Relativity

Bahram Mashhoon

REVIEW 3 major objections 3 minor 32 references

Cosmic Jets in General Relativity

T0 review · 3 major / 3 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read In certain time-dependent solutions of general relativity, free test particles and null rays asymptotically line up with respect to comoving observers into jets whose measured speed approaches the speed of light; the same alignment is…

desk verdict A mostly sound review of the author's own geodesic jet results, with one genuinely new scalar-field solution; the abstract outruns the demonstrated wave-scenario claims. read the letter →

arxiv 2506.07669 v1 pith:47OZ2MYU submitted 2025-06-09 gr-qc

Bahram Mashhoon This is my paper

classification gr-qc

keywords generalrelativitycosmicjetsKasnerspacetimeplanegravitationalwavesgeodesicmotionscalarwaveequationfiducialobserversjetandcounterjet

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

This paper argues that general relativity alone can form cosmic jets: small bodies and light rays that, as measured by observers at rest in a time-dependent gravitational field, asymptotically line up in a common direction and approach the speed of light. It establishes this in two exact vacuum spacetimes: the Kasner cosmology, where geodesics line up along the axis that is contracting, and plane gravitational waves, where, when the two wave exponents have opposite signs, geodesics line up along the propagation direction while a counterjet appears toward the wavefront singularity. The paper also solves the scalar wave equation in these spacetimes and shows that, in the geometric-optics limit, the wave phase reproduces the same jet alignment, so the effect is not an artifact of treating particles as pointlike. If correct, the result implies that collimated ultra-relativistic outflows need no plasma, magnetic field, or central engine, only a dynamic gravitational field.

What carries the argument

The load-bearing construction is the measurement of geodesic 4-velocities relative to a congruence of fiducial observers at rest in the spacetime, using their adapted orthonormal tetrad frames: $u^{\hat\alpha}=u^\mu\chi_\mu^{\hat\alpha}$, with $\chi^\mu_{\hat 0}=(-g_{tt})^{-1/2}\delta^\mu_0$. In Kasner the constants of motion $k_1,k_2,k_3$ from the spatial Killing vectors produce $W=\sum_i k_i^2 t^{-2p_i}$; as $t\to\infty$ the smallest exponent $p_1$ dominates, forcing the measured velocity toward the collapsing axis. In the plane-wave case the constants $q_0,q_1,q_2$ and the retarded time $u=t-z$ play the same role; the asymptotic direction is fixed by whether $u^{-2s_1}$ or $u^{-2s_2}$ grows with $u$, which occurs only when one exponent is negative. For scalar fields, the corresponding object is $D(u)=(C_1^2 Q^2-2C_1C_2S+C_2^2P^2)/\Delta$, whose divergence in $u$ encodes the same jet direction in the geometric-optics phase.

What would settle it

Integrate Eqs. (43)-(44) for the plane wave with $s_1=s_2=1/2$ (which satisfies the vacuum condition) and follow the measured velocity from Eq. (47): for a timelike geodesic with $q_0>1$ and $q_1,q_2\ne 0$, $\Gamma\to(1+q_0^2)/(2q_0)$ and $\hat V_z\to(1-q_0^2)/(1+q_0^2)$, so the particle moves opposite to the wave with speed below $c$. This calculation, or an analogous integration for any same-sign-exponent wave, separates the regime where the paper's jet claim holds from the regime where it does not.

Watch

Extended reading notes

Core claim

The central claim is about measured velocities, not coordinate velocities. In the Kasner metric $ds^2=-dt^2+t^{2p_1}dx^2+t^{2p_2}dy^2+t^{2p_3}dz^2$ with $p_1<p_2<p_3$ and $p_1\le 0$, every future-directed timelike or null geodesic with $k_1\ne 0$ satisfies $\hat v\to(k_1/|k_1|,0,0)$ as $t\to\infty$, a double jet along the collapsing $x$-axis whose speed tends to the speed of light; as $t\to 0$, the same mechanism aligns geodesics along the $z$-axis (or the $y$-axis when $k_3=0$). In the plane-wave spacetime $ds^2=-dt^2+dz^2+u^{2s_1}dx^2+u^{2s_2}dy^2$, $u=t-z$, with $s_1^2+s_2^2=s_1+s_2$, timelike and null geodesics satisfy $\hat V\to(0,0,1)$ as $u\to\infty$ whenever $s_1$ and $s_2$ have opposite signs, so the jet moves exactly in the direction of wave propagation at unit speed; a counterjet appears as $u\to 0$. When both exponents are positive, the asymptotic speed stays below the speed of light and can even point opposite to the wave if $q_0>1$. The scalar-field analysis shows that, in the fast-jet regime, the phase integral $\int D(u)\,du$ diverges as $u\to\infty$, so massive and massless scalar waves exhibit the same directional locking.

Load-bearing premise

The wave-scenario jet reaching the speed of light depends entirely on the two plane-wave exponents having opposite signs; the paper offers no physical mechanism or observational constraint that selects that parameter range, and for same-sign exponents the measured speed stays below $c$ and can even reverse direction.

Editorial extensions

If this is right

In the Kasner collapse scenario, any free particle or null ray with nonzero momentum along the collapsing $x$-axis is observed to join a double jet along that axis, with speed asymptotically equal to $c$; near $t\to 0$ the same locking occurs along the $z$-axis.
In the wave scenario with opposite-sign exponents, both timelike and null geodesics asymptotically travel exactly in the direction of the wave at speed $c$, and a counterjet develops on approach to the wavefront singularity $u=0$.
For plane waves with $s_1>0$ and $s_2>0$, the jet speed remains below $c$ and its direction depends on $q_0$; particles with $q_0>1$ move opposite to the wave, so the light-speed wave jet is a special parameter regime rather than a generic property.
The scalar-wave geometric-optics correspondence implies the alignment is shared by massive and massless matter waves, so the jet phenomenon is not an artifact of treating particles as pointlike.
The two scenarios are exact vacuum solutions of Einstein's equations; if such alignment occurs in realistic dynamic fields, it would constitute a purely gravitational mechanism for jet collimation.

Reading between the lines

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

Editorial inference: the sign-only dependence on $k_1$ in Eq. (15) means that even an arbitrarily small momentum along the collapsing axis eventually dominates; this threshold-free locking could be checked by numerical integration of the geodesic equations with small $k_1$.
Editorial inference: because the counterjet at $u\to 0$ is always directed along $+z$ regardless of the exponents, a finite gravitational-wave burst should produce a jet/counterjet asymmetry tied to the arrival of the wavefront, which is in principle observable with test masses or clocks along the propagation direction.
Editorial inference: the paper leaves the connection to astrophysical jets open; a natural next step is to ask whether the purely gravitational alignment direction can compete with magnetohydrodynamic collimation in a spacetime containing a long-wavelength gravitational wave.

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.

Desk Editor's Note

read the letter

Quick take: the geodesic sections are correct and clearly derived, and the explicit scalar-wave solution for the elliptically polarized plane-wave background (Eq. 65) is a real new calculation. But the abstract oversells the wave scenario: the speed-c alignment only occurs for unbounded power-law profiles with opposite-sign exponents, not for generic plane gravitational waves. The paper deserves a serious referee but needs a revised abstract and a clear caveat about profile generality.

What's actually new: the scalar field analysis in Section V, especially Eq. (65), which I haven't seen in the cited prior work (refs 9, 14, 15, 32). The Kasner and plane-wave geodesic results are reviews of earlier papers, mostly by the author, but they are derived explicitly and correctly. The paper is also honest that there is no known connection to astrophysical jets.

Where it's soft: the abstract says the wave scenario involves a jet in the wave direction and a counterjet, with speed approaching c, as if it were a generic property. The paper itself shows this requires s1 and s2 to have opposite signs (Section IV.A, IV.B). In that regime, one transverse scale factor in metric (28) collapses to zero while the other diverges as u→∞. That's not a generic plane wave; it's a singular, eternally growing/collapsing power-law profile. For a bounded sandwich wave with H_i(u) bounded between positive constants, the transverse velocity components stay finite, null rays keep transverse components, and there is no speed-c alignment. The u→0 behavior is interesting, but it concerns the singularity, not a propagating wave pulse.

The scalar-wave discussion is presented as strengthening the wave scenario, but it uses the same geometry and the standard WKB correspondence, so it's a consistency check, not independent confirmation. The citation pattern is heavily self-referential, but that's appropriate for a review of the author's own prior work; the new part is clearly identified.

Verdict: the core geodesic mathematics holds up. The framing needs work. A serious referee should ask for a revised abstract and an explicit statement that the speed-c wave jet applies to the unbounded power-law classes with opposite-sign exponents, and that bounded plane waves don't exhibit it. With that revision, this is a solid paper. Send it to peer review; don't desk reject.

Referee Report

3 major / 3 minor

Summary. This paper reviews two mechanisms—called "cosmic jets"—by which free test particles and null rays in exact solutions of general relativity can asymptotically align with a preferred spatial direction as measured by comoving fiducial observers. In the Kasner collapse scenario, Section II derives the geodesic equations from the constants of motion and shows that as t→∞ the measured 3-velocity tends to (±1,0,0) with speed approaching c; as t→0 an analogous double jet forms along the contracting z-axis. Sections III and V study scalar test fields in the same and related spacetimes and connect the WKB/eikonal limit to the geodesic results. In the wave scenario, Section IV treats the vacuum plane-wave metric ds²=-dt²+dz²+u^{2s1}dx²+u^{2s2}dy² and claims that, in addition to a counterjet, timelike and null geodesics form a jet along the propagation direction with speed approaching c. The detailed calculation shows that this alignment holds only for opposite-sign exponents (s1>0,s2<0) or (s1<0,s2>0), while for s1,s2>0 the asymptotic speed remains below c and the direction can be opposite to the wave for q0>1.

Significance. If accepted for their stated parameter regimes, the results provide a clean, explicit demonstration that time-dependent vacuum geometries can focus free geodesics in velocity space without matter or electromagnetic fields. The manuscript's strengths are its explicitness: the constants of motion, the tetrad projections, and the asymptotic limits in Eqs. (8)-(18) and (40)-(55) are derived step by step; the exact scalar-wave solutions in Section V are new and internally consistent; and the analysis contains no fitted parameters or numerical approximations. The Kasner part is elementary and sound. The plane-wave calculation is also correct, but the advertised generality of the wave scenario is narrower than the abstract suggests, and the scalar-wave analysis is a consistency check rather than an independent validation. The paper is therefore a useful review with a modest new contribution, and it will be publishable once the claims are scaled back to the regimes actually proven.

major comments (3)

[§IV.A, Eq. (52)] The abstract states that the wave scenario produces a cosmic jet whose speed approaches the speed of light, but the calculation in Section IV.A shows that this is true only for (s1>0,s2<0) or (s1<0,s2>0). For s1>0 and s2>0, Eq. (52) gives Γ→(1+q0²)/(2q0) and V_z→(1−q0²)/(1+q0²), whose magnitude is strictly less than 1 for every finite q0; moreover, for q0>1 the measured velocity is along −z, i.e. opposite to the wave, rather than "in the general direction of wave propagation." The abstract and the conclusions should restrict the speed-c claim to the opposite-sign regime and state the s1,s2>0 case separately.
[§IV, metric (28)] The speed-c alignment in Eqs. (51) and (53) uses H_i(u)=u^{s_i} with one exponent negative, so one transverse scale factor diverges while the other tends to zero as u→∞. The manuscript offers no argument that this unbounded power-law profile represents a generic plane gravitational wave. For a bounded sandwich wave, with P and Q in Eq. (56) bounded above and below by positive constants, the measured transverse velocity components q1/H1 and q2/H2 remain bounded, Γ does not diverge, and null geodesics do not asymptotically align with the z axis. A limitation paragraph defining the profile class for which the wave scenario holds is needed.
[§V, Eqs. (61)-(65)] The scalar-field analysis is not independent confirmation of the wave scenario. It is computed in the same metric (28)/(56), and the correspondence between the eikonal limit of the scalar equation and geodesic motion is a standard structural relation, so the agreement with Eqs. (51) and (53) is built into the setup. The text should describe Section V as a consistency check that illustrates the wave-particle correspondence, not as independent evidence that cosmic jets form.

minor comments (3)

[§III, Eq. (27)] The symbol W is reused for the sum κ1²t^{-2p1}+κ2²t^{-2p2}+κ3²t^{-2p3} after Eq. (9) defined W with k_i; the two are different quantities and should carry distinct notation.
[§V, Eq. (61)] The case C3=0 is dismissed with "there is a solution provided C3≠0," but the reader is not told why C3=0 is uninteresting. For a massive scalar the separated ansatz with C3=0 has no nontrivial solution, while for the massless field with C1=C2=0 it yields only a constant; a sentence stating this would remove ambiguity.
[§IV, Eqs. (50) and (54)] The term "counterjet" is used for the q1=q2=0 null ray in Eq. (50) and also for the s1,s2>0 null-geodesic limit in Eq. (54), but the paper does not define whether "counterjet" means exactly opposite to the wave or merely a second aligned family; defining the term would avoid confusion.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the Kasner and plane-wave jet results are derived explicitly from the metric and geodesic equations; self-citations are contextual, not load-bearing.

full rationale

The central results are derived self-containedly from the stated exact metrics. For the Kasner collapse scenario, Eqs. (5), (8), and (9) are the inputs, and Eqs. (14)-(15), (18) follow by direct asymptotic evaluation; the alignment along the collapsing axis is a mathematical consequence, not an assumed target. Similarly, in the wave scenario, the geodesic equations for metric (28) give the 4-velocity components in Eqs. (43)-(47), and the asymptotic alignments (51), (53), and (55) follow algebraically from the stated sign conditions on s1 and s2. No parameter is fitted to the jet outcome, and no uniqueness theorem or prior result is required to force the conclusion. The paper does cite the author's earlier works (e.g., [9], [14], [15], [30]-[32]) for historical context and for the claim that the scenarios have been demonstrated before, but the present derivation does not rely on those citations: every load-bearing equation is re-derived in this paper. The scalar-field analysis in Section V is not an independent validation—it uses the same spacetime geometry and the standard WKB correspondence—but it is presented as a consistency check, not as a separate first-principles prediction. The reviewer's concern that the opposite-sign plane-wave regime is only one branch of parameters is a question of scope and physical generality, not circularity. No step in the claimed derivation chain reduces to its own inputs by definition or by fitted renaming.

Assumptions & free parameters 2 free parameters · 4 assumptions · 1 invented entities

The paper introduces no fitted parameters or new entities. The free parameters are the arbitrary constants of the exact solutions (θ, p_i). The axioms are standard GR and the WKB correspondence. The central claim does not rest on any parameter fitted to data.

free parameters (2)

plane wave polarization angle θ
The angle θ parametrizes s1 and s2 via Eq. (32). It is arbitrary, not fitted, but the light-speed jet only occurs for θ in the ranges that make s1 and s2 opposite in sign.
Kasner exponents p1, p2, p3
Satisfy Eq. (6) and the ordering in Eq. (7). No specific values are fitted; the jet result holds for the whole allowed range with p1 < 0.

assumptions (4)

standard math Einstein field equations with standard matter content (vacuum or with Tμν) and the geodesic equation for free test particles.
Used throughout to define the spacetimes and particle motion; these are foundational postulates of general relativity.
domain assumption The WKB/eikonal correspondence between scalar wave propagation and geodesic motion.
Invoked in Sections III and V to connect the scalar field solutions to particle jets; this is a standard principle but is not rigorously proven in these spacetimes.
domain assumption The fiducial observers defined by U^μ = (-g_tt)^(-1/2) δ^μ_0 are physically admissible and their tetrads are parallel-propagated.
The jet velocities are defined relative to these observers (Eqs. 3-4, 33); the physical interpretation depends on this observer choice.
domain assumption The coordinate systems are valid for the asymptotic limits employed (t → ∞, t → 0, u → ∞, u → 0).
The jet behavior is an asymptotic statement; the paper assumes the limits can be taken along the geodesics without encountering coordinate singularities.

invented entities (1)

Cosmic jet
purpose: A descriptive term for the asymptotic alignment of geodesics; no new physical entity is introduced.
The term is a label for a known kinematic effect in the already-known spacetimes; it is not a new substance, force, or particle.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Cosmic Jets in General Relativity." pith.science (2026). https://pith.science/paper/47OZ2MYU

@misc{pith2026250607669,
  author       = {Pith},
  title        = {Pith review of: Cosmic Jets in General Relativity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/47OZ2MYU}},
  note         = {Machine review of arXiv:2506.07669}
}

read the original abstract

In certain general relativistic time-dependent gravitational fields, free test particles can asymptotically line up relative to fiducial static observers and produce a cosmic jet whose speed approaches the speed of light. Two scenarios for the formation of these purely gravitational jets have thus far been theoretically demonstrated: the double-jet collapse scenario and the wave scenario that involves both a cosmic jet in the general direction of wave propagation as well as a counterjet in the opposite direction. These scenarios are briefly reviewed in this paper. Moreover, to elucidate the process of jet formation in these scenarios, we study the propagation of scalar fields in related gravitational fields in connection with the correspondence between the scalar wave perturbations and the motion of free test particles and null rays.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

32 extracted references · 25 canonical work pages

[1]

M. D. Smith, Astrophysical Jets and Beams(Cambridge University Press, Cambridge, UK, 2012)

work page 2012
[2]

Relativistic Jets in Active Galactic Nuclei and Microquasars

G. Romero, M. Boettcher, S. Markoff and F. Tavecchio, “Relativistic Jets in Active Galactic Nuclei and Microquasars”, Space Sci. Rev. 207, no.1-4, 5-61 (2017). [arXiv:1611.09507 [astro- ph.HE]]

arXiv 2017
[3]

The content of astrophysical jets

G. E. Romero, “The content of astrophysical jets”, Astron. Nachr. 342, no.5, 727-734 (2021). [arXiv:2106.14346 [astro-ph.HE]]

arXiv 2021
[4]

M 87: a cosmic laboratory for decipher- ing black hole accretion and jet formation

K. Hada, K. Asada, M. Nakamura and M. Kino, “M 87: a cosmic laboratory for decipher- ing black hole accretion and jet formation”, Astron. Astrophys. Rev. 32, no.1, 5 (2024). [arXiv:2412.07083 [astro-ph.HE]]

arXiv 2024
[5]

Geometrical theorems on Einstein’s cosmological equations

E. Kasner, “Geometrical theorems on Einstein’s cosmological equations”, Am. J. Math. 43, 217-221 (1921)

work page 1921
[6]

Republication of: Geometrical theorems on Einstein’s cos- mological equations (by E. Kasner)

J. Wainwright and A. Krasi´ nski, “Republication of: Geometrical theorems on Einstein’s cos- mological equations (by E. Kasner)”, Gen. Relativ. Gravit. 40, 865-876 (2008)

work page 2008
[7]

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)

work page 2003
[8]

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

work page 2009

Show all 32 references

[9]

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
[10]

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
[11]

Gravitomagnetic Jets

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

2011 arXiv
[12]

Gravitomagnetic Accelerators

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

2011 arXiv
[13]

Double-Kasner Spacetime: Peculiar Velocities and Cosmic Jets

C. Chicone, B. Mashhoon and K. Rosquist, “Double-Kasner Spacetime: Peculiar Velocities and Cosmic Jets”, Phys. Rev. D 83, 124029 (2011). [arXiv:1104.5058 [gr-qc]] 17

2011 arXiv
[14]

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
[15]

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
[16]

Static and dynamic Melvin universes

D. Bini and B. Mashhoon, “Static and dynamic Melvin universes”, Phys. Rev. D 105, no.12, 124012 (2022). [arXiv:2202.02033 [gr-qc]]

2022 arXiv
[17]

Review of gravitomagnetic acceleration from accretion disks

J. Poirier and G. J. Mathews, “Review of gravitomagnetic acceleration from accretion disks”, Mod. Phys. Lett. A 30, no.38, 1530029 (2015)

2015
[18]

Gravitomagnetic acceleration from black hole accretion disks

J. Poirier and G. J. Mathews, “Gravitomagnetic acceleration from black hole accretion disks”, Classical Quantum Gravity 33, no.10, 107001 (2016)

2016
[19]

On Gravitational Chirality as the Genesis of Astrophysical Jets

R. W. Tucker and T. J. Walton, “On Gravitational Chirality as the Genesis of Astrophysical Jets”, Classical Quantum Gravity 34, no.3, 035005 (2017). [arXiv:1609.07322 [gr-qc]]

2017 arXiv
[20]

Chirality in Gravitational and Electromagnetic Interactions with Matter

R. W. Tucker and T. J. Walton, “Chirality in Gravitational and Electromagnetic Interactions with Matter”, Int. J. Geom. Meth. Mod. Phys. 15, 1840004 (2018). [arXiv:1805.08825 [gr-qc]]

2018 arXiv
[21]

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
[22]

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
[23]

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
[24]

Plane gravitational waves in general relativity

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

1957
[25]

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
[26]

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
[27]

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
[28]

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

2022
[29]

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]] 18

2023 arXiv
[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
[31]

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
[32]

Elliptically polarized plane gravitational waves

M. Molaei, S. Baghram and B. Mashhoon, “Elliptically polarized plane gravitational waves”, Phys. Rev. D 111, no.10, 104035 (2025). [arXiv:2501.11503 [gr-qc]]

2025 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

M. D. Smith, Astrophysical Jets and Beams(Cambridge University Press, Cambridge, UK, 2012)

work page 2012

[2] [2]

Relativistic Jets in Active Galactic Nuclei and Microquasars

G. Romero, M. Boettcher, S. Markoff and F. Tavecchio, “Relativistic Jets in Active Galactic Nuclei and Microquasars”, Space Sci. Rev. 207, no.1-4, 5-61 (2017). [arXiv:1611.09507 [astro- ph.HE]]

arXiv 2017

[3] [3]

The content of astrophysical jets

G. E. Romero, “The content of astrophysical jets”, Astron. Nachr. 342, no.5, 727-734 (2021). [arXiv:2106.14346 [astro-ph.HE]]

arXiv 2021

[4] [4]

M 87: a cosmic laboratory for decipher- ing black hole accretion and jet formation

K. Hada, K. Asada, M. Nakamura and M. Kino, “M 87: a cosmic laboratory for decipher- ing black hole accretion and jet formation”, Astron. Astrophys. Rev. 32, no.1, 5 (2024). [arXiv:2412.07083 [astro-ph.HE]]

arXiv 2024

[5] [5]

Geometrical theorems on Einstein’s cosmological equations

E. Kasner, “Geometrical theorems on Einstein’s cosmological equations”, Am. J. Math. 43, 217-221 (1921)

work page 1921

[6] [6]

Republication of: Geometrical theorems on Einstein’s cos- mological equations (by E. Kasner)

J. Wainwright and A. Krasi´ nski, “Republication of: Geometrical theorems on Einstein’s cos- mological equations (by E. Kasner)”, Gen. Relativ. Gravit. 40, 865-876 (2008)

work page 2008

[7] [7]

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)

work page 2003

[8] [8]

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

work page 2009