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On this page I collect permanent links to approved versions of some Wikipedia articles which I edited extensively (more or less).

Important notes:

  • Please do not edit this page. If you absolutely must, you can leave comments at my user talk page, although it may take some time before I see these since I expect to be fairly inactive after early April 2006.
  • Please do not try to edit these versions of Wikipedia articles! You won't alter the versions pointed to on this page, but you will revert the current version of the page, which is sure to annoy active editors, so please don't do that. If you think you have spotted an error in one of these articles, please see the most recent version and edit that (or complain in the talk page).

Thank you! ---CH 19:41, 6 April 2006 (UTC)


Some caveats:

  • Few if any of these articles were "complete" when I abandoned them to their miserable fate.
  • Some of them may even contain an error which I overlooked while hastily compiling this list (again, if you think you spotted one, don't complain to me, since I can't change the past; consult the most recent version and do what you will there).
  • If in any of these archived pages, you click on
    1. an internal link to another article, you will get the current versions of the indicated article (if it still exists); I hardly need say that the same goes for external links!
    2. an internal link to a category, you will get the current contents of that category, which may well contain all kinds of cranky pages, may no longer contain the article you were just looking at, or which indeed may longer even exist.
    3. "history", you will the most recent history; to see the history up to the version archived here, you may need to increase the lookback or even to scroll through several history pages.
    4. "talk", you will get the current talk page; to see comments contemporaneous with the version archived here, you may need to search archived talk pages for the article in question.
  • Wikimedia does not store webpages but rather reconstitutes them "on the fly" from various elements, so the Wikipedia site will try to serve archived articles as if they were written to comply with current wikipractices, which tends to result in progressively degraded appearance of archived pages. This is unfortunate, but beyond my control.

The following permalinks are organized with indentations roughly corresponding to the category tree as of 5 April 2006.


  1. Constraint counting


  1. Tidal tensor

Category:Invariant theory

  1. Newton's identities
  2. Schur polynomial

Category:Lie groups

  1. Lorentz group


  1. Crank (person)


  1. Bell's spaceship paradox
  2. Ehrenfest paradox

Category:Special functions

  1. Mathieu function

Category:Theories of gravitation

  1. Brans-Dicke theory
  2. Classical theories of gravitation
  3. Geometrodynamics
  4. Nordström's theory of gravitation
  5. Parameterized post-Newtonian formalism
  6. Polarizable vacuum
  7. Stochastic electrodynamics
  8. Whitehead's theory of gravitation
  9. Yilmaz theory of gravitation

Category:General relativity

  1. General relativity resources
  2. Geometrized unit system
  3. Geon (physics)
  4. Golden age of general relativity
  5. GRTensorII
  6. Raychaudhuri equation
  7. Sticky bead argument

Contributors to general relativity

  1. Contributors to general relativity
  2. Contributors to the mathematical background for general relativity
  3. Peter C. Aichelburg
  4. James M. Bardeen
  5. Abraham Haskel Taub
  6. Alfred Schild
  7. Amal Kumar Raychaudhuri
  8. Andrzej Trautman
  9. André Lichnerowicz
  10. Arthur Geoffrey Walker
  11. Basilis C. Xanthopoulos
  12. Brandon Carter
  13. Bruno Bertotti
  14. Carl H. Brans
  15. Clifford Martin Will
  16. Demetrios Christodoulou
  17. Dennis William Sciama
  18. Evgeny Lifshitz
  19. Ezra T. Newman
  20. George Barker Jeffery
  21. George Yuri Rainich
  22. Gunnar Nordström
  23. Hermann Bondi
  24. Isaak Markovich Khalatnikov
  25. James W. York
  26. Jørg Tofte Jebsen
  27. Louis Witten
  28. Luther P. Eisenhart
  29. Richard H. Price
  30. Richard Schoen
  31. Ronald Kantowski
  32. Roy Kerr
  33. Werner Israel
  34. Willem Jacob van Stockum
  35. William Morris Kinnersley

Category:Effects of gravitation

  1. Speed of gravity

Category:Exact solutions in general relativity

  1. Exact solutions in general relativity
  2. Aichelburg-Sexl ultraboost
  3. Bonnor beam
  4. Dust solution
  5. Electrovacuum solution
  6. Fluid solution
  7. Gravitational plane wave
  8. Gödel metric
  9. Lambdavacuum solution
  10. Monochromatic electromagnetic plane wave
  11. Null dust solution
  12. Petrov classification
  13. Pp-wave spacetime
  14. Scalar field solution
  15. Vacuum solution (general relativity)
  16. Van Stockum dust

Category:Mathematical methods in general relativity

  1. Cartan-Karlhede algorithm
  2. Congruence (general relativity)
  3. Energy condition
  4. Frame fields in general relativity
  5. Regge calculus
  6. Test particle
Category:Coordinate charts in general relativity
  1. Born coordinates
  2. Brinkmann coordinates
  3. Gaussian polar coordinates
  4. Isotropic coordinates
  5. Rindler coordinates
  6. Schwarzschild coordinates
Category:Tensors in general relativity
  1. Carminati-McLenaghan invariants
  2. Curvature invariant (general relativity)
  3. Kretschmann scalar
  4. Ricci decomposition

Category:Theorems in general relativity

  1. Birkhoff's theorem (relativity)
  2. Positive energy theorem

Unfinished work

As a courtesy, I removed the todo lists from articles I was working on, since these were mostly notes to myself which probably won't make sense to other editors. (In a few cases, I just removed the items listing suggested improvements which I believe could only be implemented by myself.)

Bel decomposition

  1. general first, specific later
    • n dimensions first, 1+3 later
  2. nontechnical first, technical later
    • mention role of Lluis Bel in first paragraph
    • in later technical paragraphs:
      • relate to matrix decomposition in MTW exercise
      • explain physical interpretation in gtr in a frame of the three pieces
      • make sure to contrast roles of frame and congruence in interpretation; choice of frame field adds additional geometric structure to the congruence
  3. add good citations at the end (original paper by Bel, MTW, plus some useful eprints on arXiv) in standard WikiProject GTR format

Bell's spaceship paradox

Tasks for expert:

Tasks for anyone:

  • copyedit (at one point we changed notation t,x,y,z -> T,X,Y,Z, and hopefully got everything changed)

Brans-Dicke theory

Tasks for expert:

  • better explanation of motivation for theory, especially variable gravitational "constant" and Dirac large number hypothesis,
  • explain Jordan "frame", Einstein "frame" [sic],
  • write and link to background articles on decomposition of metric tensor (see Carroll; see problem book for utility in comparing gravitational radiation in Brans-Dicke and other theories with gtr),
  • explain Faraoni critique (weak-field limit),
  • add material comparing exact solutions in most important cases (plane waves, static spherically symmetric perfect fluid balls) and add a good citation

Classical theories of gravitation

  • provide the promised discussion of motivations for alternatives to gtr, and sketchy comparisons of various classes of classical theories.

Congruence (general relativity)

Task for expert:

  • add case where acceleration vector does not vanish
  • add discussion of kinematics of null congruences

Tasks for anyone:

  • break up awkward long equation into a multline inlined equation

Gravitational radiation

Tasks not requiring expert knowledge:

  • remove duplicated content (e.g. Hulse and Taylor)
  • correct misspellings (I do see some of my own, but too lazy to correct 'em)
  • improve the citations by using citation templates,
  • improve obscure and clumsy writing (poor diction, inconsistent cases, split infinitives; this article is currently an grammarian's nightmare).

Tasks requiring expert knowledge:

  • the title and categorization of this article promise comparative discussion of gtr with other theories; this article should refer to articles (yet to be written) in Category:General relativity; much material currently appearing here should be moved to new articles in this category (or better yet, entirely new articles should be written from scratch, using much better diction, figures, etc.).
  • this is a highly developed field which is surveyed in several fine review papers; most textbooks have one or more chapters devoted to gravitational radiation; since this is an encylopedia article, cite these rather than research papers.
  • We need an article on Linearized theory of gravitational waves which first discusses the propagation and effect on test particles of linearized plane waves, especially monochromatic linearly and circularly polarized, then discusses multipole moments and the generation of waves.
  • Explain or at least mention linear perturbations of non-Minkowski backgrounds, but following standard textbooks this case deserves the most attention.
  • Why not an animation of the "cruciform motion" for linearly and circularly polarized waves? See MTW for hints. But don't forget to mention gravitomagnetic effects.
  • Don't forget to point out that not all radiation is quadrupole radiation.
  • This article should be contrasted with a new companion article on Far fields in general relativity which focuses on using weak-field theory to derive stationary far fields. Both weak-field rapid motion (radiation generation) and far-field stationary use a multipole expansion of the (trace-reversed) metric perturbatation tensor, but in different ways. See the textbook by Stephani for hints.
  • Very possibly a seperate article giving the detailed computations alluded to in my rewrite of examples of various kinds of radiation or non-radiating systems. It would be nice to offer animated images illustrating the various examples I gave (check with me to make sure you understand what I have in mind).
  • We need articles in Category:Exact solutions in general relativity. I've written one on Monochromatic electromagnetic plane wave and need to write the companion on monochromatic linearly polarized gravitational plane wave and monochromatic circularly polarized gravitational plane wave, and need to improve articles on pp wave spacetime and relevant coordinate systems, principally Brinkmann coordinates and Rosen coordinates. See also sticky bead argument.
  • These articles should reference new articles on relativistic multipoles and connect ultraboosts of Ernst vacuum objects (e.g. Kerr objects) to impulsive plane waves. See Aichelburg-Sexl ultraboost for the simplest special cases.
  • The phrase perturbation from flat spacetime is usually avoided in classical gravitation because there are linear and nonlinear perturbations (e.g. there are exact solutions which are nonlinear perturbations of FRW dusts).

Gravitational redshift

Tasks for expert:

  • reorganize: general/elementary first, specific/advanced later
  • make sure to clarify fact (mentioned by ErkDemon) that gravitational redshift is a prediction of metric theories in general, not just of gtr,
  • clarify fact that it doesn't assume Schwarzschild!
  • discuss weak-fields and cartesian type metric with potential (as in Einstein 1916)
  • discuss some examples of exact solutions, probably including Schwarzschild vacuum, Schwarzschild-de Sitter lambdavacuum, Reissner-Nördstrom electrovacuum, Kerr vacuum
  • in discussing Schwarzschild in Schwarzschild chart, make sure to explain meaning of coordinates, and explain the two principle null congruences,
  • in discussing Kerr vacuum, make sure to write out the two principal null congruences

Subsequent tasks for anyone:

  • spellcheck
  • improve diction, etc.
  • use proper citation templates.

Gravitational time dilation

Tasks which any Wikipedian can help with:

Tasks for expert:

  • elaborate on issues mentioned in talk page of this article
  • add citation to a standard textbook with particularly good discussion of these points


tasks for expert:

  • rewrite more along lines of most recent Mashhroon review article,
  • more NPOV,
  • be careful to explain that GEM is not the same thing at all as "gravity shielding" or EM fields allegedly producing antigravity; politely stress that GEM is mainstream but these two topics tend toward crackpottery,
  • write and link to background articles on "warp drives"; clarify relations to GEM alleged in current version,
  • maybe a small caveat about mainstream modes of partial interconversion between gravitational and EM fields; explain why these are not useful for "gravity shielding" or "exotic spacecraft propulsion" schemes!
  • in principle a better title would be gravitoelectromagnetism as per Mashhoon review but never mind,
  • distinguish carefully between weak-field, slowly moving test particle, and other assumptions,
  • explain relatation with Bel decomposition (valid generally) and mention strong-field cosmological GEM type extension of Dunbar et al.
  • distinguish between gravitomagnetism and gtr and other theories

Killing horizon

  • distinguish beteween solutions (Lorentzian manifolds) and coordinate charts
  • local versus global

Linearized gravity

Tasks for expert:

  • make sure to start all articles with orientation/executive summary for general reader, try to explain all technical terms, and cite appropriate sources,
  • stress two main applications are far field of isolated rotating object and weak-field approximation study of gravitational radiation,
  • expand and link to background article on multipole expansion: motivate and define mass, momentum, stress monopoles, reduced quadrupole tensor, explain relation to harmonic expansion of potential, explain Newtonian, Weyl, and relativistic multipoles, cite Stephani's textbook and other sources, link to any relevant discusion of multipoles in Newtonian theory and electromagnetism (see Category:Vector calculus and Category:Potential theory for some possibilities),
  • write and link to separate article on relativistic multipoles, explain the three extant versions are equivalent,
  • write and link to decomposition of metric tensor: algebraic decomposition into spin 0 pieces (gravitational potential, trace part) , spin 1 piece (vectorial part), spin 2 piece (strain tensor), versus differential decomposition of spin 2 into longitudinal part, solenoidal part, tranverse part (c.f. transverse traceless gauge): cite Carroll's textbook,
  • explain competing gauges such as transverse, synchronous, harmonic (called Lorenz gauge in this context; named for Lorenz, not Lorentz), and discuss gauge transformations,
  • Lorentz gauge valid outside ball around the source,
  • transverse traceless gauge is a special case of Lorentz gauge suitable in smallist "box" far from source,
  • throughout state which approximating assumptions are being made,
  • rewrite and link to background article on gravitoelectromagnetism following most recent review by Mashhoon, comparing with a strong field concept, the Bel decomposition of the Riemann tensor,
  • specialize here to far field versus radiation,
  • write and link to background article on Analogies between gravitational and EM radiation,
  • write and link to background article on linearized plane waves (general relativity), discussing these using TT gauge and computing curvatures, etc, discussing polarization, then discussing in terms of GEM formalism, then compare with and link to articles on strong field plane waves in gtr,
  • possibly separate article deriving quadrupole radiation formula,
  • link to appropriate discussion of problems of energy density of gravitational field in gtr,
  • write and link to article on treatment of angular momentum and mass in gtr,
  • ditto for pseudo-energy-momentum complex, including Möller complex and its competitors (cite one or two recent preprint giving best available review)
  • ditto for quasilocal mass-energy (cite LRR review by Szabados),
  • ditto for Komar mass-energy and momentum, and conformal techniques,
  • ditto for superenergy tensor, especially Bel-Robinson tensor, link to Bel decomposition,
  • discuss examples including spinning disk, rod, spring oscillator, and simple binary pulsar model: compare far field expansions with gravitational radiation production (if any), use Newtonian energy balance to estimate how system adjusts to loss of energy due to gravitational radiation (if any), compare orbital decay for binary pulsar and rotating spring oscillator (where PE relevant since shape of system changes in response to radiation of energy) and spin-down of rigidly rotating objects (where PE irrelevant since shape of system does not change in response to radiation of energy).
  • everywhere distinguish notationally between space and spacetime indices, and between abstract tesnor equations and specific components,
  • explain how weak field limits can help one identify qualitative meaning of a parameter which has arisen in a solution of EFE from assuming some symmetry Ansatz, as in Schwarzschild,
  • explain how weak field limit used to fix the constant 8 \pi in the Einstein field equation,
  • rewrite and link to gravitational lensing (distinguish between weak-field and strong-field lensing theory).

(Gosh, I'm sure I've forgotten some essential topics, but this is a start.)

Tasks for nonexpert:

  • request clarification in talk page regarding anything obscure
  • spell check, grammar patrol, improve diction
  • but please be very careful about changing equations since nonexperts might easily introduce errors

Mach's principle

  • rename Mach principles and convert Mach's principle to a redirect,
  • take account of the fact that many distinct ideas have been called "Mach's principle", leading to much confusion in the literature,
  • give an accurate account of how these are/are not validated in gtr and other major theories,
  • give pointers to the most useful references in the literature, especially recent volumes/reviews.

Mathematics of general relativity

Throughout, article should stress

  • intuitive meaning,
  • levels of structure,
  • degree to which a given mathematical technique/concept is special to gtr, Lorentzian manifolds, etc. (for example, triangularization via Gröbner basis methods is very widely applicable in applied mathematics, as are perturbation theory methods, appropriate bundling procedure very important for smooth manifolds).

Nordström's theory of gravitation

Tasks for expert:

  • write and link to proper article on Lienard-Wiechert potentials in electromagnetism,
  • write and link to article discussing conservation laws in flat versus curved spacetimes
  • article on Einstein field equation should discuss the first-order covariant differential equation for Weyl tensor in gtr (e.g. 4.90 in Carroll); link to discussion of analogous first-order covariant differential equation in this article,
  • discuss degrees of freedom and compare with gtr,
  • cite Dicke article and discuss weak versus strong EP for Nordström's (second) theory,
  • discuss issue of effect of internal energy on motion of extended falling bodies,
  • write and link to article on double null coordinates, including discussion of the wave equation,
  • "already linearized" vacuum solutions and generation of gravitational radiation

Tasks for anyone:

  • correct typos

Defects in my last version include:

  1. it is largely left to reader to distinguish between wave equation, raising/lowering/trace, wrt \eta_{ab}, \; g_{ab}
  2. it is largely left to the reader to figure out \phi = \exp(\psi) \approx 1 + \psi, so that small \psi corresponds to weak fields, but due to arbitrary additive constants in gravitational potential, in weak fields either of these can be identified with Newtonian potential (\psi more natural for comparison with Einstein's later weak-field metric for gtr).

Riemann tensor (general relativity)

Rindler coordinates

Tasks for expert:

  • write and link to article on Fermat metric
  • write and link to article on Killing horizons
  • elaborate on analogy between Rindler horizon and event horizon
  • elaborate on analogy between Rindler chart and a Newtonian "almost-homogeneous gravitational field with linear potential gradient"

Tasks for anyone:

  • correct spelling, grammar
  • complain on talk page if anything is not clear

Speed of gravity

Tasks for expert:

  • better discussion of Newtonian gravitation, e.g. Poisson equation
  • better discussion of aberration, updating
  • fuller and strictly WP:NPOV discussion of Kopeikin controversy
  • write and link to biography of Steve Carlip
  • write and link to articles on Bondi radiation formalism (especially news function)
  • prune list of citations (keep most relevant pro and con citations)

Tasks for anyone:

Whitehead's theory of gravitation

Tasks for expert:

  • add material mathematically defining Whitehead's theory
  • add material explaining effects mentioned in the article