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
- general first, specific later
- n dimensions first, 1+3 later
- 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
- 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:
- write and link to articles on expansion tensor, vorticity tensor, path curvature (relativity) (don't forget to link latter two with congruence (general relativity) and Raychaudhuri equation.)
- currently this article uses etc. for Rindler frame field and etc. for Bell frame field, while Rindler coordinates uses for Rindler frame field and etc. for Minkowski frame field (corresponding to static observers in the Cartesian chart). This notational conflict should probably be resolved.
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:
- read some discussions of good organization
- How to write a great article
- Organization of articles from WikiProject GTR.
- completely rewrite and reorganize this article,
- spellcheck, improve the often very awkward diction.
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
Gravitomagnetism
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
- partial derivatives to covariant derivatives; explain what this means.
- discussion of levels of structure and local vs. global,
- exterior calculus, including covector and Hodge dual,
- intuition for Spinors,
- Cartan-Karlhede algorithm,
- Newman-Penrose formalism, GHP formalism, ADM formulation, other initial value formulations, Cauchy evolution, characteristic evolution, Cauchy characteristic matching - relation to computing wave generation.
- matching/junction conditions.
- EIH approximation (geodesics and inertial motion of test particles),
- geodesic equations and Papapetrou-Dixon equations (motion of spinning test-particles),
- relativistic multipole moments,
- link to article on computation of connection and curvature via Cartan's method using exterior calculus,
- congruence (general relativity) and discussion of kinematical decomposition for timelike and null vector fields,
- the Ricci tensor directly couples to immediate presence of mass-energy-momentum,
- via Lanczos tensor potential for Weyl tensor, Weyl indirectly couples to mass-energy,
- local versus global isometries, conserved currents,
- isotropy subgroup, holonomy subgroup, new article on spacetime holonomy (groups, classification of spacetimes etc.) .
- integration by parts in curved spacetimes,
- nonlocality of gravitational field energy-momentum in general relativity,
- discussion and links to article explaining triangularization of Killing equations (etc.),
- conformal structure, e.g. Carter-Penrose diagrams,
- list various methods used in establishing Penrose-Hawking singularity theorems,
- list open problems in gtr having more to do with math than physics, e.g. rigorous classification of spacetime singularities,
- links to general references, point out specialized articles contain specialized references.
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:
- it is largely left to reader to distinguish between wave equation, raising/lowering/trace, wrt
- it is largely left to the reader to figure out , so that small 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 ( more natural for comparison with Einstein's later weak-field metric for gtr).
Riemann tensor (general relativity)
- Discuss curvature invariants and Carminati-McLenaghan invariants
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:
- improve diction, etc.
- help monitor edits by User:Kopeikins (apparently Sergei Kopeikin in real life) and User:Tomvf (apparently Tom Van Flandern in real life) of the sections concerning their controversial claims for possible violations of WP:NPOV, and remind them of WP:AUTO as needed.
Whitehead's theory of gravitation
Tasks for expert:
- add material mathematically defining Whitehead's theory
- add material explaining effects mentioned in the article