%A E. J. Hinch %A M. A. H. MacCallum %T Notes on Mathematical Methods I %I Cambridge SRC Mathematics Teaching Committee %C Cambridge %D 1968 %Y 000 %K mmrefs %A G. F. R. Ellis %A M. A. H. MacCallum %T A class of homogeneous cosmological models %J CMP %V 12 %P 108-141 %D 1969 %Y 001 EllMac69.pdf %U EllMac69 %K QMW relgrp mmrefs %F Bian_C %L KSMH 1088 %A M. A. H. MacCallum %T A class of homogeneous cosmological models %R Ph.D. thesis %I University of Cambridge %D 1970 %Y 001A Book %K mmrefs %F Bian_C %A M. A. H. MacCallum %A J. M. Stewart %A B. G. Schmidt %T Anisotropic stresses in homogeneous cosmologies %J CMP %V 17 %P 343 %D 1970 %Y 002 MacSteSch70.pdf %U MacSteSch70 %K QMW relgrp mmrefs %F Bian_C %L KSMH 1005 %A M. A. H. MacCallum %A G. F. R. Ellis %T A class of homogeneous cosmological models II: observations %J CMP %V 19 %P 31-64 %D 1970 %U MacEll70 %Y 003 MacEll70.pdf %K QMW relgrp mmrefs %A J. M. Stewart %A M. A. H. MacCallum %A D. W. Sciama %T Thermodynamics and cosmology %J Comments in Astrophys. and Space Phys. %V 2 %P 206-8 %D 1970 %U SteMacSci70 %Y 004 SteMacSci70.pdf %K QMW relgrp mmrefs %A M. A. H. MacCallum %T On the mixmaster universe problem %J Nature (Phys. Sci.) %V 230 %P 112-3 %D 1971 %F Bian_9 %Y 005 %K QMW relgrp mmrefs %A M. A. H. MacCallum %T A class of homogeneous cosmological models. III. Asymptotic behaviour %J CMP %V 20 %P 57-84 %D 1971 %Y 006 Mac71.pdf %U Mac71 %K QMW relgrp mmrefs %F Bian_C %A M. A. H. MacCallum %T On the pulsating universe of {Sengupta} %J PLA %V 35 %P 474 %D 1971 %Y 007 %K QMW relgrp mmrefs %A M. A. H. MacCallum %A A. H. Taub %T Variational principles and spatially homogeneous universes, including rotation %J CMP %V 25 %P 173-189 %D 1972 %U MacTau72 %Y 008 MacTau72.pdf %K QMW relgrp mmrefs %F Bian_C %L KSMH 2676 %A M. A. H. MacCallum %T On criteria of cosmological spatial homogeneity %J PLA %V 40 %P 325-6 %D 1972 %Y 009 %K QMW relgrp mmrefs %F Bian_C %A M. A. H. MacCallum %T On `diagonal' Bianchi cosmologies %J PLA %V 40 %P 385-6 %D 1972 %Y 010 %K QMW relgrp mmrefs %L KSMH 0808 %F Bian_C %A R. Penrose %A M. A. H. MacCallum %T Twistor theory: an approach to the quantisation of fields and space-time %J Phys. Reports (Phys. Lett. C) %V 6 %P 241-316 %D 1973 %O (Russian translation: 'Teoria tvistorov: podkhod k kvantovanalo polyem i prostantsva-vremeni', translated by A.G. Sergeev, in 'Tvistorii i kalibrovochnie polya, cbornik statei', pp. 131-224, ed. V.V. Zharinov, Mir, Moscow, 1983) %Y 011 and 11B %K QMW relgrp mmrefs %A M. A. H. MacCallum %A A. H. Taub %T The averaged Lagrangian and high-frequency gravitational waves %J CMP %V 30 %P 153-170 %D 1973 %U MacTau73 %Y 012 MacTau73.pdf %K QMW relgrp mmrefs %A M. A. H. MacCallum %T Cosmological models from the geometric point of view %D 1973 %E E. Schatzman %I Gordon and Breach %C New York %U Book and Mac73.pdf %Y 013 Book %K QMW relgrp mmrefs %B Carg\`ese Lectures in Physics, vol.6 %C New York %I Gordon and Breach %P 61-174 %F Bian_C %L KSMH 0320 %G 2001.11387 %O From email from Taylor and Francis "Given that the material was pre-digital you are permitted to scan and post the printed original." %A M. A. H. MacCallum %T Quantum cosmological models %P 174-218 %D 1975 %B Quantum gravity: an Oxford symposium %E C.J. Isham, R. Penrose and D.W. Sciama %I Oxford University Press %C Oxford %Y 014 Book %U Book %K QMW relgrp mmrefs %A M. A. H. MacCallum %T Cosmology and curved space quantum theory %P 148-151 %D 1976 %B Transactions of the International Astronomical Union, vol. XVIA, part 3 (Section 5 of the report of Commission 47) %E G. Contopoulos %I D. Reidel and Co. %C Dordrecht %Y 015 %K QMW relgrp mmrefs %A M. A. H. MacCallum %T Comment on `{A} class of Bianchi type VI cosmological models with electromagnetic field' by {Dunn} and {Tupper} %J ApJ %V 212 %P 946 %D 1977 %U Mac77 %F Bian_60 %Y 016 Mac77.pdf %K QMW relgrp mmrefs %A M. A. H. MacCallum %T Anisotropic cosmologies %J Rendiconti di Seminario Matematico Univers. Politec. Torino %V 36 %P 27-34 %D 1978 %Y 017 %K QMW relgrp mmrefs %F Bian_C %A V. A. Belinski %A M. A. H. MacCallum %T Is gravity turbulent near cosmological singularities? %R Preprint %I Landau Institute and Queen Mary %D 1978 %O Gravity Essay competition entry: selected for Honorable Mention %K mmrefs %Y 018A %A M. A. H. MacCallum %T Anisotropic and inhomogeneous relativistic cosmologies %P 533-580 %D 1979 %B General relativity: an Einstein centenary survey %E S.W. Hawking and W. Israel %I Cambridge University Press %C Cambridge %K QMW relgrp mmrefs %U Books %Y 018 and 18B Book %F Bian_C %O Russian translation: `Obshchaya teoria otnositel'nosti' edited by Ya. A. Smorodinskii and V.B. Braginskii, Mir, Moscow, 1983. Also reprinted on pp. 179-236 in ``The early universe: reprints'', ed. E.W. Kolb and M.S. Turner, Addison-Wesley, Reading, Mass. 1988. %A M. A. H. MacCallum %T The mathematics of anisotropic cosmologies %B Proceedings of the First International Cracow School of Cosmology %E M. Demia\'nski %C Berlin %I Springer-Verlag %D 1979 %P 1-59 %V 109 %B Physics of the expanding universe %S Lecture Notes in Physics %C Berlin and Heidelberg %U Book %Y 019 Book %K QMW relgrp mmrefs %F Bian_C %A M. A. H. MacCallum %T Comment %J GRG %V 10 %P 1039-40 %D 1979 %O Contribution to the GR8 symposium on singularities %Y 020 %K QMW relgrp mmrefs %A D. Kramer %A H. Stephani %A M. A. H. MacCallum %A E. Herlt %T Exact solutions of Einstein's field equations %P 1-425 %D 1980 %I Deutscher Verlag der Wissenschaften, Berlin, and Cambridge University Press %C Cambridge %O (Russian translation: "Tochnie resheniya uravnenii Einshteina", 418 pp., translated by I.V. Mitskievich, V.D. Zakharov and S.V. Rumyantsev and edited by Yu. S. Vladimirov, Energoisdat, Moscow, 1982) %Y 021 and 21B Book %U Book %K QMW relgrp mmrefs equref %A M. A. H. MacCallum %T Locally isotropic spacetimes with non-null homogeneous hypersurfaces %B Essays in General Relativity: a Festschrift for Abraham Taub %E F.J. Tipler %C New York %I Academic Press %D 1980 %P 121-138 %Y 022 Book %U Book %K QMW relgrp mmrefs %A M. A. H. MacCallum %A S. T. C. Siklos %T Homogeneous and hypersurface-homogeneous algebraically special Einstein spaces %H See KSMH 3285 and 6749 for final results %P 54-55 %D 1980 %B Abstracts of contributed papers for the 9th international conference on general relativity and gravitation, Jena, DDR, 1980, vol. 1 %E E. Schmutzer %P 54-55 %I International Society on General Relativity and Gravitation %C Jena %Y 032 Originally not numbered (29A) but Harvey paper abandoned %K QMW relgrp mmrefs %A W. B. Bonnor %A M. A. H. MacCallum %T The Melnick-Tabensky solutions have high symmetry %U BonMac82 %J J. Math. Phys. %V 23 %N 9 %P 1639-40 %D 1982 %Y 023 BonMac82.pdf %K QMW relgrp mmrefs equref %A A. Karlhede %A M. A. H. MacCallum %T On determining the isometry group of a Riemannian space %U KarMac82 %J Gen. Rel. Grav. %V 14 %P 673-82 %D 1982 %X The authors present an extension of the recently discussed algorithm fordeciding the equivalence problem for Riemannian metrics. The extensiondetermines the structure constants of the isometry group and enables theauthors to obtain some information about its orbits including theform ofthe Killing vectors in canonical coordinates. %Y 024 %U KarMac82.pdf %K QMW relgrp mmrefs equref %A M. A. H. MacCallum %T Relativistic cosmology for astrophysicists %P 9-33 %D 1982 %B Origin and evolution of the galaxies %E V. de Sabbata %I World Scientific %C Singapore %O Also, in revised form, in {\em Origin and evolution of the galaxies}, (1983) ed.\ B.J.T. and J.E. Jones, volume 97 of Nato Advanced Study Institute Series, p. 9 (D.Reidel and Co., Dordrecht). %Y 025 and 25B Book %U Books %K QMW relgrp mmrefs %A M. A. H. MacCallum %T Relativistic cosmologies %J Irish Astron. J. %V 15 %P 125-127 %D 1982 %Y 036 %K QMW relgrp mmrefs %A M. A. H. MacCallum %A A. Spero %A D. A. Szafron %T On the geometry of the {Zel'manov-Grishchuk} homogeneity criterion %J Phys. Lett. A %V 87 %P 157-8 %D 1982 %Y 026 and 026A %O Also unpublished note on Grishchuk's criterion %K QMW relgrp mmrefs %A M. A. H. MacCallum %A A. Moussiaux %A P. Tombal %A J. Demaret %T Comment on ``{On} the general solution for `diagonal' vacuum Bianchi type III model with a cosmological constant'' %Y 027 MacMouTom82.pdf %K QMW relgrp mmrefs %U MacMouTom82 %H The only new thing is covered by a more general remark %J J. Phys. A %V 15 %N 5 %P 1757-8 %D 1982 %X The particular Bianchi type III solution given by Moussiaux et al. (see ibid., vol.14, no.8, p.L277-80, 1981) is shown to be contained in a generalsolution for locally-rotationally-symmetric hypersurface-homogeneous modelsgiven by Cahen and Defrise (1968). %A M. A. H. MacCallum %T Relativistic cosmology for astrophysicists %B Proceedings of the 7th International School of Cosmology and Gravitation, Erice, Sicily %E B.J.T. Jones and J.E. Jones %C Dordrecht %I D. Reidel %D 1983 %P 9-39 %Y 025C Book %U Book %K mmrefs %A M. A. H. MacCallum %T Classifying metrics in theory and practice %B Unified Field Theories of more than 4 Dimensions Including Exact Solutions. Proceedings of the International School of Cosmology and Gravitation %E V. De\0Sabbata and E. Schmutzer %C Singapore %I World Scientific %D 1983 %P 352-82 %X In order to deal systematically with exact solutions of Einstein's equation, it is necessary to resolve the 'equivalence problem' of deciding whether or not two Riemannian manifold, given explicitly in terms of coordinates, are (locally) the same, i.e. whether or not there is a coordinate transformation relating the two metrics. Although no formally decidable procedure is available, it is possible to reduce the problems to a set of algebraic equations which fix the possible coordinates transformations (of essential coordinates), and check the dependences of the remaining functions on these coordinates. The most effective way to express this procedure, using frames in which the metric is constant, is due to Cartan (1946). For the special case of four dimensional spacetimes it has been improved by Karlhede (1980). Theprogram SHEEP is used %Y 034 %K QMW relgrp mmrefs equref %A M. A. H. MacCallum %T Static and stationary `cylindrically symmetric' Einstein-Maxwell fields and the solutions of {Van} den {Bergh} and {Wils} %J J. Phys. A %V 16 %N 16 %P 3853-66 %D 1983 %M LivRevCA %L KSMH 3878 %X The author considers stationary 'cylindrically symmetric' solutions of the Einstein-Maxwell equations whose metric takes 'block diagonal' form based on orbits of a two-parameter subgroup of the isometries and in which the Maxwell field lie in surfaces orthogonal to those orbits. It is shown that if the Maxwell field is non-null, it either inherits the metric symmetry orvaries with one more of the coordinates in a specific way. The cases in which the metric symmetry is inherited are discussed further. Their generalsolutions consist of three families in which the equations can be reduced to the equation for the third Painleve transcendent followed by quadratures; one of these families is new, while the two such families given by Chitre et al. (1975) are equivalent. It is shown how the particular solutions expressible in elementary functions (none of them new)arise. All previous solutions known to the author are identified. The calculations were done using the computer algebra system SHEEP. The literature on this class of metrics is reviewed. In particular, the discussion given in the recent paper by Van den Bergh and Wils (1983) is amplified. The conditions for extra symmetry, and for the solutions to be static, are derived in a manner which clarifies their physical and mathematical origin, and relates the results to the methods for invariant classification of metrics developed in recent years. %Y 035 Mac83.pdf %U Mac83 %K QMW relgrp mmrefs equref %A M. A. H. MacCallum %T Proposed format for recording the invariant characterization of exact solutions %P 301-3 %D 1983 %B Contributed papers of the 10th international conference on general relativity and gravitation. Vol. 1. Classical relativity. %E B. Bertotti, F. de Felice and A. Pascolini %I Consiglione Nazionale di Ricerce %C Rome %Y 046 %K QMW relgrp mmrefs equref %A J. E. {\AA}man %A R. A. d'Inverno %A G. C. Joly %A M. A. H. MacCallum %T Quartic equations and classification of the Riemann tensor in General Relativity %V 174 %P 47-58 %D 1984 %B EUROSAM 84: Proceedings of the 1984 European conference on symbolic and algebraic manipulation %E J. Fitch %S Lecture Notes in Computer Science %I Springer Verlag %C Berlin and Heidelberg %M LivRevCA %Y 037 %K QMW relgrp mmrefs equref %A W. B. Bonnor %A J. N. Islam %A M. A. H. MacCallum\0(eds.) %T Classical general relativity (Proceedings of the 1983 London conference on classical (non-quantum) general relativity) %I Cambridge University Press %C Cambridge %D 1984 %P 1-269 %Y 038A Book %U Book %K QMW relgrp mmrefs %A D. Kramer %A H. Stephani %A M. A. H. MacCallum %A E. Herlt %T Exact solutions of Einstein's field equations: corrections %D 1984 %P 1-19 %R Preprint (unpublished) %I Queen Mary College %L Kramer et al. 1984 %Y 045 %K QMW relgrp mmrefs notpub %A M. A. H. MacCallum %T Algebraic computing in general relativity %P 145-171 %D 1984 %B Classical general relativity (Proceedings of the 1983 London conference on classical (non-quantum) general relativity) %E W.B. Bonnor, J.N. Islam and M.A.H. MacCallum %I Cambridge University Press %C Cambridge %M LivRevCA %Y 038 Book %U Book %K QMW relgrp mmrefs %A M. A. H. MacCallum %T Exact Solutions and Singularities. Report of Workshop A2 %C Dordrecht %I D. Reidel Publishing Comp. %D 1984 %P 69-81 %B General Relativity and Gravitation (Proceedings of the 10th international conference on general relativity and gravitation, Padova, 1983) %E B. Bertotti, F. de Felice and A. Pascolini %Y 039 %K QMW relgrp mmrefs %A M. A. H. MacCallum %T Exact solutions in cosmology %P 334-366 %D 1984 %B Solutions of Einstein's equations: techniques and results (Retzbach, Germany, 1983) %S Lecture Notes in Physics %V 205 %E C. Hoenselaers and W. Dietz %I Springer Verlag %C Berlin and Heidelberg %Y 040 Book %U Book %K QMW relgrp mmrefs %A J. E. {\AA}man %A R. A. d'Inverno %A G. C. Joly %A M. A. H. MacCallum %T Progress on the equivalence problem %V 204 %P 89-98 %D 1985 %B EUROCAL 85: proceedings of the European conference on computer algebra, Linz, Austria, vol. 2 %S Lecture Notes in Computer Science %E B.F. Caviness %I Springer Verlag %C Berlin and Heidelberg %Y 048 Book %U Book %M LivRevCA %K QMW relgrp mmrefs equref %A M. A. H. MacCallum %T On some Einstein-Maxwell fields of high symmetry %J Gen. Rel. Grav. %V 17 %N 7 %P 659-68 %D 1985 %X The author investigates static axisymmetric, stationary cylindrically symmetric and nonstatic spatially homogeneous space-times which have been previously studied in a series of papers by Raychaudhuri, Datta, Bera, and De (1960-74). In most cases the general solutions of the problems tackled are now known, and are repeated here. The earlier papers are analyzed; whileerrors (some pointed out by Carminati and McIntosh (1980)) and duplications are found, it is believed that the papers discussed contain the first occurrences of three of the solutions. The author's calculations have been verified using the computer algebra system SHEEP. %Y 030 Mac85.pdf %U Mac85 %K QMW relgrp mmrefs equref %A M. A. H. MacCallum %T Understanding the solutions of Einstein's equations %J Quart. J. Roy. Astron. Soc. %V 26 %P 127-136 %D 1985 %O Invited lecture given at the G.C. McVittie 80th birthday meeting. Also appeared in abbreviated form in {\em Bull. Inst. Maths. Applns.} {\bf 21}, 85-6, 1985. %Y 041 and 41A %K QMW relgrp mmrefs equref %A M. A. H. MacCallum\0(ed.) %T Galaxies, axisymmetric systems and relativity: essays presented to W.B. Bonnor on his 65th birthday %I Cambridge University Press %C Cambridge %D 1985 %P 1-300 %Y 043B Book %U Book %K QMW relgrp mmrefs %A M. A. H. MacCallum %T Relativistic cosmological models %P 183-228 %D 1985 %B Observational and theoretical aspects of relativistic astrophysics and cosmology (Proceedings of the 1984 Santander School) %E J.L. Sanz and L.J. Goicoechea %I World Scientific %C Singapore %Y 047 Book %U Book %K QMW relgrp mmrefs equref %A M. A. H. MacCallum %A N. Van\0den\0Bergh %T Non-inheritance of static symmetry by Maxwell fields %D 1985 %P 138-148 %B Galaxies, axisymmetric systems and relativity: essays presented to W.B. Bonnor on his 65th birthday %E M.A.H. MacCallum %I Cambridge University Press %C Cambridge %Y 043 Book %U Book %K QMW relgrp mmrefs equref %A M. A. H. MacCallum %A J. E. {\AA}man %T Algebraically independent $n$-th derivatives of the Riemannian curvature spinor in a general spacetime %J CQG %V 3 %N 6 %P 1133-41 %D 1986 %F CAinGR %Y 044 MacAma86 %U MacAma86 %K QMW relgrp mmrefs equref %M LivRevCA N Too much detail %X Explicit sets of spinor nth derivatives of the Riemann curvature spinor forageneral spacetime are specified for each n so that they contain the minimal number of components enabling all derivatives of order m to be expressed algebraically in terms of these sets for n