@string{AandA = "Astron. Astrophys."}
@string{AandG = "Astron. \& Geophys."}
@string{AdP = "Ann. d. Phys. (Leipzig)"}
@string{AIHPA = "Ann. Inst. H. Poincar\'e A: Phys. Th\'eorique"}
@string{AJ = "Astron. J."}
@string{APNY = "Ann.Phys. (N.Y.)"}
@string{ApJ = "Astrophys. J."}
@string{ApJLett = "Astrophys. J. Lett."}
@string{ARAA = "Ann. Rev. Astron. Astrophys."}
@string{ASS = "Astrophys. Sp. Sci."}
@string{CQG = "Class. Quantum Grav."}
@string{CMP = "Commun. math. phys."}
@string{GRG = "Gen. Relativ. Gravit."}
@string{IJMPD = "Int. J. Mod. Phys. D"}
@string{IJTP = "Int. J. Theor. Phys."}
@string{JCAP = "J. Cosm. Astroparticle Phys."}
@string{JMP = "J. Math. Phys."}
@string{JPA = "J. Phys. A"}
@string{MNRAS = "Mon. Not. Roy. Astr. Soc."}
@string{Nature = "Nature"}
@string{NPB = "Nucl. Phys. B"}
@string{PASP = "Publ. Astr. Soc. Pacific"}
@string{PCPS = "Math. Proc. Cam. Phil. Soc."}
@string{PhysRep = "Phys. Reports"}
@string{PLA = "Phys. Lett. A"}
@string{PLB = "Phys. Lett. B"}
@string{PNAS = "Proc. Nat. Acad. Sci. U.S."}
@string{PTP = "Prog. Theor. Phys."}
@string{PR = "Phys. Rev."}
@string{PRA = "Phys. Rev. A"}
@string{PRD = "Phys. Rev. D"}
@string{PRL = "Phys. Rev. Lett."}
@string{PRSA = "Proc. Roy. Soc. London A"}
@string{QJRAS = "Quart. J. Roy. Astr. Soc."}
@string{Science = "Science"}
@string{CCA = "ACM Comm. Computer Alg."}
@string{CPC = "Computer Phys. Comm."}
@string{JSC = "J. Symb. Comp."}
@string{Programmirovannie ="Programmirovannie"}
@BOOK{HinMac68,
author={E. J. Hinch and M. A. H. MacCallum},
title={Notes on Mathematical Methods {I}},
publisher={Cambridge SRC Mathematics Teaching Committee},
address={Cambridge},
year={1968}
}
@ARTICLE{EllMac69,
author={G.F.R. Ellis and M.A.H. MacCallum},
title={A class of homogeneous cosmological models},
journal={CMP},
volume={12},
pages={108-141},
year={1969}
}
@ARTICLE{MacSteSch70,
author={M. A. H. MacCallum and J. M. Stewart and B. G. Schmidt},
title={Anisotropic stresses in homogeneous cosmologies},
journal={CMP},
volume={17},
pages={343},
year={1970}
}
@TECHREPORT{Mac70,
author={M. A. H. MacCallum},
title={A class of homogeneous cosmological models},
institution={University of Cambridge},
number={Ph.D. thesis},
year={1970}
}
@ARTICLE{MacEll70,
author={M. A. H. MacCallum and G. F. R. Ellis},
title={A class of homogeneous cosmological models {II}:
observations},
journal={CMP},
volume={19},
pages={31-64},
year={1970}
}
@ARTICLE{SteMacSci70,
author={J. M. Stewart and M. A. H. MacCallum and D. W. Sciama},
title={Thermodynamics and cosmology},
journal={Comments in Astrophys. and Space Phys.},
volume={2},
pages={206-8},
year={1970}
}
@ARTICLE{Mac71,
author={M. A. H. MacCallum},
title={A class of homogeneous cosmological models. {III}.
{A}symptotic behaviour},
journal={CMP},
volume={20},
pages={57-84},
year={1971}
}
@ARTICLE{Mac71a,
author={M. A. H. MacCallum},
title={On the mixmaster universe problem},
journal={Nature (Phys. Sci.)},
volume={230},
pages={112-3},
year={1971}
}
@ARTICLE{Mac71b,
author={M. A. H. MacCallum},
title={On the pulsating universe of {Sengupta}},
journal={PLA},
volume={35},
pages={474},
year={1971}
}
@ARTICLE{Mac72,
author={M. A. H. MacCallum},
title={On criteria of cosmological spatial homogeneity},
journal={PLA},
volume={40},
pages={325-6},
year={1972}
}
@ARTICLE{Mac72a,
author={M. A. H. MacCallum},
title={On `diagonal' {Bianchi} cosmologies},
journal={PLA},
volume={40},
pages={385-6},
year={1972}
}
@ARTICLE{MacTau72,
author={M. A. H. MacCallum and A. H. Taub},
title={Variational principles and spatially homogeneous
universes, including rotation},
journal={CMP},
volume={25},
pages={173-189},
year={1972}
}
@ARTICLE{MacTau73,
author={M. A. H. MacCallum and A. H. Taub},
title={The averaged {{Lagrang}ian} and high-frequency
gravitational waves},
journal={CMP},
volume={30},
pages={153-170},
year={1973}
}
@INCOLLECTION{Mac73,
author={M. A. H. MacCallum},
title={Cosmological models from the geometric point of view},
booktitle={Carg\`ese Lectures in Physics, vol.6},
editor={E. Schatzman},
publisher={Gordon and Breach},
address={New York},
pages={61-174},
year={1973}
}
@ARTICLE{PenMac73,
author={R. Penrose and M. A. H. MacCallum},
title={Twistor theory: an approach to the quantisation of
fields and space-time},
journal={Phys. Reports (Phys. Lett. C)},
volume={6},
pages={241-316},
note={(Russian translation: 'Teoria tvistorov: podkhod k
kvantovanalo polyem i prostantsva-vremeni', translated
by A.{G}. {S}ergeev, in 'Tvistorii i kalibrovochnie
polya, cbornik statei', pp. 131-224, ed. {V}.{V}.
{Z}harinov, Mir, Moscow, 1983)},
year={1973}
}
@INCOLLECTION{Mac75,
author={M. A. H. MacCallum},
title={Quantum cosmological models},
booktitle={Quantum gravity: an Oxford symposium},
editor={C.J. Isham and R. Penrose and D.W. Sciama},
publisher={Oxford University Press},
address={Oxford},
pages={174-218},
year={1975}
}
@INCOLLECTION{Mac76,
author={M. A. H. MacCallum},
title={Cosmology and curved space quantum theory},
booktitle={Transactions of the International Astronomical Union, vol. XVIA, part 3 (Section 5 of the report of Commission 47)},
editor={G. Contopoulos},
publisher={D. Reidel and Co.},
address={Dordrecht},
pages={148-151},
year={1976}
}
@ARTICLE{Mac77,
author={M. A. H. MacCallum},
title={Comment on `{A} class of {Bianchi} type {VI}
cosmological models with electromagnetic field' by
{Dunn} and {Tupper}},
journal={ApJ},
volume={212},
pages={946},
year={1977}
}
@TECHREPORT{BelMac78,
author={V. A. Belinski and M. A. H. MacCallum},
title={Is gravity turbulent near cosmological singularities?},
institution={Landau Institute and Queen Mary},
note={Gravity Essay competition entry: selected for Honorable
Mention},
number={Preprint},
year={1978}
}
@ARTICLE{Mac78,
author={M. A. H. MacCallum},
title={Anisotropic cosmologies},
journal={Rendiconti di Seminario Matematico Univers. Politec. Torino},
volume={36},
pages={27-34},
year={1978}
}
@INCOLLECTION{Mac79,
author={M. A. H. MacCallum},
title={Anisotropic and inhomogeneous relativistic cosmologies},
booktitle={General relativity: an Einstein centenary survey},
editor={S.W. Hawking and W. Israel},
publisher={Cambridge University Press},
address={Cambridge},
pages={533-580},
note={Russian translation: `Obshchaya teoria otnositel'nosti'
edited by Ya. {A}. {S}morodinskii and V.{B}.
{B}raginskii, Mir, Moscow, 1983. {A}lso reprinted on
pp. 179-236 in ``The early universe: reprints'', ed.
{E}.{W}. {K}olb and M.{S}. {T}urner, Addison-Wesley,
Reading, Mass. 1988.},
year={1979}
}
@ARTICLE{Mac79a,
author={M. A. H. MacCallum},
title={Comment},
journal={GRG},
volume={10},
pages={1039-40},
note={(Contribution to the GR8 symposium on singularities.)},
year={1979}
}
@INCOLLECTION{Mac79b,
author={M. A. H. MacCallum},
title={The mathematics of anisotropic cosmologies},
booktitle={Physics of the expanding universe},
editor={M. Demia\'nski},
publisher={Springer-Verlag},
address={Berlin and Heidelberg},
volume={109},
pages={1-59},
series={Lecture Notes in Physics},
year={1979}
}
@BOOK{KraSteMac80,
author={D. Kramer and H. Stephani and M. A. H. MacCallum and E. Herlt},
title={Exact solutions of {Einstein's} field equations},
publisher={Deutscher Verlag der Wissenschaften, Berlin, and Cambridge University Press},
address={Cambridge},
pages={1-425},
note={(Russian translation: "Tochnie resheniya uravnenii
Einshteina", 418 pp., translated by {I}.{V}.
{M}itskievich, V.{D}. {Z}akharov and S.{V}.
{R}umyantsev and edited by Yu. {S}. {V}ladimirov,
Energoisdat, Moscow, 1982)},
year={1980}
}
@INCOLLECTION{MacSik80,
author={M. A. H. MacCallum and S. T. C. Siklos},
title={Homogeneous and hypersurface-homogeneous algebraically
special {Einstein} spaces},
booktitle={Abstracts of contributed papers for the 9th international conference on general relativity and gravitation, Jena, {DDR}, 1980, vol. 1},
editor={E. Schmutzer},
publisher={International Society on General Relativity and Gravitation},
address={Jena},
pages={54-55},
year={1980}
}
@INCOLLECTION{Mac80,
author={M. A. H. MacCallum},
title={Locally isotropic spacetimes with non-null homogeneous
hypersurfaces},
booktitle={Essays in General Relativity: a Festschrift for Abraham Taub},
editor={F.J. Tipler},
publisher={Academic Press},
address={New York},
pages={121-138},
year={1980}
}
@INCOLLECTION{Mac81,
author={M. A. H. MacCallum},
title={Relativistic Cosmology for Astrophysicists},
booktitle={Proceedings of the 7th International School of Cosmology and Gravitation, Erice, Sicily},
editor={B.J.T. Jones and J.E. Jones},
publisher={D. Reidel},
address={Dordrecht},
pages={9-39},
year={1981}
}
@ARTICLE{BonMac82,
author={W. B. Bonnor and M. A. H. MacCallum},
title={The Melnick-Tabensky solutions have high symmetry},
journal={J. Math. Phys.},
volume={23},
number={9},
pages={1639-40},
year={1982}
}
@ARTICLE{KarMac82,
author={A. Karlhede and M. A. H. MacCallum},
title={On determining the isometry group of a {Riemannian}
space},
journal={Gen. Rel. Grav.},
volume={14},
pages={673-82},
year={1982},
annote={The authors present an extension of the recently
discussed algorithm fordeciding the equivalence
problem for {Riemannian} metrics. {T}he
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.}
}
@ARTICLE{MacMouTom82,
author={M. A. H. MacCallum and A. Moussiaux and P. Tombal and J. Demaret},
title={Comment on ``{On} the general solution for `diagonal'
vacuum {Bianchi} type {III} model with a cosmological
constant''},
journal={J. Phys. A},
volume={15},
number={5},
pages={1757-8},
year={1982},
annote={The particular Bianchi type III solution given by
Moussiaux et al. (see ibid., vol.14, no.8,
p.{L}277-80, 1981) is shown to be contained in a
generalsolution for locally-rotationally-symmetric
hypersurface-homogeneous modelsgiven by Cahen and
Defrise (1968).}
}
@ARTICLE{MacSpeSza82,
author={M. A. H. MacCallum and A. Spero and D. A. Szafron},
title={On the geometry of the {Zel'manov-Grishchuk}
homogeneity criterion},
journal={Phys. Lett. A},
volume={87},
pages={157-8},
note={Also unpublished note on Grishchuk's criterion},
year={1982}
}
@ARTICLE{Mac82,
author={M. A. H. MacCallum},
title={Relativistic cosmologies},
journal={Irish Astron. J.},
volume={15},
pages={125-127},
year={1982}
}
@INCOLLECTION{Mac82a,
author={M. A. H. MacCallum},
title={Relativistic cosmology for astrophysicists},
booktitle={Origin and evolution of the galaxies},
editor={V. de Sabbata},
publisher={World Scientific},
address={Singapore},
pages={9-33},
note={Also, in revised form, in ``Origin and evolution of the
galaxies'', ed. B.{J}.{T}. and J.{E}. {J}ones, Nato
Advanced Study Institute Series, 97, pp. 9-39,
D.{R}eidel and Co., Dordrecht, 1983.},
year={1982}
}
@INCOLLECTION{Mac83,
author={M. A. H. MacCallum},
title={Classifying metrics in theory and practice},
booktitle={Unified Field Theories of more than 4 Dimensions Including Exact Solutions. {P}roceedings of the International School of Cosmology and Gravitation },
editor={V. {De Sabbata} and E. Schmutzer},
publisher={World Scientific},
address={Singapore},
pages={352-82},
year={1983},
annote={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. {A}lthough 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. {T}he most
effective way to express this procedure, using frames
in which the metric is constant, is due to {Cartan}
(1946). {F}or the special case of four dimensional
spacetimes it has been improved by Karlhede (1980).
Theprogram {SHEEP} is used}
}
@INCOLLECTION{Mac83a,
author={M. A. H. MacCallum},
title={Proposed format for recording the invariant
characterization of exact solutions},
booktitle={Contributed papers of the 10th international conference on general relativity and gravitation},
editor={B. Bertotti and F. de Felice and A. Pascolini},
publisher={Consiglione Nazionale di Ricerce},
address={Rome},
pages={301-3},
year={1983}
}
@ARTICLE{Mac83b,
author={M. A. H. MacCallum},
title={Static and stationary `cylindrically symmetric'
{Einstein}-{Maxwell} fields and the solutions of {Van}
den {Bergh} and {Wils}},
journal={J. Phys. A},
volume={16},
number={16},
pages={3853-66},
year={1983},
annote={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. {I}t 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. {T}he cases in
which the metric symmetry is inherited are discussed
further. {T}heir 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. {I}t is shown how the particular
solutions expressible in elementary functions (none of
them new)arise. {A}ll previous solutions known to the
author are identified. {T}he calculations were done
using the computer algebra system {SHEEP}. {T}he
literature on this class of metrics is reviewed. {I}n
particular, the discussion given in the recent paper
by Van den Bergh and Wils (1983) is amplified. {T}he
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.}
}
@BOOK{BonIslMac84,
author={W. B. Bonnor and J. N. Islam and M. A. H. MacCallum~(eds.)},
title={Classical general relativity (Proceedings of the 1983
London conference on classical (non-quantum) general
relativity)},
publisher={Cambridge University Press},
address={Cambridge},
pages={1-269},
year={1984}
}
@TECHREPORT{KraSteMac84,
author={D. Kramer and H. Stephani and M. A. H. MacCallum and E. Herlt},
title={Exact solutions of {Einstein's} field equations:
corrections},
institution={Queen Mary College},
pages={1-19},
number={Preprint (unpublished)},
year={1984}
}
@INCOLLECTION{Mac84,
author={M. A. H. MacCallum},
title={Algebraic computing in general relativity},
booktitle={Classical general relativity (Proceedings of the 1983 London conference on classical (non-quantum) general relativity)},
editor={W.B. Bonnor and J.N. Islam and M. A. H. MacCallum},
publisher={Cambridge University Press},
address={Cambridge},
pages={145-171},
year={1984}
}
@INCOLLECTION{Mac84a,
author={M. A. H. MacCallum},
title={Exact Solutions and Singularities. {R}eport of Workshop
A2},
booktitle={General Relativity and Gravitation (Proceedings of the 10th international conference on general relativity and gravitation, Padova, 1983)},
editor={B. Bertotti and F. de Felice and A. Pascolini},
publisher={D. Reidel Publishing Comp.},
address={Dordrecht},
pages={69-81},
year={1984}
}
@INCOLLECTION{Mac84b,
author={M. A. H. MacCallum},
title={Exact solutions in cosmology},
booktitle={Solutions of Einstein's equations: techniques and results (Retzbach, Germany, 1983)},
editor={C. Hoenselaers and W. Dietz},
publisher={Springer Verlag},
address={Berlin and Heidelberg},
volume={205},
pages={334-366},
series={Lecture Notes in Physics},
year={1984}
}
@INCOLLECTION{AmadInJol84,
author={J. E. {\AA}man and R. A. d'Inverno and G. C. Joly and M. A. H. MacCallum},
title={Quartic equations and classification of the {Riemann}
tensor in General Relativity},
booktitle={EUROSAM 84: Proceedings of the 1984 European conference on symbolic and algebraic manipulation},
editor={J. Fitch},
publisher={Springer Verlag},
address={Berlin and Heidelberg},
volume={174},
pages={47-58},
series={Lecture Notes in Computer Science},
year={1984}
}
@INCOLLECTION{MacBer85,
author={M. A. H. MacCallum and N. {Van den Bergh}},
title={Non-inheritance of static symmetry by {Maxwell} fields},
booktitle={Galaxies, axisymmetric systems and relativity: essays presented to W.{B}. {B}onnor on his 65th birthday},
editor={M. A. H. MacCallum},
publisher={Cambridge University Press},
address={Cambridge},
pages={138-148},
year={1985}
}
@ARTICLE{Mac85,
author={M. A. H. MacCallum},
title={On some {Einstein}-{Maxwell} fields of high symmetry},
journal={Gen. Rel. Grav.},
volume={17},
number={7},
pages={659-68},
year={1985},
annote={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 {Raychaud}huri,
Datta, Bera, and De (1960-74). {I}n most cases the
general solutions of the problems tackled are now
known, and are repeated here. {T}he 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. {T}he author's
calculations have been verified using the computer
algebra system {SHEEP}.}
}
@INCOLLECTION{Mac85a,
author={M. A. H. MacCallum},
title={Relativistic cosmological models},
booktitle={Observational and theoretical aspects of relativistic astrophysics and cosmology (Proceedings of the 1984 Santander School)},
editor={J.L. Sanz and L.J. Goicoechea},
publisher={World Scientific},
address={Singapore},
pages={183-228},
year={1985}
}
@ARTICLE{Mac85b,
author={M. A. H. MacCallum},
title={Understanding the solutions of {Einstein's} equations},
journal={Quart. J. Roy. Astron. Soc.},
volume={26},
pages={127-136},
note={Invited lecture given at the G.C. McVittie 80th
birthday meeting. Also appeared in abbreviated form in
{\em Bull. {I}nst. {M}aths. {A}pplns.} {\bf 21}, 85-6,
1985.},
year={1985}
}
@BOOK{Mac85c,
author={M. A. H. MacCallum~(ed.)},
title={Galaxies, axisymmetric systems and relativity: essays
presented to W.{B}. {B}onnor on his 65th birthday},
publisher={Cambridge University Press},
address={Cambridge},
pages={1-300},
year={1985}
}
@INCOLLECTION{AmadInJol85,
author={J. E. {\AA}man and R. A. d'Inverno and G. C. Joly and M. A. H. MacCallum},
title={Progress on the equivalence problem},
booktitle={EUROCAL 85: proceedings of the European conference on computer algebra, Linz, Austria, vol. 2},
editor={B.F. Caviness},
publisher={Springer Verlag},
address={Berlin and Heidelberg},
volume={204},
pages={89-98},
series={Lecture Notes in Computer Science},
year={1985}
}
@ARTICLE{MacAma86,
author={M. A. H. MacCallum and J. E. {\AA}man},
title={Algebraically independent $n$-th derivatives of the
{Riemannian} curvature spinor in a general spacetime},
journal={Class. Quant. Grav.},
volume={3},
number={6},
pages={1133-41},
year={1986},
annote={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