Prof. Malcolm A.H. MacCallum

Current positions

Emeritus Professor of Applied Mathematics, School of Mathematical Sciences,
Queen Mary University of London
Golden Oldies Editor and Associate Editor, "General Relativity and Gravitation"
Webmaster, Old Maidstonian Society and St. John of Jerusalem Festival Chorus, Hackney

Other Positions since retirement from QMUL in 2009

Director, Heilbronn Institute for Mathematical Research (2009-12)
Visiting Professor, Department of Mathematics, University of Bristol (2009-12)
President, International Society on General Relativity and Gravitation (2010-13)
Member, Research Policy Committee, London Mathematical Society (2010-14)
Chair, Advisory Board, University of York Department of Mathematics (2012-17)
Deputy President, International Society on General Relativity and Gravitation (2013-16)
Member, Crighton Medal Committee, Institute of Mathematics and its Applications
  and London Mathematical Society (2015)

Contents of this page

This page gives information on:


School of Mathematical Sciences
Queen Mary University of London
Mile End Road
London E1 4NS

+44 (0)20 7882 5494 (department)
or +44 7967 666810 (Mobile)
or Skype: mahmacc

Last updated 25 February 2022

Disclaimer: Any opinion or statement on this page or other pages by me is my responsibility alone. This page has not been reviewed or approved by Queen Mary University of London.

Description of my research interests

Most aspects of classical non-Newtonian gravity theory.
Computer algebra applied to differential equations (nothing to do with gravity).

In general relativity and gravity theory, my particular interests are in spacetime invariants and their applications; exact solutions of the Einstein equations; applications of algebraic computing; anisotropic and/or inhomogeneous cosmologies; theory of gravitational waves; black holes; and asymptotics. I have also written on twistor theory, and on thermodynamics.

In computer algebra, I am interested in the design and applications of manipulators for use in differential geometry and gravity theory, and in the solution of ordinary differential equations, and I use in particular REDUCE and SHEEP/CLASSI in those applications.

I have recently become interested in quantum computing, but more as a spectator than a participant.

My early work, beginning with my Ph.D., initially under the late Dennis Sciama and subsequently under George Ellis, was in spatially-homogeneous relativistic cosmological models (work later mentioned in Ellis's FRS citation!). Ellis and I provided the first comprehensive overview of the non-tilted cases, giving a classification, metric forms, various exact solutions, general theorems, and first treatments of the observational and dynamical properties. This led naturally, because those models provided the early examples, to an interest in the early days of quantum cosmology. It also led to an interest in covariant methods and exact solutions in cosmology, areas in which I have continued to work throughout my career.

During a visit by the late Abe Taub to Cambridge, he became interested in my explanation of why the obvious reduced Lagrangian for spatially-homogeneous relativistic cosmologies gave wrong answers in certain cases. He arranged for me to visit Berkeley in 1971 to work on that, and then again the next year for work on the averaged Lagrangian for gravitational waves. The resulting interest in waves has again continued.

Stephen Hawking arranged a series of lectures in Cambridge by Roger Penrose (now Sir Roger Penrose, O.M., and a Nobel Prize winner) on twistors. My notes on this, originally intended just for private circulation, grew into a well-known review with Penrose as lead author.

After moving to London, I met Hans Stephani, through the late Bill Bonnor. Soon afterwards Hans asked me to work with him, Dietrich Kramer and Eddie Herlt on a book on exact solutions, which came out in 1980. This became (for all of us) our most widely-cited work. It led to a series of papers on exact solutions in various contexts, a topic on which I still work. A second edition of the book itself, with Cornelius Hoenselaers as fifth author, appeared in 2003, and a corrected paperback edition in 2009. Sadly all my co-authors had by 2020 passed away.

The 1970s work on our first edition showed me that some computer algebraic methods were needed. My student Gordon Joly researched possible systems and we made contact with Inge Frick and Jan Åman, authors of SHEEP and CLASSI. Through them I became involved in the equivalence of geometries, following the ideas of Cartan as developed by Anders Karlhede. The late Stephen Siklos also played a role in development of my ideas here. Theory and practice in this area is another still continuing area of my work. Later it tied up with work on asymptotics of spacetimes (with, perhaps, links to gravitational wave theory), in particular with Piotr Chrusciel and Jacek Jezierski.

Contact with computer algebra led me to start to use it in teaching and other research, and the teaching use, as well as a role as editor on a book by Stephani on Lie symmetry methods, led me to research in its use for differential equations. This has become a research interest independent of the relativity work.

A short Curriculum vitae

Professor Malcolm A.H. MacCallum,
M.A., Ph.D., F.I.M.A., F.R.A.S., F.Inst.P.

Current status
Emeritus Professor of Applied Mathematics, Queen Mary University of London, since 2009
Golden Oldies Editor and Associate Editor, "General Relativity and Gravitation"
Previous emloyment
University of York (2012-17):
  Chair, Advisory Board, University of York Mathematics Department
University of Bristol (2009-12):
  Director, Heilbronn Institute for Mathematical Research, and
  Visiting Professor of Mathematics, University of Bristol
Queen Mary University of London (current working name) (1976-2009)
Queen Mary College until 1989, then Queen Mary and Westfield College until 2013:
  Professor of Applied Mathematics 1986-2009;
  Vice-Principal for Science and Engineering 2002-5;
  Head of the Department of Computer Science, 1999-2002;
  Dean of the Faculty of Informatics and Mathematical Sciences 1987-90 and 1996-1999;
  Director of Mathematics 1993-96;
  Reader in Applied Mathematics, 1981-6;
  Lecturer in Applied Mathematics, 1976-81
Queens' College, City University of New York: (1991-2)
  Visiting Distinguished Professor of Physics
Institut Henri Poincaré (1991)
  Université Paris VI, Laboratoire de Physique Théorique, Chercheur Associé
Monash University, Melbourne (1988):
  Visiting Professor
University of Catania, Sicily (1977 and 1978):
  Visiting Professor
King's College, Cambridge (1970-76):
  Assistant Lecturer in Mathematics and Official Fellow;
  Financial Tutor 1972-76;
  Acting Director of Studies in Mathematics 1974;
University of California, Berkeley (1971 and 1972)
  Research Mathematician

Membership of international bodies and learned societies
International Society on General Relativity and Gravitation: Deputy President, 2013-16; President 2010-13; Secretary and Treasurer 1995-2010; Founder Member 1971; Nominating Committee 1980-86; Committee 1983-92, 1995-2016; member, Scientific Committee, GR conferences GR10-12 and GR15-21; Chairman, Scientific Committee, GR11, Stockholm 1986.

From 1989-2009 I ran an information service for researchers in gravity, sponsored by the GRG Society and now run by Luciano Rezzolla and hosted at Frankfurt, after a period at the Albert Einstein Institute, Potsdam: see the Hyperspace Web site.

General Relativity and Gravitation: Associate Editor, 2006-; Chair, "Golden Oldies" committee 2014-
Classical and Quantum Gravity: (First) Honorary Editor, 1984-1988. Editorial Board 1992-6
Journal of Symbolic Computation: Applications Section Editor 1987-2001

London Mathematical Society: Council 1997-2003; Crighton Prize Committee (joint with Institute of Mathematics and its Applications) 2015; Research Policy Committee 2008-14; Women in Mathematics Committee 1999-2004; Prizes Committee 2005-6; Nominating Committee, elected 2006-8, appointed 2000 and 2002; Computer Systems Group (Chair; later Convenor) 2000-4; Finance Committee, 1998-2002; Applied Mathematics Working Group (Convenor) 1998-2000; Building Working Party 1997-8.

Member, International Astronomical Union (and Commission 47: Cosmology).
General chair, ISSAC 94, International Symposium on Symbolic and Algebraic Computation, Oxford, U.K.

Higher Education
King's College, Cambridge 1963-70 (Open Scholar 1963-5, Senior Scholar 1965-66)

B.A. (Cantab.) with First Class Honours in the Mathematics Tripos Part I (1964), Prelims to Part II (1965), and Part II (1966), and Distinction in Part III (1967).
M.A. (Cantab.) 1970
Ph.D. (Cantab.) 1971

Other activities
Member, Sub-panel 21 (Applied Mathematics), RAE2008 (UK Research Assessment Exercise) 2005-8.
Member, Mathematical Sciences Sub-Committee, University Grants Committee, 1988-1989 and Mathematical Sciences Research Assessment Panel, Universities Funding Council, 1989: adviser to Applied Mathematics Research Assessment Panel, HEFCE 2001.
(Also numerous London University and Queen Mary bodies).


I have published over 160 papers, review articles and books: a full list is available from this Web page. I have also written parts of the widely-distributed computer algebra system for relativity, SHEEP/CLASSI, and a simple ODE solver for REDUCE, now in the distributed REDUCE library.

Publications and preprints since 2016

  • M. A. H. MacCallum
    Spacetimes with continuous local isotropy
    Preprint, QMUL (2022)
    A summary of the series of 2021 papers on this topic
    To appear in a special number of Int. J. Mod. Phys. D for the 4th Punjab University Conference on Gravitation and Cosmology, PUICGC4.

  • G. F. R. Ellis and M. A. H. MacCallum
    Editorial note to: A threedimensional formulation of the Bianchi identities for vacuum gravitational fields by Manfred Trümper
    Gen. Relativ. Gravit. 53, 111 (2021)

  • M. A. H. MacCallum
    Spacetimes with continuous local isotropies III: null rotations
    Gen. Relativ. Gravit. 53, 96 (2021)
    Available on line .

  • M. A. H. MacCallum
    Spacetimes with continuous local isotropies II: boosts
    Gen. Relativ. Gravit. 53, 61 (2021)
    Available on line .

  • M. A. H. MacCallum
    Spacetimes with continuous local isotropies I: spatial rotations
    Gen. Relativ. Gravit. 53, 57 (2021)
    Available on line .

  • M. A. H. MacCallum
    Totally symmetrized spinors and null rotation invariance
    Class. Quantum Grav. 37, 195011 (2020)
    Available on line .

  • F. De Paolis, I. Hussain, M. A. H. MacCallum, and A. Qadir
    Editorial (Preface of the Special Issue: Proceedings of the Sixth Italian-Pakistani Workshop on Relativistic Astrophysics)
    Int. J. Mod. Phys. D 28(16), 2002001 (2019).

  • M. A. H. MacCallum
    Singularity studies: a bystander’s view
    Write-up, Queen Mary University of London (2019)
    Talk given at the Sixth Italian-Pakistani Workshop on Relativistic Astrophysics, Islamabad, January 2019. Not included in the Proceedings
    Available on line .

  • M. A. H. MacCallum
    Invariants, singularities and horizons
    Int. J. Mod. Phys. D 28(16), 2040002 (2019).

  • M. A. H. MacCallum
    Computer algebra in gravity research
    Living Reviews in Relativity 21, 6 (2018)
    Available on line .

  • D. Brooks, P. C. Chavy-Waddy, A. A. Coley, A. Forget, D. Gregoris, M. A. H. MacCallum, and D. D. McNutt
    Cartan Invariants as Event Horizon Detectors
    Gen. Relativ. Gravit. 50, 37 (2018)
    This version was an ``Editor's choice" in the journal. A more detailed version is available online.

  • J. D. Gibbon, S. C. Cowley, N. Joshi, and M. A. H. MacCallum
    Martin David Kruskal. 28 September 1925 - 26 December 2006
    Biographical Memoirs of the Royal Society (2017)
    Preprint available on line .
    Online version as published is at

    List of published papers, books etc

    This sub-page gives access to a complete list of my publications in refer or BibTeX format. The refer format list includes work in preparation ('refer' is a standard Berkeley Unix bibliographic program: the GNU (and hence Linux) version differs slightly. BibTeX is the bibliographic package designed to work with LaTeX)

    The same list is also available in HTML form suitable for reading in the browser.

    Reports on past Research Council grants

    Posting these was a condition of the grants

    Useful links

    And some links just for fun or interest