Prof. Malcolm A.H. MacCallum
Current positions
Emeritus Professor of Applied Mathematics,
School of Mathematical Sciences,
Queen Mary University of London
Webmaster, Old Maidstonian Society and Hackney Festival Chorus
Other Positions since retirement from QMUL
Golden Oldies Editor and Associate
Editor, "General
Relativity and Gravitation" (2014-24)
President,
International Society on General Relativity and Gravitation
(2010-13); Deputy President (2013-2016)
Chair, Advisory
Board, University of York
Department of Mathematics (2012-17)
Member, Crighton Medal Committee, Institute of Mathematics and its
Applications
and
London Mathematical Society (2015)
Member, Research Policy Committee,
London Mathematical Society (2010-14)
Director,
Heilbronn Institute for Mathematical Research (2009-12)
Visiting Professor,
Department of Mathematics, University of Bristol
(2009-12)
Contents of this page
This page gives information on:
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Last updated 7 September 2026
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.
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.
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
Previous employment
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
Friedrich-Schiller Universität, Jena: (1996)
Professor of Physics
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,
2006-24; Chair, "Golden Oldies" committee 2014-24
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.
Other activities
University of York (2012-17): Chair, Advisory Board, University of York Mathematics Department
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).
Higher Education
King's College, Cambridge 1963-70 (Open Scholar 1963-5, Senior Scholar
1965-66)
Degrees
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
Publications
I have published over 170 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.
M. A. H. MacCallum
Two discs and a missing triangle: the maximally extended Kerr black hole
revisited
(2026)
Submitted to Gen. Relativ. Gravit.
Available on line .
M. A. H. MacCallum
Comment: Exact vacuum solution with Hopf structure in general
relativity
(2026)
To appear in Phys. Rev. D
Available on line .
M. A. H. MacCallum
Spacetimes with continuous local isotropy
Int. J. Mod. Phys. D 31(11), 2240005 (2022).
Selected papers of the 4th Punjab University International Conference on Gravitation and Cosmology
Guest editors: Muhammad Sharif, Francesco De Paolis, Gonzalo J. Olmo
and M. Zaeem Ul Haq Bhatti
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
(2021)
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.
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.
Posting these was a condition of the grants
And some links just for fun or interest