*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.

Computer algebra applied to differential equations (nothing to do with gravity).

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

In computer algebra, I am interested in use of computer algebra systems in teaching and research, in particular the use of REDUCE and SHEEP, in the design and use of manipulators for tensors in differential geometry and gravity theory, and in the solution of ordinary differential equations.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 (later to be 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 by Penrose on twistors. My notes on this, originally intended just for private circulation, grew into a well-known review, jointly with Penrose. After moving to London, through Bill Bonnor I met the late Hans Stephani who soon afterwards asked me to work with him (and Dietrich Kramer and Eddie Herlt) on a book on exact solutions, which came out in 1980. This is now (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. The 1970s work on the book 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. Stephen Siklos also played a role in development of my ideas here. The theory and practice in this area has led to another still continuing area of 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.

M.A., Ph.D., F.R.A.S., F.Inst.P.

**Current status**

Emeritus Professor of Applied Mathematics,
Queen Mary, University of London

Deputy President, International Society on General Relativity and
Gravitation

Chair, Advisory Board, University of York Mathematics Department

Golden Oldies Editor and Associate Editor, "General
Relativity and Gravitation"

**Previous positions**

*University of Bristol*:

Director, Heilbronn Institute for Mathematical Research, and
Visiting Professor of Mathematics, University of Bristol (2009-12)

*Queen Mary University of London* (Queen Mary College until 1989,
then
Queen Mary and Westfield College 1989-2013, with working name
Queen Mary, University of London)

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*, Visiting Distinguished
Professor of Physics (Fall semester 1991)

*Institut Henri Poincaré*, Université Paris VI, Laboratoire de
Physique Théorique, Chercheur Associé 1991 (3 months)

*Monash University*, Melbourne, 1988: Visiting Professor

*University of Catania*, Sicily, 1977 and 1978: Visiting Professor

*King's College, Cambridge* 1970-76: Financial Tutor 1972-76;
Acting Director of Studies in Mathematics 1974;
Assistant Lecturer in Mathematics and Official Fellow 1970-76

*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-; member, Scientific Committee, 10th
Conference (GR10),
Padua, 1983; GR12, Boulder 1989; GR15, Pune, 1997;
GR16, Durban, 2001; GR17, Dublin 2004; GR18, Sydney, 2007; GR19,
Mexico City, 2010; GR20, Warsaw 2013.
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 hosted at the Albert Einstein
Institute: 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; 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)

**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

**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).

**Publications**

I have published over 140 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. Akbar and M. A. H. MacCallum

**Static Axisymmetric Einstein Equations in Vacuum: Symmetry, New Solutions and Ricci Solitons**

(2015)

Available on line . - T. Buchert, M. Carfora, G. F. R. Ellis, E. W. Kolb, M. A. H. MacCallum,
J. J. Ostrowski, S. Räsänen, B. F. Roukema, L. Andersson, A. A. Coley,
and D. L. Wiltshire

**Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?**

(2015)

Available on line . - M.A.H. MacCallum

**A century of general relativity**

Mathematics Today (2015)

Semi-popular review. In press. To appear in October 2015. - A. Ashtekar, B.K. Berger, J. Isenberg, and M.A.H. MacCallum (eds.)

**General Relativity and Gravitation: A Centennial Perspective**

Cambridge University Press, Cambridge (2015) - M. A. H. MacCallum

**Milestones of general relativity: Hubble's law (1929) and the expansion of the universe**

CQG*32*, 124002 (2015)

http://stacks.iop.org/0264-9381/32/124002

Available on line . - M. A. H. MacCallum

**Einstein's field equations**

In*The Princeton Companion to Applied Mathematics*, ed. N. J. Higham. M. R. Dennis, P. Glendinning, P. A. Martin, F. Santosa, and J. Tanner, pages 144-145. Princeton University Press, Princeton (2015). - M. A. H. MacCallum

**Spacetime invariants and their uses**

In*Proceedings of the International Conference on Relativistic Astrophysics, Lahore, February 2015*, ed. M. Sharif, pages 122-128. Punjab University Press, Lahore (2015)

The complete proceedings are available for downloading at http://icra.pu.edu.pk/ProceedingsFinal.pdf

Available on line . - A. Ashtekar, B.K. Berger, J. Isenberg, and M.A.H. MacCallum

**General Relativity and Gravitation: A Centennial Perspective**

(2014)

Editorial introductions from the Cambridge University Press book

Available on line . - M.A.H. MacCallum

**Reflections on the geometrization of physics**

In*Mathematical Structures of the Universe*, ed. M. Eckstein, M. Heller, and S.J. Szybka, pages 389-406. Copernicus Center Press, Krakow (2014) - M.A.H. MacCallum

**Einstein's field equations**

Preprint, QMUL (2014)

To appear in the Princeton Companion to Applied Mathematics, ed. N. Higham et al. - M.A.H. MacCallum

**Exact solutions of Einstein's field equations**

Scholarpedia*8(12)*, 8584 (2013)

Available on line . - M.A.H. MacCallum and W. Kundt

**Editorial note to: Pascual Jordan, Jürgen Ehlers and Rainer K. Sachs, Contributions to the theory of pure gravitational radiation. Exact solutions of the field equations of the general theory of relativity II**

Gen. Rel. Grav.*45*, 2683-2689 (2013). - A. Krasinski, G.F.R. Ellis, and M.A.H. MacCallum (editors)

**Golden Oldies in General Relativity: Hidden Gems**

Springer, Heidelberg (2013). - M.A.H. MacCallum

**Mathematics in security and intelligence**

Science in Parliament*69*(2), 21-26 (2012)

Contribution to 'Mathematics Matters', a session organised by the Parliamentary and Scientific Committee with the Council for the Mathematical Sciences, on 15 March 2012. Reprinted in Mathematics Today, vol 48, no. 4, p. 160. - G.F.R. Ellis, R. Maartens, and M.A.H. MacCallum

**Relativistic cosmology**

Cambridge University Press, Cambridge (2012). - M.A.H. MacCallum

**Editorial note to: T. Levi-Civita, The physical reality of some normal spaces of Bianchi and to: Einsteinian $ds^2$ in Newtonian fields IX: The analog of the logarithmic potential**

Gen. Rel. Grav.*43*, 2297-2306 (2011). - J. Gariel, M.A.H. MacCallum, G. Marcilhacy, and N.O. Santos

**Kerr Geodesics, the Penrose Process and Jet Collimation by a Black Hole**

Astron. Astrophys.*515*, A15-19 (2010)

Available on line .

## 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- Gravitational Waves and Gravitational Collapse Visiting Researcher: N.O. Santos (2007)
- Visiting Researcher: Prof. N.O. Santos (2005-6)
- Global models describing isolated bodies in equilibrium in general relativity Postdoc: Raul Vera; Visiting Fellows: Marc Mars and J.M.M. Senovilla (2001-3)
- Mathematical Applications of Super-Energy Tensors Visiting Fellow: J.M.M. Senovilla (1999-2000)
- Black Holes in non-flat backgrounds Visiting Fellow: C.V. Vishveshwara (1998-99)

## Useful links

- The Cathode project
- Hyperspace: GR information
- Computer Algebra Information:
- Aldor
- Axiom
- MAGMA
- Reduce
- Reduce at Codemist (CSL)
- CONVODE (ODE solver program in Reduce)
- Cain (Computer Algebra Information Network)
- SymbolicNet
- Barcodes Inc List of resources

- Learned societies etc
- ACM (Association of Computing Machinery)
- (UK) Institute of Physics
- London Mathematical Society
- Newton Institute, Cambridge
- (UK) Conference of Profs. of Applied Mathematics

- UK Mirror service
- Strings Wiki
- Dunsby's GR course
- Funding agencies

## And some links just for fun or interest