Papers by Malcolm Maccallum
Lecture Notes in Computer Science, 1985
ABSTRACT The equivalence problem in general relativity arises from the arbitrariness of coordinat... more ABSTRACT The equivalence problem in general relativity arises from the arbitrariness of coordinate choice and is the problem of deciding whether two apparently, different space-times are (locally) identical or not. Here we review the basic procedure for resolving this question, and its practical implementation, as presented in previous papers, and report on recent theoretical and practical research in this area. Some of the techniques are of interest in other problems; in particular, they may be applicable to tests of the equivalence of systems of differential equations.
The Petrov classification of the Weyl conformal curvature and the Plebanski or Segre classificati... more The Petrov classification of the Weyl conformal curvature and the Plebanski or Segre classification of the Ricci tensor of spacetimes in general relativity both depend on multiplicities of the roots of quartic equations. The coefficients in these quartic equations may be complicated functions of the space-time coordinates. We review briefly the general theory of quartic equations and then consider practical algorithms for determination of the multiplicities of their roots and hence for the classification of Riemann tensors. Preliminary results of tests of computer implementations of these algorithms, using the computer algebra system SHEEP, are reported.
Mathematics of Computation, 1993
Relativistic Cosmology, 2009
ABSTRACT Part I. Foundations: 1. The nature of cosmology; 2. Geometry; 3. Classical physics and g... more ABSTRACT Part I. Foundations: 1. The nature of cosmology; 2. Geometry; 3. Classical physics and gravity; Part II. Relativistic Cosmological Models: 4. Kinematics of cosmological models; 5. Matter in the Universe; 6. Dynamics of cosmological models; 7. Observations in cosmological models; 8. Light-cone approach to relativistic cosmology; Part III. The Standard Model and Extensions: 9. Homogeneous FLRW universes; 10. Perturbations of FLRW universes; 11. The cosmic background radiation; 12. Structure formation and gravitational lensing; 13. Confronting the Standard Model with observations; 14. Acceleration from dark energy or modified gravity; 15. 'Acceleration' from large scale inhomogeneity?; 16. 'Acceleration' from small scale inhomogeneity?; Part IV. Anisotropic and Inhomogeneous Models: 17. The space of cosmological models; 18. Spatially homogeneous anisotropic models; 19. Inhomogeneous models; Part V. Broader Perspective: 20. Quantum gravity and the start of the Universe; 21. Cosmology in a larger setting; 22. Conclusion: our picture of the Universe; Appendix; References; Index.
Physics Today, 1992
This book is a self-contained introduction to key topics in ad-vanced general relativity. The ope... more This book is a self-contained introduction to key topics in ad-vanced general relativity. The opening chapter reviews the subject, with strong emphasis on the geometric structures un-derlying the theory. The second chapter discusses 2-component spinor theory, its usefulness for ...
Physical Review Letters, 1998
The usual approaches to the definition of energy give an ambiguous result for the energy of field... more The usual approaches to the definition of energy give an ambiguous result for the energy of fields in the radiating regime. We show that for a massless scalar field in Minkowski space-time the definition may be rendered unambiguous by adding the requirement that the energy cannot increase in retarded time. We present a similar theorem for the gravitational field, proved elsewhere, which establishes that the Trautman-Bondi energy is the unique (up to a multiplicative factor) functional, within a natural class, which is monotonic in time for all solutions of the vacuum Einstein equations admitting a smooth "piece" of conformal null infinity J
Physical Review D, 1998
It is shown that the only functionals, within a natural class, which are monotonic in time for al... more It is shown that the only functionals, within a natural class, which are monotonic in time for all solutions of the vacuum Einstein equations admitting a smooth "piece" of conformal null infinity J ( , are those depending on the metric only through a specific combination of the Bondi 'mass aspect' and other next-to-leading order terms in the metric. Under the extra condition of passive BMS invariance, the unique such functional (up to a multiplicative factor) is the Trautman-Bondi energy. It is also shown that this energy remains well-defined for a wide class of 'polyhomogeneous' metrics.
We review the matching conditions for a collapsing anisotropic cylindrical perfect fluid, recentl... more We review the matching conditions for a collapsing anisotropic cylindrical perfect fluid, recently discussed in the literature (2005 {\it Class. Quantum Grav.} {\bf 22} 2407). It is shown that radial pressure vanishes on the surface of the cylinder, contrary to what is asserted in that reference. The origin of this discrepancy is to be found in a mistake made in one step of the calculations. Some comments about the relevance of this result in relation to the momentum of Einstein--Rosen waves are presented.
Mathematics and Computers in Simulation, 1996
... [14] MAH MacCallum and JEF Skea, SHEEP: A computer algebra system for general relativity, in:... more ... [14] MAH MacCallum and JEF Skea, SHEEP: A computer algebra system for general relativity, in: MJ Reboucas and WL Roque, eds., Algebraic Computing in General Relativity, Lecture Notes from the First Brazilian School on Computer Algebra, Vol. IT (Oxford Univ. ...
Journal of Symbolic Computation, 1997
We present an approach to computing the Darboux polynomials required in the Prelle-Singer algorit... more We present an approach to computing the Darboux polynomials required in the Prelle-Singer algorithm which avoids algebraic extensions of the constant field, and describe a partial implementation in REDUCE in which the leading terms of the polynomials are obtained by a modified version of the method described by Christopher and Collins.
International Journal of Theoretical Physics, 2006
We examine various well known exact solutions available in the literature to investigate the rece... more We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in ref. [20] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic equilibrium. It is seen that this criterion is fulfilled only by (i) the regular solutions having a vanishing surface density together with the pressure, and (ii) the singular solutions corresponding to a non-vanishing density at the surface of the configuration . On the other hand, the regular solutions corresponding to a non-vanishing surface density do not fulfill this criterion. Based upon this investigation, we point out that the exterior Schwarzschild solution itself provides necessary conditions for the types of the density distributions to be considered inside the mass, in order to obtain exact solutions or equations of state compatible with the structure of general relativity. The regular solutions with finite centre and non-zero surface densities which do not fulfill the criterion [20], in fact, can not meet the requirement of the 'actual mass' set up by exterior Schwarzschild solution. The only regular solution which could be possible in this regard is represented by uniform (homogeneous) density distribution.
General Relativity and Gravitation, 2007
A usual causal requirement on a viable theory of matter is that the speed of sound be at most the... more A usual causal requirement on a viable theory of matter is that the speed of sound be at most the speed of light. In view of various recent papers querying this limit, the question is revisited here. We point to various issues confronting theories that violate the usual constraint.
Classical and Quantum Gravity, 1998
A limiting diagram for the Segre classi cation of the energy-momentum tensor is obtained and disc... more A limiting diagram for the Segre classi cation of the energy-momentum tensor is obtained and discussed in connection with a Penrose specialization diagram for the Segre types. A generalization of the coordinate-free approach to limits of Paiva et al. to include non-vacuum space-times is made. Geroch's work on limits of space-times is also extended. The same argument also justi es part of the procedure for classi cation of a given spacetime using Cartan scalars.
Astronomy and Astrophysics, 2010
Aims. We re-examine the possibility that astrophysical jet collimation may arise from the geometr... more Aims. We re-examine the possibility that astrophysical jet collimation may arise from the geometry of rotating black holes and the presence of high-energy particles resulting from a Penrose process, without the help of magnetic fields. Methods. Our analysis uses the Weyl coordinates, which are revealed better adapted to the desired shape of the jets. We numerically integrate the 2D-geodesics equations. Results. We give a detailed study of these geodesics and give several numerical examples. Among them are a set of perfectly collimated geodesics with asymptotes ρ = ρ 1 parallel to the z−axis, with ρ 1 only depending on the ratios Q E 2 −1 and a M , where a and M are the parameters of the Kerr black hole, E the particle energy and Q the Carter's constant.
General Relativity and Gravitation, 2006
Uploads
Papers by Malcolm Maccallum