Publications of Professor J A G Vickers
Refereed papers in Journals
1. The positivity of the Bondi mass
J. Phys. A: Math. Gen. 14 L389-391 (1981) (with M Ludvigsen)
2. A simple proof of the positivity of the Bondi mass
J. Phys. A: Math. Gen. 15 L67-70 (1982) (with M Ludvigsen)
3. Trapped surfaces and the positivity of the Bondi mass
J. Phys. A: Math. Gen. 15 L473-476 (1982) (with M Ludvigsen)
4. Momentum, angular momentum and their quasi-local null surface extensions
J. Phys. A: Math. Gen. 16 1155-68 (1983) (with M Ludvigsen)
5. An inequality relating mass and electric charge in general relativity
J. Phys. A: Math. Gen. 16 1169-74 (1983) (with M Ludvigsen)
6. An inequality relating total mass and the area of a trapped surface in general relativity
J. Phys. A: Math. Gen. 16 3349-3353 (1983) (with M Ludvigsen)
7. Unstable singularities in general relativity
Class. Quantum Grav. 2 755-773 (1985)
8. Exceptional sets in Kolmogorov-Arnold-Moser theory
J. Phys. A: Math. Gen. 19 349-374 (1986) (with M M Dodson)
9. Everywhere invariant spaces of metrics and isometries
GRG 18 1093-1103 (1986) (with R A d'Inverno and S T Swift)
10. Generalised Cosmic Strings
Class. Quantum Grav. 3 12-22 (1986)
11. Metric Diophantine approximation and Hausdorff dimension on manifolds
Math. Proc. Cam. Phil. Soc. 105 574-558 (1989) (with M M Dodson and B P Rynne)
12. Averaging in multifrequency systems
Nonlinearity 2 134-145 (1989) (with M M Dodson and B P Rynne)
13. The large scale bending of Cosmic Strings
Class. Quantum Grav. 7 1-14 (1990) (with C J S Clarke and G F R Ellis)
14. Diophantine approximation and a lower bound for Hausdorff dimension
Mathematika 37 59-73 (1990) (with M M Dodson and B P Rynne)
15. Dirichelet's theorem and Diophantine approximation on manifolds
J Number Theory 36 85-88 (1990) (with M M Dodson and B P Rynne)
16. Quasi-regular singularities and cosmic strings
Class. Quantum Grav. 7 731-741 (1990)
17. Diophantine approximation by linear forms on manifolds
18. The Karlhede classification of type D space-times
Class. Quantum Grav. 7 2005-2015 (1990) (with R A d'Inverno and J M Collins)
19. Khintchine type theorems on manifolds
Acta Arithmetica 57 115-130 (1990) (with M M Dodson and B P Rynne)
20. Upper bounds for the Karlhede classification of type D space-times
Class. Quantum Grav. 8 L215-217 (1991) (with R A d'Inverno and J M Collins)
21. Singularities, distributional curvature and cosmic strings.
Rendiconti di Seminario Matematico di Torino 50 1-25 (1992)
22. The Hausdorff dimension of small divisors for lower dimensional KAM-tori
Proc. R. Soc. A 439 359-371 (1992) (with M M Dodson J Poschel and B P Rynne)
23. The Hausdorff dimension of exceptional sets associated with normal forms
J. LMS 49 614-624 (1994) (with M M Dodson and B P Rynne)
24. 2+2 decomposition of Ashtekar's variables.
Class. Quantum Grav. 12 753-768 (1995) (with R A d'Inverno)
25. A spacetime calculus invariant under null rotations
Proc. R. Soc. A 450 693-709, (1995) (with M P Machado Ramos)
26. Combining Cauchy and characteristic codes I : The vacuum cylindrically symmetric problem
Phys Rev D 52 6863-6867 (1995) (with C J S Clarke and R A d'Inverno)
27. A spacetime calculus based on a single null direction
Class. Quantum Grav. 13 1579-1587 (1996) (with M P Machado Ramos)
28. Invariant differential operators and the Karlhede classification of type N vacuum solutions
Class. Quantum Grav. 13 (1996) (with M P Machado Ramos)
29. Simultaneous Diophantine approximation and asymptotic formulae on manifolds
J Number Theory 58 298-316 (1996) (with M M Dodson and B P Rynne)
30. Combining Cauchy and characteristic codes III : The interface for axial symmetry
Phys Rev D 54 1 - 10 (1996) (with R A d'Inverno)
31. Generalised functions and distributional curvature of cosmic strings
Class. Quantum Grav. 13 2485-2498 (1996) (with C J S Clarke and J P Wilson)
32. Combining Cauchy and characteristic codes IV : The characteristic field equations
Phys Rev D 56 722-784 (1997) (with R A d'Inverno)
Phys Rev D 58 4019-4031 (with M R Dubal and R A d'Inverno)
34. Invariance of the distributional curvature of the cone under smooth diffeomorphisms
Class. Quantum Grav. 16 579-588 (1999) (with J
P
35. Integration using invariant operators: conformally flat radiation metrics
Class. Quantum Grav. 16 589-604 (1999) (with S B Edgar)
36. Generalised hyperbolicity in conical space-times
Class. Quantum Grav. 17 1333-1360 (2000) (with
J P
37. Diffeomorphism invariant construction of nonlinear generalized functions
Ann. der Physik 11 507-510 (2000) (with M Grosser, M Kunzinger, R Steinbauer, H Urbantke)
Phys. Rev. D62 (2000) (with K R P Sjödin and U Sperhake)
39. Dynamic Cosmic Strings II.
Numerical evolution of excited cosmic strings Phys. Rev. D62 (2000)(with U Sperhake and K R P Sjödin)
40. Conflicting Arrows of Time
Nature 403 609 (2000) (article for News and Views with P T Landsberg)
41. Metric-Affine gravity and the Nester-Witten 2-form
J. Geometry and Physics 39 265-275 (2001) (with M Godina and P Matteucci)
42. A global theory of algebras of generalized functions
Advances in Mathematics 166 50-72 (2002) (with M Grosser, M Kunzinger and R Steinbauer)
43. Intrinsic characterization of manifold-valued generalized functions
Proceedings of the LMS 87 451-470 (2003) (with M Kunzinger and R Steinbauer)
44. Generalized flows and singular ODEs on differentiable manifolds
Acta Appl. Math. 80 221-241 (2004) (with M Kunzinger, M Oberguggenberger and R Steinbauer)
45. Generalised connections and curvature
Math. Proc. Cam. Phil. Soc. 497-521 (2005) (with M Kunzinger and R Steinbauer)
46. Global Gronwall estimates for integral curves on Riemannian manifolds
Rev. Mat. Complut. 19 133-137 (2006) (with M Kunzinger, H Sichl and R Steinbauer)
47. The use of generalised functions and distributions in general relativity
Class. Quantum Grav. 23 R91-R114 (2006) (with R Steinbauer)
48. Hamiltonian analysis of the double null 2+2 decomposition of Ashtekar variables
Class. Quantum Grav. 23 3747-3761 (2006) (with R A d'Inverno and P Lambert)
Class. Quantum Grav. 23 4511-4522 (2006) (with R A d'Inverno and P Lambert)
50. Weak singularities in general relativity
International Journal of Modern Physics A. Particles and Fields, Gravitation, Cosmology, Nuclear Physics 17 2779 (2006)
51. Sheaves of nonlinear generalized functions and manifold valued distributions
Transactions of the AMS 361 5177-5192 (2009) (with M Kunzinger and R Steinbauer)
52. On the Geroch-Traschen class of metrics
Class. Quantum Grav. 26 065001 1-19 (2009) (with R Steinbauer)
53. Block diagonalisation of four-dimensional metrics
Class. Quantum Grav. 26 235014 1-23 (2009) (with J D E Grant)