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

 Proc. Ind. Acad. Sc. 100 221-229 (1990) (with M M Dodson and B P Rynne)

 

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)

 

33. Combining Cauchy and characteristic codes V : CCM for a spherical spacetime containing a perfect fluid

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 Wilson)

 

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 Wilson)

 

37. Diffeomorphism invariant construction of nonlinear generalized functions

Ann. der Physik 11 507-510 (2000) (with M Grosser, M Kunzinger, R Steinbauer, H Urbantke)

 

38. Dynamic Cosmic Strings I

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)

 

49. Hamiltonian analysis of the double null 2+2 decomposition of general relativity expressed in terms of self-dual bivectors

 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)