Abstract
Using K-causal relation introduced by Sorkin and Woolgar [1], we generalize results of Garcia-Parrado and Senovilla [2,3] on causal maps. We also introduce causality conditions with respect to K-causality which are analogous to those in classical causality theory and prove their inter-relationships. We introduce a new causality condition following the work of Bombelli and Noldus [4] and show that this condition lies in between global hyperbolicity and causal simplicity. This approach is simpler and more general as compared to traditional causal approach [5,6] and it has been used by Penrose et al [7] in giving a new proof of positivity of mass theorem. C 0-space-time structures arise in many mathematical and physical situations like conical singularities, discontinuous matter distributions, phenomena of topology-change in quantum field theory etc.
Similar content being viewed by others
References
R D Sorkin and E Woolgar, Class. Quant. Grav. 3, 1971 (1996)
A Garcia-Parrado and J M Senovilla, Class. Quant. Grav. 20, 625 (2003)
A Garcia-Parrado and J M Senovila, Class. Quant. Grav. 21, 661 (2004)
L Bombelli and J Noldus, Class. Quant. Grav. 21, 4429 (2004)
S W Hawking and G F R Ellis, The large scale structure of space-time (Cambridge Univ. Press, Cambridge, 1973)
R Penrose, Techniques of differential topology in relativity (SIAM, Philadelphia, 1972)
R Penrose, R D Sorkin and E Woolgar, gr-qc/9301015
P S Joshi, Global aspects in gravitation and cosmology (Oxford Press, Oxford, 1993)
D P Rideout and R D Sorkin, Phys. Rev. D61, 024002 (2000)
R D Sorkin, gr-qc/0309009
R D Sorkin gr-qc/ 0710.1675
K Martin, Class. Quant. Grav. 23, 1241 (2006)
M Rainer, Int. J. Mod. Phys. D4, 397 (1995)
M Rainer, Gravitation and cosmology 1, 121 (1995)
R Wald, General relativity (Univ. of Chicago Press, 1984)
J K Beem, P E Ehrlich and K L Easley, Global Lorentzian geometry (Monographs Textbooks, Pure Appl. Mathematics, Dekker Inc., New York, 1996)
H F Dowker, R S Garcia and S Surya, Class. Quant. Grav. 17, 4377 (2000)
E Minguzzi, gr-qc/0703128
S W Hawking and R K Sachs, Commun. Math. Phys. 35, 287 (1974)
J K Beem, Gen. Relativ. Gravit. 8(4), 245 (1977)
R Geroch, J. Math. Phys. 11, 437 (1970)
J Dieckmann, Gen. Relativ. Gravit. 20(9), 59 (1988)
E C Zeeman, J. Math. Phys. 5, 490 (1964)
C J S Clarke and P S Joshi, Class. Quant. Grav. 5, 19 (1988)
K Martin and P Panangaden, gr-qc/0407093
H F Dowker, R S Garcia and S Surya, Class. Quant. Grav. 17, 697 (2000)
K Martin and P Panangaden, Commun. Math. Phys. 267, 563 (2006)
J Hilgert and G Olafsson, Causal symmetric spaces, geometry and harmonic analysis (Academic Press, New York, 1997)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Janardhan, S., Saraykar, R.V. K-causal structure of space-time in general relativity. Pramana - J Phys 70, 587–601 (2008). https://doi.org/10.1007/s12043-008-0021-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12043-008-0021-4