Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T15:20:16.334Z Has data issue: false hasContentIssue false
  • English
  • Français

Apparent horizons in vacuum Robinson-Trautman spacetimes

Published online by Cambridge University Press:  17 February 2009

E. W. M. Chow  and
A. W.-C. Lun
E. W. M. Chow
Affiliation:
Department of Mathematics, Monash University, Clayton 3168, Australia.
A. W.-C. Lun
Affiliation:
Department of Mathematics, Monash University, Clayton 3168, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Vacuum asymptotically flat Robinson-Trautman spacetimes are a well known class of spacetimes exhibiting outgoing gravitational radiation. In this paper we describe a method of locating the past apparent horizon in these spacetimes and discuss the properties of the horizon. We show that the past apparent horizon is non-timelike and that its surface area is a decreasing function of the retarded time. A numerical simulation of the apparent horizon is also discussed.

Type
Research Article
Information
The ANZIAM Journal , Volume 41 , Issue 2 , October 1999 , pp. 217 - 230
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Anninos, P., Bernstein, D., Brandt, S., Libson, J., Masso, J., Seidel, E., Smarr, L., Suen, W.-M. and Walker, P., “Event horizons of numerical black holes”, in General Relativity (MG7 Proceedings) (eds. Ruffini, R. and Keiser, M.), (World Scientific, Singapore, 1995).Google Scholar
[2]Chruściel, P. T., “Semi-global existence and convergence of solutions of the Robinson-Trautman (2-dimensional Calabi) equation”, Commun. Math. Phys. 137 (1991) 289–313.CrossRefGoogle Scholar
[3]Collins, W., “Mechanics of apparent horizons”, Phys. Rev. D45 (1992) 495–498.Google ScholarPubMed
[4]Cook, G. and York, J. M., “Apparent horizons for boasted and spinning black holes”, Phys. Rev. D41 (1990) 1077–1085.Google Scholar
[5]Foster, J. and Newman, E. T., “Note on the Robinson-Trautman solutions”, J. Math. Phys. 18 (1967) 189–194.CrossRefGoogle Scholar
[6]Gibbons, G., Hawking, S., Horowitz, G. and Perry, M., “Positive mass theorems for black holes”, Commun. Math. Phys. 88 (1983) 295–308.CrossRefGoogle Scholar
[7]Hawlang, S. W. and Ellis, G. F. R., The Large Scale Structure of Space-time (Cambridge University Press, Cambridge, 1973).Google Scholar
[8]Hayward, S. A., “General laws of black-hole dynamics”, Phys. Rev. d49 (1994) 6467–6474.Google ScholarPubMed
[9]Hoenselaers, C. and Perjés, Z., “Remarks on the Robinson-Trautman solutions”, Class. Quantum Grav. 10 (1993) 375–383.CrossRefGoogle Scholar
[10]Lukács, B., Perjés, Z., Porter, J. and Sebestyén, I., “Lyapunov functional approach to radiative metrics”. Gen. Rel. Grav. 16 (1984) 691–701.CrossRefGoogle Scholar
[11]Lun, A. W. and Chow, E. W. M., “The role of the apparent horizon in the evolution of Robinson-Trautman Einstein-Maxwell space-times”, in Confronting the Infinite (eds. Carey, A., Ellis, W., Pearce, P. and Thomas, A.), (World Scientific, Singapore, 1995).Google Scholar
[12]Nakamura, T., Kojima, Y. and Oohara, K., “A method of determining apparent horizons in three-dimensional numerical relativity”, Phys. Lett. 106A (1984) 235–238.CrossRefGoogle Scholar
[13]Penrose, R., “Naked singularities”, Ann. NY Acad. Sci. 224 (1973) 115–134.CrossRefGoogle Scholar
[14]Penrose, R. and Rindler, W., Spinors and Space-time, Volume 1 (Cambridge University Press, Cambridge, 1984).CrossRefGoogle Scholar
[15]Perjés, Z., “Robinson-Trautman space-times”, in Proceedings of the 5th Marcel Grossman Meeting (eds. Blair, D. G. and Buckingham, M. J.), (World Scientific, Singapore, 1989).Google Scholar
[16]Prager, D. and Lun, A. W. C., “Numerical integration of the Robinson-Trautman equation”, in General Relativity (MG7 Proceedings) (eds. Ruffini, R. and Keiser, M.), (World Scientific, Singapore, 1995).Google Scholar
[17]Rendall, A. D., “Existence and asymptotic properties of global solutions of the Robinson-Trautman equation”, Class. Quantum Grav. 5 (1988) 1339–1347.CrossRefGoogle Scholar
[18]Robinson, I. and Trautman, A., “Spherical gravitational waves”, Phys. Rev. Lett. 4 (1960) 431–432.CrossRefGoogle Scholar
[19]Schmidt, B., “Existence of solutions of the Robinson-Trautman equation and spatial infinity”, Gen. Rel. Grav. 20 (1988) 65–70.CrossRefGoogle Scholar
[20]Singleton, D., “Numerical evolution of the Robinson-Trautman equation”, in Proceedings of the 5th Marcel Grossman Meeting (eds. Blair, D. G. and Buckingham, M. J.), (World Scientific, Singapore, 1989).Google Scholar
[21]Singleton, D., “On global existence and convergence of vacuum Robinson-Trautman solutions”, Class. Quantum Grav. 7 (1990) 1333–1343.CrossRefGoogle Scholar
[22]Singleton, D., “Robinson-Trautman solutions of Einstein's equations”, Ph. D. Thesis, Monash University, 1990.Google Scholar
[23]Tod, K. P., “More on Penrose's quasi-local mass”, Class. Quantum Grav. 3 (1986) 1169–1189.CrossRefGoogle Scholar
[24]Tod, K. P., “Analogues of the past horizon in the Robinson-Trautman metrics”, Class. Quantum Grav. 6 (1989) 1159–1163.CrossRefGoogle Scholar
[25]Vandyck, M. A. J., “On the time evolution of some Robinson-Trautman solutions”, Class. Quantum Grav. 4 (1987) 759–767.CrossRefGoogle Scholar