Measures of gravitational entropy: Self-similar spacetimes

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 62, Issue 4, 2000, Pages 1-5

  Pelavas, Nicos ^a   Lake, Kayll ^a  

^a QUEEN S UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17044396765     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.62.044009     Document Type: Article

References (18)

1. See, for example, R. Penrose, in General Relativity: An Einstein Centennial Volume, edited by W. Israel and S. W. Hawking (Cambridge University Press, Cambridge, England, 1979). An updated readable account is given in R. Penrose, The Emperor's New Mind (Oxford University Press, Oxford, 1990).
2. See, for example, R. Penrose, in General Relativity: An Einstein Centennial Volume, edited by W. Israel and S. W. Hawking (Cambridge University Press, Cambridge, England, 1979). An updated readable account is given in R. Penrose, The Emperor's New Mind (Oxford University Press, Oxford, 1990).
3. The Weyl curvature hypothesis has been interpreted in a number of ways, but the form proposed by Penrose is made clear in a comment by Penrose in T. Rothman "A Phase Space Approach to Gravitational Entropy," South African Relativistic Cosmology Symposium, 1999, gr-qc/9906002.
4. K. Anguige and K. P. Tod, Ann. Phys. (N.Y.) 276, 257 (1999).
5. S. M. Scott and G. Ericksson, in Proceedings of the International of the Seminar on Mathematical Cosmology, Potsdam, 1998, edited by M. Rainer and H.-J. Schmidt (WSPC, Singapore, 1998).
6. See, for example, B. O'Neill, Semi-Riemannian Geometry (Academic, New York, 1983).
7. We use classical index notation throughout. This is done for readability. The calculations reported here are, for the most part, far more easily executed with spinors.
8. See, for example, S. W. Goode, A. A. Coley, and J. Wainwright, Class. Quantum Grav. 9, 445 (1992) and references therein.
9. T. Rothman and P. Anninos, Phys. Rev. D 55, 1948 (1997).
10. W. B. Bonnor, Phys. Lett. A 122, 305 (1987).
11. B. J. Carr and A. A. Coley, Class. Quantum Grav. 16, R13 (1999) and references therein.
12. K. Yano, The Theory of Lie Derivatives and its Applications (North-Holland, Amsterdam, 1955).
13. Setting φ=0 in what follows shows the evolution along the Killing trajectories of a stationary spacetime.
14. See, for example, R. Penrose and W. Rindler, Spinors and Spacetime (Cambridge University Press, Cambridge, England, 1984), Vol. 1.
15. Pi is even; this applies to invariants built out of trace-free Ricci, Weyl and conjugate Weyl tensors.
16. i be odd.
17. qiε{S,C,C*} without regard for the configuration of the indicies.
18. GRTensorII is a package which runs within MapleV. It is entirely distinct from packages distributed with MapleV and must be obtained independently. The GRTensorII software and documentation is distributed freely on the World-Wide-Web from the address http://grtensor.phy.queensu.ca