Galactic Potentials

Physical Review Letters

Volumn 92, Issue 5, 2004, Pages 511011-511014

  Lake, Kayll ^a  

^a QUEEN S UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; BOUNDARY CONDITIONS; DOPPLER EFFECT; FUNCTIONS; GRAVITATION; INFORMATION ANALYSIS; MAPPING; NEWTONIAN FLOW; ROTATION; THEOREM PROVING;

GALACTIC POTENTIALS; GEODESIC ORBITS;

GEODESY;

EID: 1642344781     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. See, for example, L. Bergstrom, Rep. Prog. Phys. 63, 793 (2000).
2. An influential early work is S. Faber and J. Gallagher, Annu. Rev. Astron. Astrophys. 17, 135 (1979). For a recent review, see Y. Sofue and V. Rubin, Annu. Rev. Astron. Astrophys. 39, 137 (2001).
3. An influential early work is S. Faber and J. Gallagher, Annu. Rev. Astron. Astrophys. 17, 135 (1979). For a recent review, see Y. Sofue and V. Rubin, Annu. Rev. Astron. Astrophys. 39, 137 (2001).
4. See, for example, R. Sanders and S. MCGaugh, Annu. Rev. Astroa Astrophys. 40, 263 (2002).
5. There are a large number of recent works is the same general spirit as this paper. See, for example, U. Nucamendi, M. Salgado, and D. Sudarsky, Phys. Rev. D 63, 125016 (2001); L. Cabral-Rosetti, T. Matos, D. Nuñez, and Roberto A. Sussman, Classical Quantum Gravity 19, 3603 (2002); F. E. Schunck, astro-ph/9802258; E.W. Mielke and F. E. Schunck, Phys. Rev. D 66, 023503 (2002) ; S. Bharadwaj and S. Kar, Phys. Rev. D 68, 023516 (2003).
6. There are a large number of recent works is the same general spirit as this paper. See, for example, U. Nucamendi, M. Salgado, and D. Sudarsky, Phys. Rev. D 63, 125016 (2001); L. Cabral-Rosetti, T. Matos, D. Nuñez, and Roberto A. Sussman, Classical Quantum Gravity 19, 3603 (2002); F. E. Schunck, astro-ph/9802258; E.W. Mielke and F. E. Schunck, Phys. Rev. D 66, 023503 (2002) ; S. Bharadwaj and S. Kar, Phys. Rev. D 68, 023516 (2003).
7. There are a large number of recent works is the same general spirit as this paper. See, for example, U. Nucamendi, M. Salgado, and D. Sudarsky, Phys. Rev. D 63, 125016 (2001); L. Cabral-Rosetti, T. Matos, D. Nuñez, and Roberto A. Sussman, Classical Quantum Gravity 19, 3603 (2002); F. E. Schunck, astro-ph/9802258; E.W. Mielke and F. E. Schunck, Phys. Rev. D 66, 023503 (2002) ; S. Bharadwaj and S. Kar, Phys. Rev. D 68, 023516 (2003).
8. There are a large number of recent works is the same general spirit as this paper. See, for example, U. Nucamendi, M. Salgado, and D. Sudarsky, Phys. Rev. D 63, 125016 (2001); L. Cabral-Rosetti, T. Matos, D. Nuñez, and Roberto A. Sussman, Classical Quantum Gravity 19, 3603 (2002); F. E. Schunck, astro-ph/9802258; E.W. Mielke and F. E. Schunck, Phys. Rev. D 66, 023503 (2002) ; S. Bharadwaj and S. Kar, Phys. Rev. D 68, 023516 (2003).
9. There are a large number of recent works is the same general spirit as this paper. See, for example, U. Nucamendi, M. Salgado, and D. Sudarsky, Phys. Rev. D 63, 125016 (2001); L. Cabral-Rosetti, T. Matos, D. Nuñez, and Roberto A. Sussman, Classical Quantum Gravity 19, 3603 (2002); F. E. Schunck, astro-ph/9802258; E.W. Mielke and F. E. Schunck, Phys. Rev. D 66, 023503 (2002) ; S. Bharadwaj and S. Kar, Phys. Rev. D 68, 023516 (2003).
10. We use geometrical units throughout, a signature of +2 and the summation convention.
11. Here an overdot (̇) signifies differentiation with respect to an affine parameter, the proper time in the timelike case.
12. Henceforth we do not explicitly write out functions of r [e.g., Φ ≡ Φ(r)], and we use / Φ d/dr.
13. For a careful derivation, see E. Schrödinger, Expanding Universes (Cambridge University Press, Cambridge, England, 1956).
14. 2, where c is the constant of integration. Both (7) and (9) require c < 0, and so the required potential is of the anti-de Sitter form, though there is no suggestion that c is universal. This already makes clear that there is a fitting problem in the sense that if Φ(∞) = 0 then the fundamental character of Φ(r) changes in the intervening region.
15. 2 + β), where α and β are positive constants characteristic of a particular galaxy.
16. 2 + β), where α and β are positive constants characteristic of a particular galaxy.
17. 2 + β), where α and β are positive constants characteristic of a particular galaxy.
18. 2)] and d is a constant of integration (≠ 0)
19. 2). Alternate full rotation curves, not just a "halo" component, can be considered and Φ solved in exactly the same way. In general, one would expect recourse to numerical procedures, but in all cases Φ must satisfy conditions (7), (9), and (17).
20. 2). Alternate full rotation curves, not just a "halo" component, can be considered and Φ solved in exactly the same way. In general, one would expect recourse to numerical procedures, but in all cases Φ must satisfy conditions (7), (9), and (17).
21. 2). Alternate full rotation curves, not just a "halo" component, can be considered and Φ solved in exactly the same way. In general, one would expect recourse to numerical procedures, but in all cases Φ must satisfy conditions (7), (9), and (17).
22. D. Lovelock, J. Math. Phys. (N.Y.) 13, 874 (1972).
23. See K. Lake, Phys. Rev. D 67, 104015 (2003) for the case H = 0. Somewhat simpler forms of the procedure described there have been given recently by D. Martin and M. Visser, gr-qc/0306109, and by Jan Gogolin (private communication). Here we continue to use Φ and Φ because of conditions (7), (9), and (17).
24. See K. Lake, Phys. Rev. D 67, 104015 (2003) for the case H = 0. Somewhat simpler forms of the procedure described there have been given recently by D. Martin and M. Visser, gr-qc/0306109, and by Jan Gogolin (private communication). Here we continue to use Φ and Φ because of conditions (7), (9), and (17).
25. See K. Lake, Phys. Rev. D 67, 104015 (2003) for the case H = 0. Somewhat simpler forms of the procedure described there have been given recently by D. Martin and M. Visser, gr-qc/0306109, and by Jan Gogolin (private communication). Here we continue to use Φ and Φ because of conditions (7), (9), and (17).
26. 2φ ≃ 1 - 2m/r. (33) Neither of the approximations (32) nor (33) produce a workable Newtonian limit for our considerations here.
27. P. Musgrave and K. Lake, Classical Quantum Gravity 13, 1885 (1996).
28. This is a package which runs within MAPLE. It is entirely distinct from packages distributed with MAPLE and must be obtained independently. The GRTensorII software and documentation is distributed freely on the World Wide Web from the address http://grtensor.org