Regular coordinate systems for Schwarzschild and other spherical spacetimes

American Journal of Physics

Volumn 69, Issue 4, 2001, Pages 476-480

  Martel, Karl ^a   Poisson, Eric ^a  

^a UNIVERSITY OF GUELPH   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044526438     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. B. F. Schutz, A First Course in General Relativity (Cambridge U. P., Cambridge, 1985).
2. C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).
3. R. M. Wald, General Relativity (Univ. of Chicago, Chicago, 1984).
4. P. Painlevé, "La Mécanique classique et la théorie de la relativité," C. R. Acad. Sci. (Paris) 173, 677-680 (1921).
5. A. Gullstrand, "Allegemeine Lösung des statischen Einkörper-problems in der Einsteinschen Gravitations theorie," Ark. Mat., Astron. Fys. 16 (8), 1-15 (1922).
6. K. Lake, "A class of quasi-stationary regular line elements for the Schwarzschild geometry" (1994) (unpublished), posted on http://. xxx.1an1.gov/abs/gr-qc/9407005.
7. R. Gautreau and B. Hoffmann, "The Schwarzschild radial coordinate as a measure of proper distance," Phys. Rev. D 17, 2552-2555 (1978).
8. R. Gautreau, "Light cones inside the Schwarzschild radius," Am. J. Phys. 63, 431-439 (1995).
9. i; they do not reach infinity.
10. S. Corley and T. Jacobson, "Lattice Black Holes," Phys. Rev. D 57, 6269-6279 (1998).
11. This strategy was used by I. D. Novikov to construct yet another set of coordinates for Schwarzschild spacetime. The reference is I. D. Novikov, Doctoral dissertation, Shternberg Astronomical Institute, Moscow (1963). The Novikov coordinates are discussed in Sec. 31.4 of Ref. 2. Unlike the coordinates considered in this paper, the Novikov coordinates are comoving with respect to the observers to which they are attached. This means that these observers move with a constant value of Novikov's spatial coordinates.
12. H. P. Robertson and T. W. Noonan, Relativity and Cosmology (Saunders, Philadelphia, 1968).
13. P. Kraus and F. Wilczek, "A simple stationary line element for the Schwarzschild geometry, and some applications," Mod. Phys. Lett. A 9, 3713-3719 (1994).
14. C. Doran, "A new form of the Kerr solution," Phys. Rev. D 61, 067503-067506 (2000).
15. max, and the new coordinates would not be defined everywhere. These cases, however, are discussed in Refs. 7 and 8. See the remark in Ref. 9.
16. 2 in Eq. (4.1) can then be absorbed into a rescaling of the time coordinate. In other words, there is no loss of generality involved in setting ψ=0 if ψ is initially an arbitrary constant.