The total space-time of a point-mass when Λ≠0, and its consequences for the Lake-Roeder black hole

Physica A: Statistical Mechanics and its Applications

Volumn 227, Issue 1-2, 1996, Pages 131-140

  Abrams, Leonard S ^a  

^a Minimax   (United States)

Author keywords

Black holes; Boundaries; Incomplete space times

Indexed keywords

EID: 0010087851     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/0378-4371(95)00383-5     Document Type: Article

References (19)

1. F.J. Tipler, C.J.S. Clarke, and G.F.R. Ellis, in General Relativity and Gravitation: one hundred years after the birth of Albert Einstein, A. Held, ed. (Plenum Press, 1980), p. 97.
2. B.G. Schmidt, Gen. Rel. Gravitation 1 (1969) 269.
3. R.P. Geroch, J. Math. Phys. 9 (1968) 450.
4. C.T.J. Dodson, Gen. Rel. Gravitation 10 (1979) 969.
5. S.W. Hawking and G.F.R. Ellis, The large scale structure of space time (Camb. Univ, Press, Cambridge, 1973), p. 276.
6. 2, which in fact can only be obtained from the general one (2.1) by a transformation equivalent to r* = [C(r)]1/2. Despite Weyl's use of this transformation for the case Λ = 0, which makes it impossible to determine the location of the point-mass in terms of r*, he nonetheless asserted (on p. 131) that the point-mass in that case was located at r* = 2ml Of course, he was familiar with Schwarzschild's and Flamm's papers, which likewise put the point-mass there, but it is curious that he did not assert this in connection with his derivation of the point-mass for Λ ≠ 0 some 90 pages later. [Weyl dropped the assertion that the point-mass for Λ = 0 was at r* = 2m in subsequent editions of his book. It would seem to be worthwhile to look into Weyl's correspondence with Einstein, Flamm, Hilbert, etc., in the hopes of finding out what caused him to switch the point-mass position from r* = 2m to r* = 0.]
7. 2, which in fact can only be obtained from the general one (2.1) by a transformation equivalent to r* = [C(r)]1/2. Despite Weyl's use of this transformation for the case Λ = 0, which makes it impossible to determine the location of the point-mass in terms of r*, he nonetheless asserted (on p. 131) that the point-mass in that case was located at r* = 2ml Of course, he was familiar with Schwarzschild's and Flamm's papers, which likewise put the point-mass there, but it is curious that he did not assert this in connection with his derivation of the point-mass for Λ ≠ 0 some 90 pages later. [Weyl dropped the assertion that the point-mass for Λ = 0 was at r* = 2m in subsequent editions of his book. It would seem to be worthwhile to look into Weyl's correspondence with Einstein, Flamm, Hilbert, etc., in the hopes of finding out what caused him to switch the point-mass position from r* = 2m to r* = 0.]
8. N. Stavroulakis, Ann. Fond. Louis de Broglie 6 (1981) 287.
9. R.K. Sachs and H. Wu, General Relativity for Mathematicians (Springer, New York, 1977) p. 27. The isometry involved must be orientation- and time-orientation-preserving. Here and henceforth, the unqualified words "isometry" or "isometric" will always be understood to refer to such isometries only.
10. K. Lake and R.C. Roeder, Phys. Rev. D15 (1977) 3513.
11. H. Laue and M. Weiss, Phys. Rev. D16 (1977) 3376.
12. By "extendibility" here will always be meant analytic extendibility.
13. J. Eiesland, Trans. Am. Math. Soc. 27 (1925) 213.
14. 2/6 because of an error. See C. Lanczos, Phys. Zeitschr. XXIII (1922) 539.
15. L.S. Abrams, Can. J. Phys. 67 (1989) 919.
16. Ref. [6], p. 226: "Sie entspricht dem Fall, dass um das Zentrum ein Massenkugel liegt." ("This corresponds to the case, in which a spherical mass lies at the center.").
17. N. Doughty, Am. J. Phys. 49 (1981) 412.
18. J.L. Synge, Relativity: The General Theory (North-Holland, Amsterdam, 1960), pp. 256, 281.
19. G.F.R. Ellis and B. Schmidt, Gen. Rel. Gravitation 8 (1977) 915.