This article is a celebration of the centenary of Schwarzschild's presentations of his external and internal solutions describing spacetime outside and inside an incompressible, spherically symmetric body. I give a review of these solutions and how they have been interpreted physically.
References
1.
K.
Schwarzschild
, Gesammelte Werke/Collected Works
, edited by H. H.
Voigt
(Springer
, Berlin
, 1992
), Vols. 1
–3
.2.
K.
Schwarzschild
, “Über das gravitationsfeld eines massenpunktes nach der Einstein'schen theorie
,” Sitzungsberichte der Königlich-Preussischen Akademie der Wissenschaften 189–196 (1916). English translation: “On the gravitational field of a point mass, According to Einstein's theory
,” Gen. Relativ. Gravitation
35
, 951
–959
(2003
);3.
J.
Eisenstaedt
, “The early interpretation of the schwarzschild solution
,” in Einstein and the History of General Relativity: Einstein Studies
, edited by D.
Howard
and J.
Stachel
(Birkhauser
, Boston
, 1989
), Vol. 1
, pp. 213
–234
.4.
5.
K.
Schwarzschild
, “Über das gravitationsfeld einer kugel aus inkompressibler flüssigkeit
,” Sitzungsber. K. Preuss. Akad. Wiss.
February, 424
–434
(1916
). English translation: “On the gravitational field of a sphere of incompressible liquid, According to Einstein's theory,” Abraham Zelmanov J. 1, 20–32 (2008);e-print arXiv:physics/9912033 (
1999
).6.
J.
Droste
, “The field of a single centre in Einstein's theory of gravitation and the motion of a particle in that field
,” K. Ned. Akad. Wet. Proc.
19
, 197
–215
(1917
);reprinted in
J.
Droste
, Gen. Relativ. Gravitation
34
, 1545
–1563
(2002
).7.
C.
Corda
, “A clarification on the debate on ‘the Original Schwarzschild Solution’
,” Electron. J. Theor. Phys.
8N25
, 65
–82
(2011
).8.
Ø.
Grøn
and S.
Hervik
, Einstein's General Theory of Relativity
(Springer
, New York
, 2007
).9.
S. J.
Crothers
, “The Schwarzschild solution and its implications for gravitational waves
,” Talk at Verhandlungen der Deutsche Physikalische Gesellschaft, Munich 2009; http://www.holoscience.com/news/img/DPS%20talk.pdf.10.
D.
Hilbert
, “Die grundlagen der physik (zweite mitteilungen)
,” Nachr. Ges. Wiss. Göttingen Math. Phys.
Kl
, 53
–76
(1917
).11.
L. S.
Abrams
, “Black holes: The legacy of Hilbert's error
,” Can. J. Phys.
67
, 919
–926
(1989
).12.
S.
Antoci
, “David Hilbert and the origin of the ‘Schwarzschild Solution’
,” in Meteorological and Geophysical Fluid Dynamics
, edited by W.
Schröder
, Science edition (Bremen
, 2004); e-print arXiv:physics/0310104 (2003
).13.
S.
Antoci
and D. E.
Liebscher
, “Reconsidering Schwarzschild's original solution
,” Astron. Nachr.
322
, 137
–142
(2001
).14.
15.
J. M. M.
Senovilla
, “The Schwarzschild solution: Corrections to the editorial note
,” Gen. Relativ. Gravitation
39
, 685
–693
(2007
).16.
Ø.
Grøn
, Lecture Notes on the General Theory of Relativity
(Springer
, New York
, 2009
).17.
A. J. S.
Hamilton
and J. P.
Lisle
, “The river model of black holes
,” Am. J. Phys.
76
, 519
–532
(2008
).18.
S.
Braeck
and Ø.
Grøn
, “A river model of space
,” Eur. Phys. J. Plus
128
, 24
(2013
).19.
J. V.
Narlikar
and T.
Padmanabhan
, “The Schwarzschild solution: Some conceptual difficulties
,” Found. Phys.
18
, 659
–668
(1988
).© 2016 American Association of Physics Teachers.
2016
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