Statement of spherically symmetric spacetimes
Front page of Arkiv för Matematik, Astronomi och Fysik where Jebsen's work was published
In general relativity , Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat . This means that the exterior solution (i.e. the spacetime outside of a spherical, nonrotating, gravitating body) must be given by the Schwarzschild metric . The converse of the theorem is true and is called Israel's theorem.[ 1] [ 2] The converse is not true in Newtonian gravity.[ 3] [ 4]
The theorem was proven in 1923 by George David Birkhoff (author of another famous Birkhoff theorem , the pointwise ergodic theorem which lies at the foundation of ergodic theory ). In 2005, Nils Voje Johansen, Finn Ravndal, Stanley Deser [citation needed ] stated that the theorem was allegedly published two years earlier by a little-known Norwegian physicist, Jørg Tofte Jebsen .[ 5] [ 6] [non-primary source needed ] [original research? ]
^ Israel, Werner (25 December 1967). "Event Horizons in Static Vacuum Space-Times" . Physical Review . 164 (5): 1776–1779. Bibcode :1967PhRv..164.1776I . doi :10.1103/PhysRev.164.1776 – via American Physical Society.
^ Straumann, Norbert (2013). General Relativity . Graduate Texts in Physics (2nd ed.). Springer Graduate texts in Physics. p. 429. Bibcode :2013gere.book.....S . doi :10.1007/978-94-007-5410-2 . ISBN 978-94-007-5409-6 .
^ Padmanabhan, Thanu (1996). Cosmology and Astrophysics through problems . Cambridge University Press. pp. 8, 150. ISBN 0-521-46783-7 .
^ Padmanabhan, Thanu (2015). "5". Sleeping beauties in theoretical physics: 26 Surprising insights . Lecture Notes in Physics. Vol. 895. Springer Lecture notes in Physics. pp. 57–63. Bibcode :2015sbtp.book.....P . doi :10.1007/978-3-319-13443-7 . ISBN 978-3-319-13442-0 . ISSN 0075-8450 .
^ J.T. Jebsen, Über die allgemeinen kugelsymmetrischen Lösungen der Einsteinschen Gravitationsgleichungen im Vakuum , Arkiv för matematik, astronomi och fysik, 15 (18), 1 - 9 (1921).
^ J.T. Jebsen, On the general symmetric solutions of Einstein's gravitational equations in vacuo , General Relativity and Cosmology 37 (12), 2253 - 2259 (2005).