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We prove that smooth asymptotically flat solutions to the Einstein vacuum equations which are assumed to be periodic in time, are in fact stationary in a neighborhood of infinity.
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Demetrios Christodoulou, The formation of black holes in general relativity , EMS Monographs in Mathematics, European Mathematical Society (EMS), Zürich, 2009
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1993
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Anthony Rizzi, Angular momentum in general relativity: a new definition , Phys. Rev. Lett. 81
1998
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by same author, The global initial value problem in general relativity , Proceedings of the 9th Marcel Grossmann meeting (Rome), World Sci. Publishing, 2002, pp. 44–54
2002
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Mihalis Dafermos, On “time-periodic” black-hole solutions to certain spherically symmetric Einstein-matter systems , Comm. Math. Phys. 238
2003
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Sergiu Klainerman and Francesco Nicolò, The evolution problem in general relativity , Progress in Mathematical Physics, vol. 25, Birkhäuser Boston, Inc., Boston, MA, 2003
2003
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by same author, Peeling properties of asymptotically flat solutions to the Einstein vacuum equations , Classical Quantum Gravity 20
2003
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Piotr T. Chruściel and Gregory J. Galloway, A poor man’s positive energy theorem , Classical Quantum Gravity 21
2004
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Piotr T. Chruściel, A poor man’s positive energy theorem. II. Null geodesics , Classical Quantum Gravity 21
2004
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Spyros Alexakis, Alexandru D. Ionescu, and Sergiu Klainerman, Hawking’s local rigidity theorem without analyticity , Geom. Funct. Anal. 20
2010
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J. Bičák, M. Scholtz, and P. Tod, On asymptotically flat solutions of Einstein’s equations periodic in time. I. Vacuum and electrovacuum solutions , Classical Quantum Gravity 27
2010
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by same author, On asymptotically flat solutions of Einstein’s equations periodic in time: II. Spacetimes with scalar-field sources , Classical Quantum Gravity 27
2010
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2013
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Simon Brendle, Rotational symmetry of self-similar solutions to the Ricci flow , Invent. Math. 194
2013
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by same author, On the local extension of Killing vector-fields in Ricci flat manifolds , J. Amer. Math. Soc. 26
2013
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2014
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Eric Poisson and Clifford Will, Gravity: Newtonian, post-newtonian, relativistic , Cambridge University Press, 2014
2014
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