Abstract
We conjecture an interpretation in terms of multipole moments of the obstructions to smoothness at infinity found for time-symmetric, conformally-flat initial data by Kroon (Commun Math Phys 244(1):133–156, 2004).
References
Bäckdahl, T.: Relating the Newman–Penrose constants to the Geroch–Hansen multipole moments. Class. Quantum Gravity 26, 175021 (2009)
Brill, D.R., Lindquist, R.W.: Interaction energy in geometrostatics. Phys. Rev. (2) 131, 471–476 (1963)
Dain, S., Kroon, J.A.V.: Conserved quantities in a black hole collision. Class. Quantum Gravity 19(4), 811–815 (2002)
Friedrich, H.: Gravitational fields near space-like and null infinity. J. Geom. Phys. 24(2), 83–163 (1998)
Friedrich, H., Kánnár, J.: Bondi-type systems near spacelike infinity and the calculation of the Newman–Penrose constants. J. Math. Phys. 41(4), 2195–2232 (2000)
Kroon, J.A.V.: A new class of obstructions to the smoothness of null infinity. Commun. Math. Phys. 244(1), 133–156 (2004)
Kroon, J.A.V.: A rigidity property of asymptotically simple spacetimes arising from conformally flat data. Commun. Math. Phys. 298(3), 673–706 (2010)
Misner, C.W.: The method of images in geometrostatics. Ann. Phys. 24, 102–117 (1963)
Newman, E.T., Penrose, R.: New conservation laws for zero rest-mass fields in asymptotically flat space-time. Proc. R. Soc. Lond. A 305, 175–204 (1968). doi:10.1098/rspa.1968.0112
Acknowledgments
We are grateful to Prof Valiente Kroon for discussions. JG is grateful to St. John’s College, Oxford for a Visiting Scholarship during which this work was carried out. He is also grateful to the Mathematical Institute in Oxford for their hospitality.
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Grant, J., Tod, P. Valiente Kroon’s obstructions to smoothness at infinity. Gen Relativ Gravit 47, 18 (2015). https://doi.org/10.1007/s10714-015-1861-0
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DOI: https://doi.org/10.1007/s10714-015-1861-0